The intersection of databases, logic, and artificial intelligence gave raise to deductive databases. Deductive database systems are database management systems built around a logical model of data, and their query languages allow expressing logical queries. A deductive database system includes procedures for defining deductive rules which can infer information (in the so-called intensional database) in addition to the facts loaded in the (so-called extensional) database. The logic model for deductive databases is closely related to the relational model and, in particular, with the domain relational calculus. Datalog is the most known deductive query language (which syntactically is a Prolog subset) where constructed terms are not allowed as other non-declarative constructs such as the cut.

Also following the relational model, relational database systems are well-known and widespread nowadays. Their formal query languages include relational algebra and relational calculi but, in practical systems, the de-facto and ANSI/ISO standard SQL is the language of choice of every relational database vendor. Whilst SQL and relational formal languages implement a limited form of logic, deductive database languages implement advanced forms of logic. Database languages are conceived to be specific-purpose rather than general-purpose languages, and are targeted at solving database queries. This is contrary to the case of Prolog, for instance, which is intended as a general-purpose language and its strengths must not be missed with those of Datalog.[1]

This manual describes DES, a deductive system which born from the need for teaching Datalog, and to have a simple, interactive, multiplatform, and affordable system (not necessarily efficient) for students, so that they can grasp the fundamental concepts behind a deductive database with Datalog, Relational Algebra, Tuple Relational Calculus, Domain Relational Calculus and SQL as query languages. All these query languages do operate over the same shared database. Pure and extended Datalog are supported. Also, SQL is supported with a reasonable coverage of the standard for teaching purposes, and nevertheless with some novel extensions. Supported (extended) relational algebra includes duplicates, outer joins and recursion. Both relational calculi and algebra are supported following the syntax of [Diet01]. Original development of DES was driven by the need for such a tool with features that no other deductive system (see related work in Section 1.5) enjoyed at the time.

This system is not targeted as a complete deductive database, so that it does not provide transactions, security, and other features present in current database systems, but it has grown in different areas. In particular, it has been added with several additions coming from research and practical applications. Its web page des.sourceforge.net contains many use cases of this system in teaching, researching and applications. Statistics also reveal it has become a widely-used system along time.

As a condensed description, the Datalog Educational System (DES) is a free, open-source, multiplatform, portable, Prolog-based implementation of a deductive database system. DES 6.8 is the current implementation, which enjoys Datalog, Relational Algebra, Tuple Relational Calculus, Domain Relational Calculus and SQL query languages, full recursive evaluation with memoization techniques, full-fledged arithmetic, stratified negation, duplicates and duplicate elimination, restricted predicates, integrity constraints, ODBC connections to external relational database management systems (RDBMSs), Datalog and SQL tracers, a textual API for external applications, and novel approaches to hypothetical SQL queries and Datalog rules, declarative debugging of Datalog queries and SQL views, test case generation for SQL views, modes, null values support, (tabled) outer join, aggregate predicates, and Fuzzy Datalog. The system is implemented on top of Prolog and it can be used from a Prolog interpreter running on any OS supported by such interpreter. Moreover, Windows, Linux and Mac OS X executables are also provided. The graphical and configurable IDE ACIDE [Saen07] has been specifically adapted to work with DES. An on-line front-end, DESweb, is also available at https://desweb.fdi.ucm.es.

As being said already, though DES was developed for teaching purposes, it has been used to develop some novel extensions as introduced next.

1.1 Some Novel Extensions in DES

A novel contribution implemented in this system is a declarative debugger of Datalog queries (with several approaches along time [CGS07, CGS08]), which relies on program semantics rather than on the computation mechanism. The debugging process is usually started when the user detects an unexpected answer to a query. By asking questions about the intended semantics, the debugger looks for incorrect program relations. The initial implementation was superseded by a recent one [CGS15a] for which more detailed user answers are allowed. See Section 5.10.

Also, a similar declarative approach has been used to implement an SQL declarative debugger, following [CGS11b]. There, possible erroneous objects correspond to views, and the debugger looks for erroneous views asking the user whether the result of a given view is as expected. In addition, trusted views are supported to prune the number of questions. This was extended to also include user information about wrong and missing tuples [CGS12a]. See Section 5.11.

Following the need for catching program errors when handling large amounts of data, we also include a test case generator for SQL correlated views [CGS10a]. Our tool can be used to generate positive, negative and both positive-negative test cases. See Section 0.

Decision support systems usually require assuming that some data are added to or removed from the current database to make deductions. In this line, DES introduces Hypothetical Datalog rules [Saen13] following [Bonn90] (Section 4.1.21). The novel concept of restricted predicates was introduced to provide support for negative assumptions in [Saen15] (Section 4.1.19). Hypothetical Datalog has been extended to the fuzzy setting, which opens new frontiers, such as modifying the semantics of fuzzy predicates with assumptions and fuzzy equations (Section 4.1.22). Also, limited domain predicates (tightly related to referential integrity constraints) are a new class of predicates with a finite meaning and that widen the queries on them, notably with non-closed negation calls (Section 4.1.20). Also, DES included a novel ASSUME clause for supporting hypothetical SQL queries and views [DES2.6], which was later changed first to make temporary relations (common table expressions - CTE) local to their contexts, and, second, to support negative assumptions in [DES3.7] (Section 4.2.9.4). For positive assumptions, ASSUME statements can be alternatively specified with a WITH clause with minor changes. Both are compiled into hypothetical Datalog rules. This makes a WITH encapsulation something natural in the realms of hypothetical Datalog.

For dealing with vagueness and imprecise information, Fuzzy logic programming has been applied to develop a fuzzy deductive database following [JS10] (Section 4.1.22), with Fuzzy Datalog as its query language.

Finally, as this system is targeted mainly towards teaching, we have provided an SQL semantic checker [Saen19] that raises warnings for, though syntactically correct SQL statements, possible incorrect ones, following the descriptions in [BG06]. Some errors include inconsistent conditions, lack of correlations in joins, unused tuple variables and the like.

1.2 Highlights for the Current Version

This version includes several upgrades mainly following needs from teaching. First, the SQL semantic analyzer covers a wider set of errors, including those that are more common in the classroom. It detects inconsistency by resorting to functional dependencies, which can uncover typical errors in ORDER BY, GROUP BY and DISTINCT, among others. This is useful not only for this system but also for an automatic judge such as LearnSQL, which leverages this information for student feedback. TAPI commands have been extended for such a use case. Second, the Datalog debugger has been upgraded by reducing the number of questions posed to the user. Also, existing debugger commands have been extended, in particular for its TAPI interface with other systems such as DESweb and its graphical Datalog debugger. Third, an experimental implementation of the semi-naïve differential optimization has been performed in the DES engine, allowing for a better performance of linear recursive predicates. Fourth, the new version 0.19 of the desktop Java application ACIDE has been bundled with DES, including: colour themes, file encoding, stability and usability improvements. Finally, various enhancements and new commands have been added to DES, along with several refinements. Section 9.1 includes the complete list of enhancements, changes and fixed bugs.

1.3 Features of DES in Short

· Free, multiplatform, portable, and open-source.

It can be used in any OS platform (Windows, Mac, Linux, ...), running on one of the supported Prolog interpreters. Moreover, portable executable applications are provided for Windows, Mac, and Linux.

· Interactive.

Based on a command line interpreter, you can play with DES by submitting queries, modifying the database, and processing commands.

· Five query languages and one shared database.

Datalog, SQL, Relational Algebra (RA), Tuple Relational Calculus (TRC), Domain Relational Calculus (DRC) and with access to the same database, either locally or externally stored (via ODBC connections and/or persistent predicates). Examine the equivalent Datalog code resulting from compiling other languages (/show_compilations on).

· Graphical user interface.

The Java-based ACIDE graphical environment (screenshot) has been configured for a specific connection to DES via the textual application programming interface (TAPI). It enjoys Datalog, SQL, RA, TRC, and DRC syntax highlighting, command buttons and interactive console, therefore easing its use by decreasing the number of keystrokes. In addition, an Emacs environment can be used.

· Online graphical user interface.

A basic online front-end DESweb is available at https://desweb.fdi.ucm.es, which can be used to try DES without installing it. Though it has many less features than the desktop Java front-end, it suffices for many needs in introductory courses.

· Database updates.

The database can be modified with both SQL DML and system commands.

· Null values and outer joins for three languages: Datalog, RA and SQL.

· Aggregates.

Typical aggregates as count, sum, min, max, avg, and times for SQL, RA and Datalog are included. Datalog aggregates include both aggregate predicates and aggregate functions (to be used in expressions). Grouping is supported and groups built on-the-fly with Datalog auto-grouping.

· Multisets.

Duplicates can be enabled or disabled in Datalog, RA and SQL processing. Discard duplicates with distinct operators.

· Hypothetical queries, views and rules in both Datalog and SQL.

Use the implication => in Datalog to build “what-if” applications in a business intelligence scenario. Use the novel ASSUME SQL clause to build hypothetical queries and views.

· Relational database access via ODBC.

ODBC sources of data can be seamlessly accessed. Connect DES to any DBMS supporting such connections (MySQL, MS Access, Oracle, ...)

· Persistency.

Predicates and relations can persist on external data sources via ODBC connections. Examine the SQL statements sent to the external database for persistent predicates (/show_sql on) .

· Modes.

An input mode warns users about the need to ground an argument in queries for an unsafe predicate.

· Highly configurable system on-the-fly.

Multiple features can be turned on and off and parameterized via commands.

· Stratified negation.

· Novel and extended SQL features include:

o Enforcement of functional dependencies.

o Hypothetical queries and views.

o DIVISION relational operation.

o Mutual and non-linear recursion

· Integrity constraints.

o Domain.

o Types.

o Primary key.

o Referential integrity.

o Functional dependency.

o Check constraints (user-defined).

o ... and several typical others.

Constraint checking can be enabled or disabled.

· Declarative debugging for Datalog and SQL.

Several declarative debuggers have been included along time in DES with the aim to debug towards intended semantics rather than procedural semantics. In addition, debugging can be used with existing external databases such as DB2, MySQL, PostgreSQL and Oracle.

· Test case generation for SQL views.

This prototype can be used for working with views over large tables and test them with the test cases, instead of with the actual tables.

· SQL database generator.

If you need SQL database instances for your benchmarks, generate them randomly at will.

· Full-fledged arithmetic.

Write arithmetical expressions with a wide set of arithmetical functions, operators and constants. Unlimited precision integer arithmetic is provided thanks to the underlying Prolog systems.

· Type system for Datalog, RA, TRC, DRC and SQL.

Whilst SQL require typed relations, Datalog predicates can be optionally typed to feeling the benefits of typed relations and type inference. Automatic type casting à la SQL in both settings can be enabled with the command /type_casting on. Explicit type casting is allowed with both an SQL function and a Datalog predicate.

· Syntax checking for all languages with informative error messages, and SQL semantic checking with informative warning messages.

· Connecting DES to the outside programmatic world.

DES can be plugged to a host system via standard streams using the textual application interface TAPI. DES can be connected to any development system supporting standard stream operations: Java, C++, VB, Python, Lua, ... Alternatively, use the underlying Prolog API's to generate executables or run-time systems with access to several languages (Java, C++, ...).

· Configurable look and feel.

o Pretty-printers for Datalog, RA and SQL.

o Single and multiline modes.

o Compact or separated display lines.

· Batch execution.

o Provide a file with DES inputs and log the results into another file. Several logs at a time are supported.

o Use batch commands and system variables for execution control.

· Fuzzy Datalog:

o Formal concepts supporting the fuzzy logic programming system Bousi~Prolog are translated into the deductive database system. Hypothetical reasoning has been also added

· Implementation includes:

o Source-to-source program transformations:

§ Safety. Safety transformations can be enabled to deal with some unsafe rules. Also, unsafe rules can be used to experiment in conjunction with modes.

§ Built-ins. Programs with outer join calls are transformed in order to be computed by the underlying tabled, fixpoint method.

o Tabling. Answer tables are used for implementing fixpoint and caching computations.

· Development mode.

This mode, when enabled, helps to understand how the system works (/development on). Transformed and compiled programs can be examined.

1.4 Future Enhancements

The following list (in order of importance) suggests some points to address for enhancing DES:

· Embed Datalog declarative debugging into the GUI ACIDE

· Disjunctive heads

· Information about cycles involving negation in the loaded program

· Complete algorithm for finding undefined information

· Constraints à la CLP (real, integer, enumerated types, strings)

If you find worthwhile for your application either some of the points above, or others not listed, please inform the author for trying to guide the implementation to the most demanded points.

1.5 Related Work

Origins of deductive databases can be found in automatic theorem proving and, later, in logic programming. Minker [Mink87] suggested that Green and Raphael [GR68] were the pioneers in discovering the relation between theorem proving and deduction in databases. They developed several question–answer systems using a version of the Robinson resolution principle [Robi65], showing that deduction can be systematically performed in a database environment. Other pioneer systems were MRPPS [MN82], DEDUCE–2 [Chan78] and DADM [KT81]. See Section 1.5 for references to other current deductive database systems.

There has been a high amount of work around deductive databases [RU95] (its interest delivered many workshops and conferences for this subject) which dealt to several systems. However, to the best of our knowledge, there is no a friendly system oriented to introducing deductive databases with several query languages to students. Nevertheless, on the one hand, we can comment some representative deductive database systems, and, on the other hand, some technological transfers to face real-world problems. Finally, we comment on existing systems with formal relational query languages.

1.5.1 Deductive Database Systems

This section collects and describes some deductive database systems developed so far:

· 4QL [MS11] (http://4ql.org/) is a recent development of a rule-based database query language with negation allowed in bodies and heads of rules, which is founded on a four-valued semantics with truth values: true, false, inconsistent and unknown. It provides means for a uniform treatment of Open and Local Closed World, other nonmonotonic/commonsense formalisms, including various variants of default reasoning, autoepistemic reasoning and other formalisms application-specific disambiguation of inconsistent information, including defeasible reasoning.

· Logic Query Language (LogiQL, http://www.logicblox.com/technology.html) is a declarative programming language derived from Datalog and developed by LogicBlox Inc. for their LogicBlox database engine. It has been designed including advanced techniques for query evaluation, concurrency management, network optimization, program analysis, declarative and reactive programming models.

· QL (https://semmle.com/ql) from Semmle is an object oriented Datalog-based language for read-only databases.

· ConceptBase [JJNS98] (http://conceptbase.sourceforge.net/) is a multi-user deductive object manager mainly intended for conceptual modelling and coordination in design environments. It is multiplatform, object-oriented, it enjoys integrity constraints, database updates and several other interesting features.

· The LDL project at MCC lead to the LDL++ system [AOTWZ03], a deductive database system with features such as X-Y stratification, set and complex terms, database updates and aggregates. It has been replaced by DeAL. The Deductive Application Language (DeAL) System (http://wis.cs.ucla.edu/deals/) is a next-generation Datalog system. The objective of the DeALS project is to extend the power of Datalog with advanced constructs with strong theoretical foundations. DeAL supports stratified aggregation, negation and XY-stratification. DeAL also supports new monotonic aggregates that can be used in recursive rules.

· DLV [FP96] (http://www.dlvsystem.com/dlv/) is a multiplatform system for disjunctive Datalog with constraints, true negation (à la Gelfond & Lifschitz) and queries. It includes the K planning system, a frontend for abductive diagnosis and Reiter's diagnosis, support for inheritance, and an SQL front-end which prototypes some novel SQL3 features. DLV^DB is an extension of DLV which provides interfaces with relational databases, taking advantage of their efficient implementations to speed-up computations.

· XSB [RSSWF97] (http://xsb.sourceforge.net/) is an extended Prolog system that can be used for deductive database applications. It enjoys a well–founded semantics for rules with negative literals in rule bodies and implements tabling mechanisms. It runs both on Unix/Linux and Windows operating systems. Datalog++ [Tang99] is a front-end for the XSB system.

· bddbddb [WL04] (http://bddbddb.sourceforge.net/) stands for BDD-Based Deductive DataBase. It is an implementation of Datalog that represents the relations using binary decision diagrams (BDD's). BDD's are a data structure that can efficiently represent large relations and provide efficient set operations. This allows bddbddb to efficiently represent and operate on extremely large relations.

· IRIS (Integrated Rule Inference System) [IRIS2008] is a Java implementation of an extensible reasoning engine for expressive rule-based languages provided as an API. Supports safe or un-safe Datalog with (locally) stratified or well-founded negation as failure, function symbols and bottom-up rule evaluation.

· Coral [RSSS94] is a deductive system with a declarative query language that supports general Horn clauses augmented with complex terms, set–grouping, aggregation, negation, and relations with tuples that contain (universally quantified) variables. It only runs under Unix platforms. There is also a version which allows object–oriented features, called Coral++ [SRSS93].

· FLORID (F-LOgic Reasoning In Databases) [KLW95] is a deductive object-oriented database system supporting F-Logic as data definition and query language. With the increasing interest in semistructured data, Florid has been extended for handling semistructured data in the context of Information Integration from the Semantic Web.

· The NAIL! project delivered a prototype with stratified negation, well–founded negation, and modularity stratified negation. Later, it added the language Glue, which is essentially single logical rules, with SQL statements wrapped in an imperative conventional language [PDR91, DMP93]. The approach of combining two languages is similar to the aforementioned Coral, which uses C++. It does not run on Windows platforms.

· Another deductive database following this combination of declarative and imperative languages is Rock&Roll [BPFWD94].

· ADITI 2 [VRK+91] is the last version of a deductive database system which uses the logic/functional programming language Mercury. It does not run on Windows platforms. There is no further development planned for Aditi.

See also the Datalog entry in Wikipedia (http://en.wikipedia.org/wiki/
Datalog).

1.5.2 Technological Transfers

Datalog has been extensively studied and is gaining a renowned interest thanks to their application to ontologies [FHH04], semantic web [CGL09], social networks [RS09], policy languages [BFG07], and even for optimization [GTZ05]. Companies as LogicBlox, Exeura, Semmle, DLVSYSTEM s.r.l. and Lixto embody Datalog-based deductive database technologies in the solutions they develop. The high-level expressivity of Datalog and its extensions has therefore been acknowledged as a powerful feature to deal with knowledge-based information.

The first commercial oriented deductive database system was the Smart Data System (SDS) and its declarative query language Declarative Reasoning (DECLARE) [KSSD94], with support for stratified negation and sets. Currently, XSB and DLV have been projected to spin-off companies and they develop deductive solutions to real-world problems.

1.5.3 Systems with Formal Relational Query Languages

Several implementations of formal relational query languages exist. One of the most known is WinRDBI (https://winrdbi.asu.edu/), a system including SQL, RA, and tuple and domain relational calculi (TRC and DRC, respectively). It includes a GUI and allows the definition of views in each language. This system is described in the book [Diet01] as a tool for learning formal languages. Another system is RAT (http://www.slinfo.una.ac.cr/rat/rat.html) which allows students to write statements in RA which are translated to SQL in order to verify the correct syntax for these expressions. RAT also allows connections to relational databases. Also, Chris Date and Hugh Darwen proposed a language called Tutorial D intended for use in teaching relational database theory, and its query language also draws on ISBL's ideas. Rel (http://reldb.org/) is an implementation of Tutorial D as a true relational database management system. LEAP (http://leap.sourceforge.net) is a relational database management system developed at the Oxford Brookes University (UK) which includes pure relational algebra. Relational Algebra System for Oracle and Microsoft SQL Server (http://www.cse.fau.edu/~marty/), developed by M.K. Solomon at the Florida Atlantic University (USA), features relational algebra with division operating on those existing RDBMS's.

2. Installation

This section explains how to download the available distributions (binary, sources, bundle with the graphical environment ACIDE), their contents, and hints for installations and configurations. If you do not want to install the system, you can use it via the online interface as explained in Section 2.3.

2.1 Downloading DES

You can download the system from the DES web page via the URL:

http://des.sourceforge.net/

There, you can find source distributions for several Prolog interpreters and operating systems, and executable distributions for MS Windows, Linux and Mac OS X.

2.1.1 Source Distribution

Under the source distribution, there are several versions depending on the Prolog interpreter you select to run DES: either SICStus Prolog [SICStus] or SWI-Prolog [SWI]. However, adapting the code in the file des_glue.pl, it could be ported to any other Prolog system. (See Section 5.22.3 for porting to unsupported systems.) We have tested DES under SICStus Prolog 4.4.1 and SWI–Prolog 7.6.4), and several operating systems (MS Windows XP/Vista/7/8/10, Ubuntu 10.04/12.04/16.04/18.04, and Mac OS X Snow Leopard/Sierra/High Sierra/El Capitán).

The source distribution comes in a single archive file containing the following:

· readmeDES<version>.txt. A quick installation guide and file release contents.

· des.pl. Core of DES, including Datalog processor.

· des_atts.pl. Attributed variables of the host Prolog system.

· des_commands.pl. System commands.

· des_common.pl. Common predicates to different files.

· des_dbigen.pl. SQL database instance random generator.

· des_dcg.pl. DCG expansion.

· des_dl_debug.pl. Datalog declarative debuggers.

· des_drc.pl. DRC processor.

· des_fuzzy.pl. Fuzzy Datalog subsystem.

· des_glue.pl. Contains particular code for the selected host Prolog system.

· des_help.pl. Help system.

· des_ini.pl. Initialization files.

· des_modes.pl. Modes for Datalog predicates and rules

· debug/des_pchr.pl. CHR program for debugging Datalog predicates

· des_persistence.pl. Persistence for Datalog predicates

· des_ra.pl. RA processor

· des_sql.pl. SQL processor

· des_sql_semantic.pl. SQL semantic checker

· des_sql_debug.pl. SQL declarative debugger

· des_tc.pl. Test case generator for SQL views

· des_trace.pl. Tracers for SQL and Datalog

· des_trc.pl. TRC processor

· des_types.pl. Type inferrer and checker for SQL, RA and Datalog

· doc/manualDES6.8.pdf. This manual

· doc/release_notes_history_DES.pdf. Releases notes history of previous versions

· examples/* Example files, some of them discussed in Section 6

· license/* A verbatim copy of the GNU Lesser General Public License for this distribution

· readmeDES6.8.txt. A quick installation guide and release notes

2.1.2 Executable Distribution

2.1.2.1 Windows

From the same URL above, you can download a Windows executable distribution in a single archive file containing the following:

· des.exe. Console executable file, intended to be started from a OS command shell, as depicted in the next figure:

· deswin.exe. Windows-application executable file, as depicted below:

Please note that the menu bar above is inherited from the host Prolog system and all its settings apply to such system, not to DES. However, there are some menu items that can be useful.

For the SICStus executable:

o File ® Save Transcript: Save the current window buffer to a file.

o Edit: For clipboard operations. "Automatic Copy" means that by selecting text, it will automatically copied to the clipboard.

o Keyboard shortcuts for clipboard are: Ctrl+Insert (Copy), and Shift+Insert (Paste)

o Settings ® Window Settings ® save lines: Number of lines in the window buffer.

o Settings ® Fonts: Select font and size

o Settings ® Save Settings: Save current settings for the next session.

For the SWI-Prolog executable:

o Edit: For clipboard operations. Automatic copy is always enabled.

o Keyboard shortcuts for clipboard are: Ctrl+C (Copy), and Ctrl+V (Paste)

o Settings ® Fonts: Select font and size

· *.dll. DLL libraries for the runtime system

· doc/manualDES6.8.pdf. This manual

· doc/release_notes_history_DES.pdf. Releases notes history of previous versions

· examples/*.dl. Example files which will be discussed in Section 6

· license/*. A verbatim copy of the GNU Lesser General Public License for this distribution

· readmeDES6.8.txt. A quick installation guide and release notes

2.1.2.2 DES+ACIDE Bundle

From the same URL above, you can download a bundle including both DES and the integrated development environment ACIDE, preconfigured to work with DES, and including the configuration file des.cnf for DES. The following figure is a snapshot of the system taken in a Windows 10 64 bit system:

2.1.2.3 Linux

From the same URL above, you can download a Linux executable distribution in a single archive file containing the following:

· des. Console executable file

· doc/manualDES6.8.pdf. This manual

· doc/release_notes_history_DES.pdf. Releases notes history of previous versions

· examples/*. Example files which will be discussed in Section 6

· license/*. A verbatim copy of the GNU Lesser General Public License for this distribution

· readmeDES6.8.txt. A quick installation guide and release notes

The following screenshot has been taken in Ubuntu 16.04 LTS 64bit:

An ACIDE bundle can be downloaded for Linux and including the configuration file des.cnf for DES. The following snapshot shows this running on Ubuntu 18.04 LTS 64bit:

2.1.2.4 Mac OS X

From the same URL above, you can download a Mac OS X executable distribution in a single archive file containing the following:

· des. Console executable file

· doc/manualDES6.8.pdf. This manual

· doc/release_notes_history_DES.pdf. Releases notes history of previous versions

· examples/*. Example files which will be discussed in Section 6

· license/*. A verbatim copy of the GNU Lesser General Public License for this distribution

· readmeDES6.8.txt. A quick installation guide and release notes

The following screenshot has been taken in Mac OS X High Sierra:

There is also an ACIDE bundle that can be downloaded for Mac OS X and including the configuration file des.cnf for DES. The following snapshot shows this running on Mac OS X High Sierra:

2.1.3 Other Interfaces

Other interfaces include Emacs and Crimson Editor.

2.1.3.1 Emacs

The first one is a contribution of Markus Triska and provides an integration of DES into Emacs. Once a Datalog file has been opened, you can consult it by pressing F1 and submit queries and commands from Emacs. This works at least in combination with SWI Prolog (it depends on the -s switch); other systems may require slight modifications. For its installation, copy des.el (as found in the contributions web page) to your home directory and add to your .emacs:

(load "~/des")

; adapt the following path as necessary:

(setq des-prolog-file "~/des/systems/swi/des.pl")

(add-to-list 'auto-mode-alist '("\\.dl$" . des-mode))

Restart Emacs, open an *.dl file to load it into a DES process (this currently only works with SWI-Prolog). If the region is active, F1 consults the text in the region. You can then interact with DES as on a terminal. Next figure shows DES running on Emacs:

2.1.3.2 Crimson Editor 3.70

The second interface run on Windows and is obtained by configuring Crimson Editor 3.70 to work with DES as an external tool whose output is captured by Crimson and input can be sent to DES. In Tools->Conf. User Tools, fill in the Preferences dialog box the path to the console executable in the Command input box. Other alternative is to start a Prolog system with an initial goal, as described in Section 2.2.1.2.

Then, in this case, pressing Ctrl+1 starts the DES console:

Crimson Editor also lets you to play with multiple editors, syntax highlighting, projects, and several useful tools. The input can be typed in the input box below or by clicking with the secondary mouse button to select Input.

2.2 Installing and Executing DES

Unpack the distribution archive file into the directory you want to install DES, which will be referred to as the distribution directory from now on. This allows you to run the system, whether you have a Prolog interpreter or not (in this latter case, you have to run the system either on MS Windows, Linux or Mac OS X).

Although there is no need for further setup and you can go directly to Section 2.2.3, you can also configure a more user-friendly way for system start. In this way, you can follow two routes depending on the operating system.

2.2.1 MS Windows

2.2.1.1 Executable Distribution

Simply create a shortcut in the desktop for executing the executable of your choice: either des.exe, or deswin.exe or des_acide.jar. The former is a console-based executable, the second is a windows-based executable, and the latter is a Java application that includes a call to the binary des.exe. Executables have been generated with SICStus Prolog and SWI-Prolog, so that all notes relating these systems in the rest of this document also apply to these executables. In addition, since it is a portable application, it needs to be started from its distribution directory, which means that the start-up directory of the shortcut must be the distribution directory.

2.2.1.2 Source Distribution

Perform the following steps:

1. Create a shortcut in the desktop for running the Prolog interpreter of your choice.

2. Modify the start directory in the “Properties” dialog box of the shortcut to the installation directory for DES. This allows the system to consult the needed files at startup.

3. Append the following options to the Prolog executable path, depending on the Prolog interpreter you use:

(a) SICStus Prolog: -l des.pl

(b) SWI-Prolog: -g "ensure_loaded(des)" (remove --win_app if present)

Another alternative is to write a batch file similar to the script file described in the next section.

2.2.2 Linux

2.2.2.1 Executable Distribution

You can create a script or an alias for executing the file des at the distribution root. This executable has been generated under SICStus Prolog, so that all SICStus notes in the rest of this document also apply to these executables. In addition, since it is a portable application, it needs to be started from its distribution directory.

2.2.2.2 Source Distribution

You can write a script for starting DES according to the selected Prolog interpreter, as follows:

(a) SICStus Prolog:

$SICSTUS –l des.pl

Provided that $SICSTUS is the variable which holds the absolute filename of the SICStus Prolog executable.

(b) SWI-Prolog:

$SWI -g "ensure_loaded(des)"

Provided that $SWI is the variable which holds the absolute filename of the SWI-Prolog executable.

2.2.3 Starting DES from a Prolog Interpreter

Besides the methods just described, you can start DES from a Prolog interpreter, whatever the OS and platform, first changing to the distribution directory, and then submitting:

?- [des].

Or better, if the system does support it:

?- ensure_loaded(des).

If the unlikely event that the system does not start by itself, then type:

?- start.

2.3 The Online Interface DESweb

An online system is available at https://desweb.fdi.ucm.es, where the following facade is presented:

If you do not have an account, you can login as a guest user (by clicking the first button Guest) This will open the following interface:

A user manual (User Guide.pdf) for this interface can be found in the panel DIRECTORY.

3. Getting Started

Whichever method you use to start DES (a script, batch file, or shortcut, as described in Section 2.2), you get the following:

*********************************************************
*                                                       *
*        DES: Datalog Educational System v.6.8         *
*                                                       *
* Type "/help" for help about commands                  *
*                                                       *
*                    Fernando Saenz-Perez (c) 2004-2025 *
*                                      DISIA FADoSS UCM *
*             Please send comments, questions, etc. to: *
*                                     fernan@sip.ucm.es *
*                                             Web site: *
*                           http://des.sourceforge.net/ *
*                                                       *
* This program comes with ABSOLUTELY NO WARRANTY, is    *
* free software, and you are welcome to redistribute it *
* under certain conditions. Type "/license" for details *
*********************************************************
DES>

Last line (DES>) is the DES system prompt, which allows you to write queries and statements in the languages Datalog, SQL, Relational Algebra (RA), Tuple Relational Calculus (TRC), and Domain Relational Calculus (DRC). Also, commands, temporary views and conjunctive queries (see next sections) can be inputs. If an error leads to an exit from DES and you have started from a Prolog interpreter, then you can write ”des.” (without the double quotes and with the dot) at the Prolog prompt to continue.

Though a query in any of the languages above can be submitted from such a prompt, there are currently six modes available which enable to use a concrete query interpreter for Datalog, SQL, RA, TRC, DRC and also Prolog (a special mode is used for fuzzy Datalog, c.f. Section 4.1.22). The Datalog mode is the default. Modes can be switched with the commands /datalog, /sql, /ra, /trc , /drc and /prolog. Note that commands always start with a slash (/). Anyway, if you are in a given mode, you can submit queries or goals to other interpreter simply by writing the query or goal after any of the previous commands. Also, if you are in Datalog mode, you can directly submit SQL, RA, TRC and DRC queries. But a Prolog query can only be submitted from either the Prolog mode or with the command /prolog.

Data are stored in an in-memory deductive database, including facts (the extensional database part) and rules (the intensional database part). All queries and goals, irrespective of the language, refer to this database. When an external database is opened (see Section 5.1), their tables and views are available and can be queried from Datalog, Prolog, RA, TRC, DRC and SQL. The term relation is interchangeably used with predicate, as are also the terms goal and query.

In contrast with interpreters of other systems, the default input mode is single-line, which means that the input will be processed after hitting the Intro key, which allows to omit the terminating character. Nonetheless, this mode can be switched to multi-line as described in Section 5.7 with the command /multiline on. However, even in this mode, commands remain as single-line inputs.

Terminal sessions in this manual correspond to actual sessions in a given DES version (not always the last one). Listings have been captured with compact listings enabled (with the command /multiline on).

3.1 Datalog Mode

In this mode, a query is sent to the Datalog processor. If it does not follow Datalog syntax, then it is sent, first, to the SQL processor (see Section 4.2) , second, to the RA processor (see Section 4.3), third, to the TRC processor (see Section 4.4), and fourth, to the DRC processor (see Section 4.4) should such query is written in any of these other query languages (See caveats in Section 3.7).

Commands (see Section 5.17) start with a slash (/) and are sent to the command processor. Commands can end with an optional dot. While in single-line mode, Datalog inputs can also end with an optional dot, the dot is required in multi-line mode. Datalog mode is the default mode and can be anyway enabled via the command /datalog.

The typical way of using the system is to write Datalog program files (with default extension .dl) and consulting them before submitting queries. Another alternative is to interactively assert program rules in the system prompt. Following the first alternative, you write the program in a text file, and then change to the path where the file is located by using the command /cd Path, where Path is the new directory (relative or absolute). Next, the command /consult FileName is used to consult the file FileName. Or, instead of changing the current directory, you can write the absolute or relative path to the file in the consult command. When writing a path, you can use interchangeably the backslash and the slash to delimit folders in Windows.

Provided that there are a number or example files in the directory examples at the distribution directory, and assuming that the current path is the distribution directory (as by default), one can use the following commands to consult the example file relop.dl:[2]

DES> /cd examples

DES> /consult relop.dl

Info: 18 rules consulted.

(where the default extension .dl can be omitted). Note that Datalog rules in files must end with a dot, in contrast to command prompt inputs, where the dot is optional in single-line input. Rules in a consulted file may span on multiple lines because a multi-line mode is enforced for such files.

Be warned that the command /consult erases the current database. If you want to keep already loaded facts and rules, use the command /reconsult instead.

Then, one can examine the contents of the database (see Section 6.1 for an explanation of the consulted program) via the command:

DES> /listing

a(a1).

a(a2).

a(a3).

b(a1).

b(b1).

b(b2).

c(a1,a1).

c(a1,b2).

c(a2,b2).

cartesian(X,Y) :-

a(X),

b(Y).

difference(X) :-

a(X),

not b(X).

full_join(X,Y) :-

fj(a(X),b(Y),X = Y).

inner_join(X) :-

a(X),

b(X).

left_join(X,Y) :-

lj(a(X),b(Y),X = Y).

projection(X) :-

c(X,Y).

right_join(X,Y) :-

rj(a(X),b(Y),X = Y).

selection(X) :-

a(X),

X = a2.

union(X) :-

a(X)

;

b(X).

Info: 18 rules listed.

Submitting a query is pretty easy:

DES> a(X)

{

a(a1),

a(a2),

a(a3)

}

Info: 3 tuples computed.

You can interactively add new rules with the command /assert, as in:

DES> /assert a(a4)

DES> a(X)

{

a(a1),

a(a2),

a(a3),

a(a4)

}

Info: 4 tuples computed.

Saving the current database, which may include such interactively added (or , if it is the case, deleted) tuples, is allowed with the command /save_ddb Filename, which saves in a plain file the Datalog rules located in the default in-memory database. Later, they can be restored with /restore_ddb Filename (this command is only an alias for /consult.) In the following session, the current database is stored, abolished (cleared), and finally restored. All the data, including the ones interactively added are eventually recovered:

DES> /save_ddb db.dl

DES> /abolish

DES> /restore_ddb db.dl

Info: 19 rules consulted.

DES> a(X)

{

a(a1),

a(a2),

a(a3),

a(a4)

}

Info: 4 tuples computed.

In addition to be able of saving the in-memory database, Section 5.2 explains how to make single predicates persistent in external SQL databases.

Another useful command is /list_et, which lists, in particular, the answers already computed. Following the last series of queries and commands above, we submit:

Answers:

{

a(a1),

a(a2),

a(a3),

a(a4)

}

Info: 4 tuples in the answer table.

Calls:

{

a(A)

}

Info: 1 tuple in the call table.

Here, we can see that the computed meaning of the queried relation is stored in an extension (answer) table, as well as the last call (cf. sections 5.22.1 and 5.22.2). The extension table keeps computed results unless either the database is changed (e.g., via /assert, /retract or /abolish commands), or a Datalog temporary view (see Section 4.1.6) is executed, or an SQL, RA, TRC or DRC query is executed, or the command /clear_et is submitted.

3.2 SQL Mode

In this mode, queries are sent to the SQL processor, whereas commands (cf. Section 5.17) are sent to the command processor. SQL queries can end with an optional semicolon in single-line mode. Multi-line mode requires the ending semicolon. SQL mode is enabled via the command /sql. Datalog, RA, TRC and DRC queries cannot be handled by this mode. Recall, however, that the Datalog mode is able to reckon SQL inputs and handle them without the need for turning on the SQL mode. The SQL mode is provided for a single language input (cf. Section 3.7) and to display language-specific syntax errors.

If we want to develop an analogous SQL example session to the Datalog example in the last section, we can submit the first inputs (also available in the file examples/relop.sql) listed below (the example is augmented to provide a first glance of SQL). Now, answer relations to SQL queries are denoted by the relation name answer. Also note that lines starting by -- are simply remarks as usual in SQL systems (though you can still use %). If you wish to automatically reproduce the following interactive session of inputs, you can type /process examples/relop.sql (notice that you must omit examples/ if you are in this directory already):

Info: Processing file 'relop.sql' ...

DES> -- Switch to SQL interpreter

DES> /sql

DES> -- Creating tables

DES> create or replace table a(a string);

DES> create or replace table b(b string);

DES> create or replace table c(a string,b string);

DES> -- Listing the database schema

DES> /dbschema

Info: Table(s):

* a(a:string)

* b(b:string)

* c(a:string,b:string)

Info: No views.

Info: No integrity constraints.

DES> -- Inserting values into tables

DES> insert into a values ('a1');

Info: 1 tuple inserted.

DES> insert into a values ('a2');

Info: 1 tuple inserted.

DES> insert into a values ('a3');

Info: 1 tuple inserted.

DES> insert into b values ('b1');

Info: 1 tuple inserted.

DES> insert into b values ('b2');

Info: 1 tuple inserted.

DES> insert into b values ('a1');

Info: 1 tuple inserted.

DES> insert into c values ('a1','b2');

Info: 1 tuple inserted.

DES> insert into c values ('a1','a1');

Info: 1 tuple inserted.

DES> insert into c values ('a2','b2');

Info: 1 tuple inserted.

DES> -- Testing the just inserted values

DES> select * from a;

answer(a.a) ->

{

answer(a1),

answer(a2),

answer(a3)

}

Info: 3 tuples computed.

DES> select * from b;

answer(b.b) ->

{

answer(a1),

answer(b1),

answer(b2)

}

Info: 3 tuples computed.

DES> select * from c;

answer(c.a, c.b) ->

{

answer(a1,a1),

answer(a1,b2),

answer(a2,b2)

}

Info: 3 tuples computed.

DES> -- Projection

DES> select a from c;

answer(c.a) ->

{

answer(a1),

answer(a2)

}

Info: 2 tuples computed.

DES> -- Selection

DES> select a from a where a='a2';

answer(a.a) ->

{

answer(a2)

}

Info: 1 tuple computed.

DES> -- Cartesian product

DES> select * from a,b;

answer(a.a, b.b) ->

{

answer(a1,a1),

answer(a1,b1),

answer(a1,b2),

answer(a2,a1),

answer(a2,b1),

answer(a2,b2),

answer(a3,a1),

answer(a3,b1),

answer(a3,b2)

}

Info: 9 tuples computed.

DES> -- Inner Join

DES> select a from a inner join b on a.a=b.b;

answer(a) ->

{

answer(a1)

}

Info: 1 tuple computed.

DES> -- Left Join

DES> select * from a left join b on a.a=b.b;

answer(a.a, b.b) ->

{

answer(a1,a1),

answer(a2,null),

answer(a3,null)

}

Info: 3 tuples computed.

DES> -- Right Join

DES> select * from a right join b on a.a=b.b;

answer(a.a, b.b) ->

{

answer(a1,a1),

answer(null,b1),

answer(null,b2)

}

Info: 3 tuples computed.

DES> -- Full Join

DES> select * from a full join b on a.a=b.b;

answer(a.a, b.b) ->

{

answer(a1,a1),

answer(a1,null),

answer(a2,null),

answer(a3,null),

answer(null,a1),

answer(null,b1),

answer(null,b2)

}

Info: 7 tuples computed.

DES> -- Union

DES> select * from a union select * from b;

answer(a.a) ->

{

answer(a1),

answer(a2),

answer(a3),

answer(b1),

answer(b2)

}

Info: 5 tuples computed.

DES> -- Difference

DES> select * from a except select * from b;

answer(a.a) ->

{

answer(a2),

answer(a3)

}

Info: 2 tuples computed.

Info: Batch file processed.

Duplicates are disabled by default, i.e., answers are set-oriented. But they can be enabled as well, which is useful in Datalog, SQL and RA queries (see Section 4.1.9). For instance:

DES> /duplicates on

Info: Duplicates are on.

DES> select a from c;

answer(c.a:string) ->

{

projection(a1),

projection(a2)

}

Info: 3 tuples computed.

You can see the equivalent Datalog rules for a given query by enabling compilation listings as in:

DES> /show_compilations on

DES> select * from a union all select * from b;

Info: SQL statement compiled to:

answer(A) :-

a(A).

answer(A) :-

b(A).

answer(a.a:string) ->

{

answer(a1),

answer(a2),

answer(a3),

answer(b1),

answer(b2)

}

Info: 5 tuples computed.

3.3 Relational Algebra Mode

In this mode, queries are sent to the Relational Algebra (RA) processor, whereas commands (cf. Section 5.17) are sent to the command processor. RA queries can end with an optional semicolon in single-line mode. Multi-line mode requires the ending semicolon. RA mode is enabled via the command /ra. Datalog, SQL, TRC and DRC queries cannot be handled by this mode. Recall, however, that the Datalog mode is able to reckon SQL, RA, TRC and DRC inputs and handle them without the need for turning on the RA mode. The relational algebra mode is provided for a single language input (cf. Section 3.7) and to display language-specific syntax errors.

If we want to develop an analogous RA example session to the former examples, we can submit the first inputs (also available in the file examples/relop.ra) listed below. Now, answer relations to RA queries are denoted by the relation name answer. As before, lines starting by either % or -- are simply remarks. If you wish to automatically reproduce the following interactive session of inputs, you can type /process examples/relop.ra (notice that you must omit examples/ if the current directory is this one already):

DES> % Creating tables

% Table creation and tuple insertion are omitted here because they are the same as in the SQL session in previous Section 3.2.

DES-RA> % Testing the just inserted values

DES-RA> select true (a);

answer(a.a:string) ->

{

answer(a1),

answer(a2),

answer(a3)

}

Info: 3 tuples computed.

DES-RA> select true (b);

answer(b.b:string) ->

{

answer(a1),

answer(b1),

answer(b2)

}

Info: 3 tuples computed.

DES-RA> select true (c);

answer(c.a:string,c.b:string) ->

{

answer(a1,a1),

answer(a1,b2),

answer(a2,b2)

}

Info: 3 tuples computed.

DES-RA> % Projection

DES-RA> project a (c);

answer(c.a:string) ->

{

answer(a1),

answer(a2)

}

Info: 2 tuples computed.

DES-RA> % Selection

DES-RA> select a='a2' (a);

answer(a.a:string) ->

{

answer(a2)

}

Info: 1 tuple computed.

DES-RA> % Cartesian product

DES-RA> a product b;

answer(a.a:string,b.b:string) ->

{

answer(a1,a1),

answer(a1,b1),

answer(a1,b2),

answer(a2,a1),

answer(a2,b1),

answer(a2,b2),

answer(a3,a1),

answer(a3,b1),

answer(a3,b2)

}

Info: 9 tuples computed.

DES-RA> % Union

DES-RA> a union b;

answer(a.a:string) ->

{

answer(a1),

answer(a2),

answer(a3),

answer(b1),

answer(b2)

}

Info: 5 tuples computed.

DES-RA> % Difference

DES-RA> a difference b;

answer(a.a:string) ->

{

answer(a2),

answer(a3)

}

Info: 2 tuples computed.

DES-RA> % Intersection

DES-RA> a intersect b;

answer(a.a:string) ->

{

answer(a1)

}

Info: 1 tuple computed.

DES-RA> % Theta Join

DES-RA> select a.a=b.b (a product b);

answer(a.a:string,b.b:string) ->

{

answer(a1,a1)

}

Info: 1 tuple computed.

DES-RA> a zjoin a.a=b.b b;

answer(a.a:string,b.b:string) ->

{

answer(a1,a1)

}

Info: 1 tuple computed.

DES-RA> % Natural Inner Join

DES-RA> a njoin c;

answer(a.a:string,c.b:string) ->

{

answer(a1,a1),

answer(a1,b2),

answer(a2,b2)

}

Info: 3 tuples computed.

DES-RA> % Left Outer Join

DES-RA> a ljoin a.a=b.b b;

answer(a.a:string,b.b:string) ->

{

answer(a1,a1),

answer(a2,null),

answer(a3,null)

}

Info: 3 tuples computed.

DES-RA> % Right Outer Join

DES-RA> a rjoin a.a=b.b b;

answer(a.a:string,b.b:string) ->

{

answer(a1,a1),

answer(null,b1),

answer(null,b2)

}

Info: 3 tuples computed.

DES-RA> % Full Outer Join

DES-RA> a fjoin a.a=b.b b;

answer(a.a:string,b.b:string) ->

{

answer(a1,a1),

answer(a2,null),

answer(a3,null),

answer(null,b1),

answer(null,b2)

}

Info: 5 tuples computed.

DES-RA> % Grouping

DES-RA> group_by a a,count(*) true (c);

answer(c.a:string,$a3:int) ->

{

answer(a1,2),

answer(a2,1)

}

Info: 2 tuples computed.

DES-RA> % Renaming

DES-RA> select a1.a<a2.a ((rename a1(a) (a)) product (rename a2(a) (a)));

answer(a1.a:string,a2.a:string) ->

{

answer(a1,a2),

answer(a1,a3),

answer(a2,a3)

}

Info: 3 tuples computed.

DES-RA> % Duplicate elimination

DES-RA> /duplicates off

Info: Duplicates are already disabled.

DES-RA> project a (c);

answer(c.a:string) ->

{

answer(a1),

answer(a2)

}

Info: 2 tuples computed.

DES-RA> /duplicates on

DES-RA> project a (c);

answer(c.a:string) ->

{

answer(a1),

answer(a2)

}

Info: 3 tuples computed.

DES-RA> distinct (project a (c));

answer(c.a:string) ->

{

answer(a1),

answer(a2)

}

Info: 3 tuples computed.

As well, you can see both the equivalent Datalog rules and SQL statement for a given RA query by enabling compilation listings and SQL display as in:

DES> /show_compilations on

DES> /show_sql on

DES> a union b

Info: Equivalent SQL query:

(

SELECT ALL *

FROM

)

UNION ALL

(

SELECT ALL *

FROM

);

Info: RA expression compiled to:

answer(A) :-

a(A).

answer(A) :-

b(A).

answer(a.a:string) ->

{

answer(a1),

answer(a2),

answer(a3),

answer(b1),

answer(b2)

}

Info: 5 tuples computed.

3.4 Tuple Relational Calculus Mode

In this mode, queries are sent to the Tuple Relational Calculus (TRC) processor, whereas commands (cf. Section 5.17) are sent to the command processor. TRC queries can end with an optional semicolon in single-line mode. Multi-line mode requires the ending semicolon. TRC mode is enabled via the command /trc. Datalog, SQL, RA and DRC queries cannot be handled by this mode. Recall, however, that the Datalog mode is able to reckon SQL, RA, TRC and DRC inputs and handle them without the need for turning on the TRC mode. The tuple relational calculus mode is provided for a single language input (cf. Section 3.7) and to display language-specific syntax errors.

If we want to develop an analogous TRC example session to the former examples, we can submit the first inputs (also available in the file examples/relop.trc) listed below. Now, answer relations to TRC queries are denoted by the relation name answer. As before, lines starting by either % or -- are simply remarks. If you wish to automatically reproduce the following interactive session of inputs, you can type /process examples/relop.trc (notice that you must omit examples/ if you are in this directory already):

DES> % Creating tables

% Table creation and tuple insertion are omitted here because they are the same as in the SQL session in previous Section 3.2.

DES-TRC> % Testing the just inserted values

DES-TRC> {A|a(A)};

Info: TRC statement compiled to:

answer(A) :-

a(A).

answer(a:string) ->

{

answer(a1),

answer(a2),

answer(a3)

}

Info: 3 tuples computed.

DES-TRC> {B|b(B)};

Info: TRC statement compiled to:

answer(B) :-

b(B).

answer(b:string) ->

{

answer(a1),

answer(b1),

answer(b2)

}

Info: 3 tuples computed.

DES-TRC> {C|c(C)};

Info: TRC statement compiled to:

answer(A,B) :-

c(A,B).

answer(a:string,b:string) ->

{

answer(a1,a1),

answer(a1,b2),

answer(a2,b2)

}

Info: 3 tuples computed.

DES-TRC> % Projection

DES-TRC> {C.a|c(C)};

Info: TRC statement compiled to:

answer(A) :-

c(A,_B).

answer(a:string) ->

{

answer(a1),

answer(a2)

}

Info: 2 tuples computed.

DES-TRC> % Selection

DES-TRC> {A|a(A) and A.a='a2'};

Info: TRC statement compiled to:

answer(A) :-

a(A),

A=a2.

answer(a:string) ->

{

answer(a2)

}

Info: 1 tuple computed.

DES-TRC> % Cartesian product

DES-TRC> {A,B|a(A) and b(B)};

Info: TRC statement compiled to:

answer(A,B) :-

a(A),

b(B).

answer(a:string,b:string) ->

{

answer(a1,a1),

answer(a1,b1),

answer(a1,b2),

answer(a2,a1),

answer(a2,b1),

answer(a2,b2),

answer(a3,a1),

answer(a3,b1),

answer(a3,b2)

}

Info: 9 tuples computed.

DES-TRC> % Union

DES-TRC> {X|a(X) or b(X)};

Info: TRC statement compiled to:

answer(A) :-

a(A)

;

b(A).

answer(a:string) ->

{

answer(a1),

answer(a2),

answer(a3),

answer(b1),

answer(b2)

}

Info: 5 tuples computed.

DES-TRC> % Difference

DES-TRC> {X|a(X) and not b(X)};

Info: TRC statement compiled to:

answer(A) :-

a(A),

not b(A).

answer(a:string) ->

{

answer(a2),

answer(a3)

}

Info: 2 tuples computed.

DES-TRC> % Intersection

DES-TRC> {X|a(X) and b(X)};

Info: TRC statement compiled to:

answer(A) :-

a(A),

b(A).

answer(a:string) ->

{

answer(a1)

}

Info: 1 tuple computed.

DES-TRC> % Theta Join

DES-TRC> {A,B|a(A) and b(B) and A.a=B.b};

Info: TRC statement compiled to:

answer(A,B) :-

a(A),

b(B),

A=B.

answer(a:string,b:string) ->

{

answer(a1,a1)

}

Info: 1 tuple computed.

DES-TRC> % Natural Inner Join

DES-TRC> {A.a,C.b|a(A) and c(C) and A.a=C.a};

Info: TRC statement compiled to:

answer(A,B) :-

a(A),

c(_C_a,B),

A=_C_a.

answer(a:string,b:string) ->

{

answer(a1,a1),

answer(a1,b2),

answer(a2,b2)

}

Info: 3 tuples computed.

3.5 Domain Relational Calculus Mode

In this mode, queries are sent to the Domain Relational Calculus (DRC) processor, whereas commands (cf. Section 5.17) are sent to the command processor. DRC queries can end with an optional semicolon in single-line mode. Multi-line mode requires the ending semicolon. DRC mode is enabled via the command /drc. Datalog, SQL, RA and TRC queries cannot be handled by this mode. Recall, however, that the Datalog mode is able to reckon SQL, RA, TRC and DRC inputs and handle them without the need for turning on the DRC mode. The tuple relational calculus mode is provided for a single language input (cf. Section 3.7) and to display language-specific syntax errors.

If we want to develop an analogous DRC example session to the former examples, we can submit the first inputs (also available in the file examples/relop.drc) listed below. Now, answer relations to TRC queries are denoted by the relation name answer. As before, lines starting by either % or -- are simply remarks. If you wish to automatically reproduce the following interactive session of inputs, you can type /process examples/relop.drc (notice that you must omit examples/ if you are in this directory already):

DES> % Creating tables

% Table creation and tuple insertion are omitted here because they are the same as in the SQL session in previous Section 3.2.

DES-DRC> % Testing the just inserted values

DES-DRC> {A|a(A)};

Info: DRC statement compiled to:

answer(A) :-

a(A).

answer(a:string) ->

{

answer(a1),

answer(a2),

answer(a3)

}

Info: 3 tuples computed.

DES-DRC> {B|b(B)};

Info: DRC statement compiled to:

answer(B) :-

b(B).

answer(b:string) ->

{

answer(a1),

answer(b1),

answer(b2)

}

Info: 3 tuples computed.

DES-DRC> {A,B|c(A,B)};

Info: DRC statement compiled to:

answer(A,B) :-

c(A,B).

answer(a:string,b:string) ->

{

answer(a1,a1),

answer(a1,b2),

answer(a2,b2)

}

Info: 3 tuples computed.

DES-DRC> % Projection

DES-DRC> {A|c(A,_)};

Info: DRC statement compiled to:

answer(A) :-

c(A,_).

answer(a:string) ->

{

answer(a1),

answer(a2)

}

Info: 2 tuples computed.

DES-DRC> % Selection

DES-DRC> {A|a(A) and A>='a2'};

Info: DRC statement compiled to:

answer(A) :-

a(A),

A>=a2.

answer(a:string) ->

{

answer(a2),

answer(a3)

}

Info: 2 tuples computed.

DES-DRC> % Cartesian product

DES-DRC> {A,B|a(A) and b(B)};

Info: DRC statement compiled to:

answer(A,B) :-

a(A),

b(B).

answer(a:string,b:string) ->

{

answer(a1,a1),

answer(a1,b1),

answer(a1,b2),

answer(a2,a1),

answer(a2,b1),

answer(a2,b2),

answer(a3,a1),

answer(a3,b1),

answer(a3,b2)

}

Info: 9 tuples computed.

DES-DRC> % Union

DES-DRC> {A|a(A) or b(A)};

Info: DRC statement compiled to:

answer(A) :-

a(A)

;

b(A).

answer(a:string) ->

{

answer(a1),

answer(a2),

answer(a3),

answer(b1),

answer(b2)

}

Info: 5 tuples computed.

DES-DRC> % Difference

DES-DRC> {A|a(A) and not b(A)};

Info: DRC statement compiled to:

answer(A) :-

a(A),

not b(A).

answer(a:string) ->

{

answer(a2),

answer(a3)

}

Info: 2 tuples computed.

DES-DRC> % Intersection

DES-DRC> {A|a(A) and b(A)};

Info: DRC statement compiled to:

answer(A) :-

a(A),

b(A).

answer(a:string) ->

{

answer(a1)

}

Info: 1 tuple computed.

DES-DRC> % Theta Join

DES-DRC> {A,B|a(A) and b(B) and A>=B};

Info: DRC statement compiled to:

answer(A,B) :-

a(A),

b(B),

A>=B.

answer(a:string,b:string) ->

{

answer(a1,a1),

answer(a2,a1),

answer(a3,a1)

}

Info: 3 tuples computed.

DES-DRC> % Natural Inner Join

DES-DRC> {A,B|a(A) and c(A,B)};

Info: DRC statement compiled to:

answer(A,B) :-

a(A),

c(A,B).

answer(a:string,b:string) ->

{

answer(a1,a1),

answer(a1,b2),

answer(a2,b2)

}

Info: 3 tuples computed.

3.6 Prolog Mode

This mode is enabled via the command /prolog and goals are sent to the Prolog processor. This is the only language mode in which Prolog inputs can be processed. Assuming that the file relop.dl has been already consulted, let’s consider the following example:

DES-Prolog> projection(X)

projection(a1)

? (type ; for more solutions, <Intro> to continue) ;

projection(a1)

? (type ; for more solutions, <Intro> to continue) ;

projection(a2)

? (type ; for more solutions, <Intro> to continue) ;

DES-Prolog> /datalog projection(X)

{

projection(a1),

projection(a2)

}

Info: 2 tuples computed.

The execution of this goal allows to noting the basic differences between Prolog and Datalog engines. First, the former searches for solutions, one-by-one, that satisfy the goal projection(X). The latter gives the whole meaning[3] of the user-defined relation projection with the query projection(X) at a time. And, second, note the default set-oriented behaviour of the Datalog engine, which discards duplicates in the answer.

3.7 Caveats

Since the Datalog mode prompt accepts Datalog, SQL, RA, TRC and DRC queries, a given query can be interpreted in more than one language. Let's consider the following system session, in which a table is created and an RA query is submitted:

DES> create table t(a int)

DES> insert into t values(1)

DES> distinct (t)

Info: Processing:

answer :-

distinct(t).

Warning: Undefined predicate(s): [t/0]

{

}

Info: 0 tuples computed.

Here, we get a missing answer as we’d expect the tuple t(1) in the result set. However, this query has been processed as a Datalog one, where distinct (t) computes the different tuples for the relation t/0 (which is not defined in this system session). To overcome such situations, simply precede the query by the language selection command, as follows:

DES> /ra distinct (t)

answer(t.a:int) ->

{

answer(1)

}

Info: 1 tuple computed.

Alternatively, switch to the other query processor:

DES> /ra

DES-RA> distinct (t)

Another example is the division operator:

DES> create table t(a int, b int)

DES> create table s(a int)

DES> t division s

Error: Incompatible schemas in division operation: t division s

DES> /ra t division s

answer(t.b:int) ->

{

}

Info: 0 tuples computed.

As the query t division s is firstly interpreted as a Datalog query, both t and s are assumed to be predicates of arity 0, which obviously are not compatible for the operation. Prepending the command /ra forces the system to interpret the input as an RA query, providing the expected result.

3.8 Getting Help

You can get useful information with the following commands:

· /help. Shows the list of available commands, which are explained in Section 5.17.

· /help Keyword. To request help on a given keyword (command or built-in).

· /builtins. Shows the list of built-ins, which are explained in Section 4.7.

If the system can find appropriate names for those which are not valid, it automatically informs the user. In particular, if a given predicate does not exist but some similar names are found (modulo misspelling), they are hinted to the user. Another hints include alternative column, table and view names are for SQL DML and DDL queries and Datalog queries. This is somewhat related to SWI-Prolog's DWIM (Do What I Mean).

Also, visit the URL for last information:

http://des.sourceforge.net/

Finally, you can contact the author via the e-mail address:

fernan@sip.ucm.es

4. Query Languages

DES has evolved from a quite simple Datalog interpreter to its current state, a system relying on a deductive database engine which can be queried with either Datalog, SQL, RA, TRC and DRC languages. In addition, a Prolog interface is also provided in order to highlight the differences between Datalog and Prolog systems. Since DES is intended to students, it has no full-blown features of either state-of-the-art Prolog, or Datalog or SQL-based systems. However, it has many features that make it appealing as an educational tool, along with the novel implementations of declarative debugging (sections 5.10 and 5.11) and the test case generator (Section 0). In this section, we describe its four query languages: Datalog, SQL, RA, and Prolog.

The database is shared by all the query languages, so that queries or goals can refer to any object defined using any language. However, there are some dependent issues that must be taken into account. For instance, once a Datalog fact is loaded into the database, the relation it defines can be queried in Datalog. But, if one wants to access this relation from either SQL, or RA, or TRC or DRC, two alternatives are provided: 1) Define the same relation in SQL via a create table statement (Section 4.2.4.1), and 2) Declare types for the table (Section 4.1.18.1). This particular issue comes from the fact that Datalog relations have unnamed attributes, and a positional reference based on variables (instead of indexes) is used for accessing those relations. In turn, SQL, RA, TRC and DRC use a notational syntax, giving names to relation arguments. To illustrate the first alternative, let’s consider the following session:

DES> /assert t(1)

DES> t(X)

{

t(1)

}

Info: 1 tuple computed.

DES> select * from t

Error: Unknown table or view "t"

DES> create table t(a int);

DES> select * from t;

answer(t.a:int) ->

{

answer(1)

}

Info: 1 tuple computed.

The error above reflects that t is not a known object for SQL statements in the database schema.

Following the second alternative to access a Datalog relation from SQL:

DES> /assert t(1)

DES> :-type(t,[a:int])

DES> select * from t

answer(t.a:int) ->

{

answer(1)

}

Info: 1 tuple computed.

4.1 Datalog

Since Datalog stems from Prolog, we have adopted almost all the Prolog syntax conventions for writing Datalog programs (the reader is assumed to have basic knowledge about Prolog). Syntax follows Prolog ISO standard [ISO00] (considering Datalog syntax as a subset of Prolog). We allow (recursive) Datalog programs with stratified negation [Ullm95], i.e., normal logic programs without function symbols. Stratification is imposed to ensure a clear semantics when negation is involved, and function symbols are not allowed in order to guarantee termination of queries, a natural requirement with respect to a (relational) database user who is not able to deal with compound data.

Commands are somewhat different for Prolog programmers as they are accustomed to (see Section 5.17). Also, exceptions are noted when necessary.

4.1.1 Syntax

Definitions for Datalog mainly come from the field of Logic Programming, following [Lloyd87], referring the reader to this book for a more general presentation of Logic Programming. Next, some definitions for understanding the syntax of programs, queries and views are introduced.

· Numbers. Integers and float numbers are allowed. A number is a float whenever the number contains a dot (.) between two digits. The range depends on the Prolog platform being used. Negative numbers are identified by a preceding minus (-), as usual.

Scientific notation is supported, as usually, in E-notation as: mEn, where m is a number (maybe including a fractional part), and n is an integer, which may start with + or – (but it is not required). The base (10) can be represented with either E or e.

If the fractional dot is included in a number, there must be (at least) a digit to its left and another to its right.

Examples of numbers are 1, 1.1, -1.0, 1.2E34, 1.2E+34, and 0.2e-34.

Note that -1., +1, .1, 1.E23, and 1E2.3 are not valid numbers. A plus sign is not part of a positive number; however, both a plus and a minus sign can be used as a prefix unary operator in arithmetical expressions (cf. Section 4.7.4.1) and also following the symbol E in scientific notation, as already seen.

· Constants. A constant can be:

o A number (either integer or float).

o Any sequence of alphanumeric characters (including the underscore _), starting with a lowercase letter.

o Any sequence of characters delimited by single quotes. If the sequence contains a single quote, it can be either escaped or to be included as part of the constant.

Examples of alphanumeric constants are foo, foo_foo, 'foo foo', '2*3', 'X', 'foo''s', and 'foo\'s'. The last two represent the same constant (foo's).

· Variables. Variables are written with alphanumeric characters, and alternatively start with either an uppercase or with an underscore (_). Anonymous variables are also allowed, which are denoted with a single underscore. Each occurrence of an anonymous variable is considered different from any other variable (either anonymous or not). For instance, in the rule a :- b(_), c(_), goals do not share variables. Any variable starting with an underscore (either anonymous or not) is removed from the answer to a query (cf. Section 4.1.7). Also, they are not taken into account for singleton variable warnings (cf. Section 5.5.5).

Examples of variables are: X, _X, _var, and _.

· Unknowns. Unknowns are represented as null values and are written alternatively as both null and '$NULL'(ID), where ID is a unique global identifier. The first form is used for normal users, whilst the second one is intended for development uses (cf. /development command in Section ).

· Operators.

o Infix, as addition (e.g., 1+2).

o Prefix, as bitwise negation (e.g., \1).

Available operators (comparisons, arithmetic, string, and date/time) can be consulted in Section 4.7.

· Terms. Terms can be:

o Non-compound. Variables or constants.

o Compound. As in Prolog, they have the form t(t1, ..., tn), where t is a function symbol (functor), and ti (1 ≤ i ≤ n) are terms. Compound terms are very restricted in DES and can only be of the following forms:

§ '$NULL'(ID) for internally representing nulls.

§ Date/time data values, with the form explained in Section 4.1.18.1.

§ Predicate patterns of the form Name/Arity for fuzzy proximity equations (see Section 4.1.22.1).

Examples of terms are: r(p), and p(X,Y), and X > Y.

· Expressions. An expression is constructed with constants, operators, and functions. An expression occurring in any comparison operator is evaluated before applying the comparison. There is one exception: the operator \== (intended for syntactic disequality) which do not evaluate their arguments. Expressions can be of different data types (integer, string, ...).

Examples of expressions are:

1/2, 10*rand, length('Hello'), year(current_date) and 'Hello, ' || 'world'

Refer to Section 4.7 for available built-in functions.

· Atoms. An atom has the form a(t1, ..., tn), where a is a predicate (relation) symbol, and ti (1 ≤ i ≤ n) are terms. If i is 0, then the atom is simply written as a.

Positive, ground atoms are used to build the Herbrand universe.

There are several built-in predicates: is (for evaluating arithmetical expressions), arithmetic functions, (infix and prefix) operators and constants, and comparison operators. Comparison operators are infix, as “less-than”. For example, 1 < 2 is a positive atom built from an infix built-in comparison operator (see Section 4.7.1).

Examples of atoms are: p, r(a,X), 1 < 2, and X is 1+2.

Note that p(1+2) and p(t(a)) are not valid atoms.

· Restricted atoms. A restricted atom has the form -A, where A is an atom built with no built-in.

· Conditions. A condition is a Boolean expression containing conjunctions (,/2), disjunctions (;/2), built-in comparison operators, constants and variables.

Examples of conditions are:

X>1, X=Y, (X>Y,Y>Z), (X=<Y;Z<0), and log(X)<sin(pi/2)

Note that the last example is valid because the arguments of the disequality are evaluable arithmetic expressions, and it can be solved whenever the rule where it occurs is safe (cf. Section 5.3).

· Relation functions. A function has the form f(a1, …, an), where f is a function name, ai are its arguments, and maps to a relation. Only built-in functions are allowed. The current provision of built-in relation functions includes, among others:

o lj(a1,a2,a3). Compute the left outer join of the relations a1 (left relation) and a2 (right relation), committing the condition (Boolean expression) a3 (join condition).

o order_by(a1,a2). Return the meaning of a1 (left relation) and a2 is the list [E1,..,En], where Ei are ordering expressions (non-declarative function).

o distinct(a1,a2). Return the distinct tuples in the meaning of a2 with respect to the tuple of arguments defined in a2 as the list [V1,..,Vn], where Vi are variables.

Note that outer join functions can be nested (see Section 4.1.11).

· Literals. Literals can be:

o Positive. An atom or restricted atom.

o Negative. A negated body of the form not Body, where Body is a body (cf. next section). Negative literals are used to express the negation (not truly classical negation) of a relation either as a query or as a part of a rule body.

o Disjunctive. A disjunctive literal is of the form l;r , where l and r are literals.

o Divided. A divided literal is of the form l division r, where l and r are literals.

Examples of literals are:

-p

r(a,X)

not q(X,b)

not (a;b)

r(a,X);not q(X,b)

1 < 2

t(X,Y) division s(Y)

X is 1+2

A literal can occur in rule bodies, queries, and view bodies.

Syntax of built-ins is explained in their corresponding forthcoming sections.

4.1.2 Rules

Datalog rules have the form head :- body, or simply head. In this last case, the rule is known as a fact. Both end with a dot. A Datalog head is either an atom or restricted atom (an atom preceded by the minus sign, cf. Section 4.1.19) that uses no built-in predicate symbol. A Datalog body contains a comma-separated sequence of literals, which may contain built-in symbols as listed in Section 4.7, as well as disjunctions (;/2) and divisions (division/2). A rule with a restricted atom as its head is called a restricting rule.

4.1.3 Programs

DES programs consist of a multiset of rules. Programs may contain remarks. A single-line remark starts with the symbol %, and ends at the end of line. Consulted programs can also contain multi-line remarks, enclosed between /* and */, which can be nested.

4.1.4 Queries

A (positive) query is the name of a relation with as many arguments as the arity of the relation (a positive literal). Each one of these arguments can be a variable or a constant; a compound term is not allowed but as an arithmetic expression. Built-in relations may require relations, lists of variables or expressions, and conditions as arguments. A negative query is written as not Query.

Queries are typed at the DES system prompt and cannot be part of consulted files, but they can be part of processed files. The answer to a query is the (multi)set of atoms matching the query which are deduced in the context of the program, from both the extensional and the intensional databases. A query with variables for all the arguments of the queried relation gives the whole set of deduced facts (meaning) defining the relation, as the query a(X) in the example of Section 3. If a query contains a constant in an argument position, it means that the query processing will select the facts from the meaning of the relation such that the argument position matches with that constant (i.e., analogous to a select relational operation). This is the case of the query a(a3) in the same example before.

You can also write conjunctive queries on the fly, such as a(X), b(X) (see Section 4.1.6). Built-in comparison operators (listed in Section 4.7.1) can be safely used in queries whenever their arguments are ground at evaluation time (equality does not require this for atomic arguments as it performs unification; cf. Section 4.7.1 for more details about equality). Disjunctive queries are also allowed too, as a(X); b(X). A query follows the same syntax as rule bodies.

If only a limited number of tuples in the answer are required, one can submit a query as top(N,Query), where N is the maximum number of tuples to be returned (See also offset predicate and Section 4.7.13). Also, query answers can be sorted with order_by (See Section 0). Duplicates can be discarded with distinct (See Section 4.1.9).

4.1.5 Temporary Views

A temporary view allows you to write a query on the fly, and provide a relation name and its arguments at will. A temporary view is therefore a rule which is added to the database; its head is considered as a query and executed. Afterwards, the rule is removed. Temporary views are useful for quickly submitting conjunctive queries and for testing the impact of adding a rule to a current relation. For instance, the view:

DES> d(X) :- a(X), not b(X)

computes the set difference between the sets a and b, provided they have been already defined.

Note that the view is evaluated in the context of the program; so, if you have more rules already defined with the same name and arity of the rule's head, the evaluation of the view will return its meaning under the whole set of rules matching the query. For instance:

DES> a(X) :- b(X)

computes the set union of the sets a and b, provided they have been already defined.

4.1.6 Automatic Temporary Views

Automatic temporary views, autoviews for short, are temporary views which do not need a head and allows you to write conjunctive queries on the fly. When you write a conjunctive query, a new temporary relation, named answer, is built with as many arguments as relevant variables occur in the conjunctive query. The identifier answer is a reserved word and cannot be used for defining any other relation. As an example of an autoview, let’s consider:

DES> a(X),b(Y)

Info: Processing:

answer(X,Y) :-

a(X),

b(Y).

{

answer(a1,a1),

answer(a1,b1),

answer(a1,b2),

answer(a2,a1),

answer(a2,b1),

answer(a2,b2),

answer(a3,a1),

answer(a3,b1),

answer(a3,b2)

}

Info: 9 tuples computed.

which computes the Cartesian product of the relations a and b, provided they have been already defined as:

a(a1).

a(a2).

a(a3).

b(b1).

b(b2).

b(a1).

4.1.7 Underscored Variables

An underscored variable (a variable starting with the underscore symbol '_') is handled similar to Prolog. It is assumed to be of no interest for the answer, so that they are discarded from the answer should they occur in the body of a query, view or autoview (even in its head)[4]. A special case of underscored variables is the anonymous variable, which is simply written as '_' (without the quotes). Several occurrences of the anonymous variable in the same rule are understood as different variables.

For instance, computing the projection of a relation t with respect to its first argument can be simply done as follows:

DES> /assert t(1,2)

DES> /assert t(2,3)

DES> t(X,_)

Info: Processing:

answer(X) :-

t(X,_).

{

answer(1),

answer(2)

}

Info: 2 tuples computed.

instead of having to resort to a temporary view such as:

DES> p(X):-t(X,Y)

Info: Processing:

p(X) :-

t(X,Y).

{

p(1),

p(2)

}

Info: 2 tuples computed.

Also, let's consider other situation, as follows:

DES> /duplicates off

DES> t(X,Y)

{

t(1,1),

t(1,2),

t(3,3)

}

Info: 3 tuples computed.

DES> t(X,X)

{

t(1,1),

t(3,3)

}

Info: 2 tuples computed.

DES> t(_X,_X)

Info: Processing:

answer :-

t(_X,_X).

{

answer

}

Info: 1 tuple computed.

Above, when underscored variables are used in the query, then you get only one answer tuple. However, if duplicates are enabled, you get two answer tuples, although the concrete values for the arguments of t are not visible:

DES> /duplicates on

DES> t(_X,_X)

Info: Processing:

answer :-

t(_X,_X).

{

answer,

answer

}

Info: 2 tuples computed.

By using anonymous variables in this query, the result becomes different:

DES> t(_,_)

Info: Processing:

answer :-

t(_,_).

{

answer,

answer

}

Info: 3 tuples computed.

In this example, the two arguments of t are not constrained to be equal. Therefore, you get three answers, one for each tuple in the relation.

As a final example, the next temporary view gets its head argument removed because _X is considered as a non-relevant variable for the outcome:

DES> v(_X):-p(_X)

Info: Processing:

v :-

p(_X).

{

}

Info: 1 tuple computed.

4.1.8 Negation

DES ensures that negative information can be gathered from a program with negated goals, provided that a restricted form of negation is used: Stratified negation [Ullm95]. This broadly means that negation is not involved in a recursive computation path, although it can use recursive rules. The following program[5] illustrates this point:

a :- not b.

b :- c,d.

c :- b.

The query a succeeds with the meaning {a}. Observe also that not a does not succeed, i.e., its meaning is the empty set.

If you are interested in how programs with negation are solved, you can find useful the following commands (cf. Section ):

DES> /pdg

Nodes: [a/0,b/0,c/0,d/0]

Arcs : [b/0+c/0,b/0+d/0,c/0+b/0,a/0-b/0]

DES> /strata

[(b/0,1),(c/0,1),(d/0,1),(a/0,2)]

The first command shows the predicate dependency graph (see, e.g., [ZCF+97]) for the loaded program. First, nodes in the graph are shown in a list whose elements P are predicates with their arities with the form predicate/arity. Next, arcs in the graph are shown in a list whose elements are either P+Q or P-Q, where P and Q are nodes in the graph. An arc P+Q means that there exists a rule such that P is the predicate for its head, and Q is the predicate for one of its literals. If the literal is negated, the arc is negative, which is expressed as P-Q. The graph for this program can be depicted as in Figure 1.

Figure 1. Predicate Dependency Graph for negation.dl

The second command shows the stratum assigned to each predicate. This assignment is computed by following an algorithm based on [Ullm95], but modified for taking advantage of the predicate dependency graph. Strata are shown as a list of pairs (P,S), where P is a predicate and S is its assigned stratum. In this example, all of the program predicates are in stratum 1 but a, which is assigned to stratum 2. This means that if the meaning of a is to be computed, then the meanings of predicates in lower strata (and only those predicates a depends on) have to be firstly computed.

Since the algorithm strata does not follow a naïve bottom-up solving, only the meanings of required predicates are computed. To illustrate this, consider the query b for the same program. DES computes the predicate dependency subgraph for b, i.e., all of the predicates which are reachable from b, and, then, a stratification is computed. Notice the different information given by the system for solving the queries a and b (here, verbose output is enabled with the command /verbose on):

DES> a

Info: Parsing query...

Info: DL query successfully parsed.

Info: Solving query a...

Info: Computing by stratum: [b].

Info: Displaying query answer...

Info: Sorting answer...

{

}

Info: 1 tuple computed.

DES> b

Info: Parsing query...

Info: DL query successfully parsed.

Info: Solving query b...

Info: Displaying query answer...

Info: Sorting answer...

{

}

Info: 0 tuples computed.

For the goal a, the system informs that b is previously computed (nevertheless taking advantage of the extension table mechanism), whereas for the goal b there is no need of resorting to the stratum-by-stratum solving.

Finally, see also Section 5.3 for limitations in the use of negation.

4.1.9 Duplicates

Duplicates in answers are removed by default. However, it is also possible to enable them with the command /duplicates on for Datalog, SQL, and RA. This allows to generate answers as multisets instead of as the typical set-oriented deductive systems behave. Computing the meaning of a relation containing duplicates in the extensional database (i.e., its facts) will include all of them in the answer, as in:

DES> /duplicates on

DES> /assert t(1)

DES> t(X)

{

t(1),

t(1)

}

Info: 2 tuples computed.

Rules can also be source of duplicates, as in:

DES> /assert s(X):-t(X)

DES> s(X)

{

s(1),

s(1)

}

Info: 2 tuples computed.

In particular, recursive rules are duplicate sources, as in:

DES> /assert t(X):-t(X)

DES> t(X)

{

t(1),

t(1)

}

Info: 4 tuples computed.

where two tuples directly come from the two facts for t/1, and the other two from the single recursive rule. Again, adding the same recursive rule yields:

DES> /assert t(X):-t(X)

DES> t(X)

{

t(1),

t(1)

}

Info: 10 tuples computed.

where this answer contains the outcome due to two tuples directly from the two facts, and four tuples for each recursive rule. The first recursive rule is source of four tuples because of the two facts and the two tuples from the second recursive rule. Analogously, the second recursive rule is source of another four tuples: two facts and the two tuples from the first recursive rule.

The rule of thumb to understand duplicates in recursive rules is to consider all possible computation paths in the dependency graph, stopping when a (recursive) node already used in the computation is reached.

It is also possible to discard duplicates for an atom with the metapredicate distinct/1. For instance, let’s consider the following with the same example above:

DES> distinct(t(X))

Info: Processing:

answer(X) :-

distinct(t(X)).

{

answer(1)

}

Info: 1 tuple computed.

Such query is equivalent to the following SQL statement, provided that metadata is available for the relation t:

DES> :-type(t(a:int))

DES> select distinct * from t

answer(t.a) ->

{

answer(1)

}

Info: 1 tuple computed.

As it would be expected, duplicates are only discarded for the call distinct(Atom), but not for other occurrences of Atom during query solving. Thus:

DES> t(X),distinct(t(X))

Info: Processing:

answer(X) :-

t(X),

distinct(t(X)).

{

answer(1),

answer(1)

}

Info: 10 tuples computed.

Compare this to the call:

DES> t(X),t(X)

Info: Processing:

answer(X) :-

t(X),

t(X).

{

answer(1),

...

answer(1)

}

Info: 100 tuples computed.

A subset of arguments in an atom can be selected for discarding duplicates. To this end, the metapredicate distinct/2 is provided. Its first argument is the list of variables for which duplicates are not required, i.e., each concrete assignment of values to all variables in the list must be different. So, let's consider the following session:

DES> /listing

t(1,1).

t(1,2).

t(2,1).

Info: 3 rules listed.

DES> distinct([X],t(X,Y))

Info: Processing:

answer(X) :-

distinct([X],t(X,Y)).

{

answer(1),

answer(2)

}

Info: 2 tuples computed.

In addition, discarding duplicates can be performed in the context of aggregates:

DES> count(distinct(t(X)),C)

Info: Processing:

answer(C)

in the program context of the exploded query:

answer(C) :-

count('$p0'(X),[],C).

'$p0'(A) :-

distinct(t(A)).

{

answer(1)

}

Info: 1 tuple computed.

See also Section 4.1.12 for discarding duplicates in aggregates.

4.1.10 Null Values

The null value is included in each program signature for denoting unknowns, in a similar way it is an inherent part of current SQL database systems. Comparing null values in Datalog opens a new scenario: Two null values are not (known to be) equal, and are (not known to be) distinct. The following illustrates this expected behaviour:

DES> null=null

{

}

Info: 0 tuples computed.

DES> null\=null

{

}

Info: 0 tuples computed.

However, for the same null value, the equality should succeed, as in the conjunctive query: X=null,X=X.

A null value is internally represented as '$NULL'(ID), where ID is a unique identifier (an integer). Development listings (enabled via the command /development on) allow to inspect these identifiers, such as in:

DES> /development on

DES> p(X,Y):-X=null,Y=null,X=Y

Info: Processing:

p(X,Y) :-

X = '$NULL'(14),

Y = '$NULL'(15),

X = Y.

{

}

Info: 0 tuples computed.

DES> p(X,Y):-X=null,Y=null,X\=Y

Info: Processing:

p(X,Y) :-

X = '$NULL'(16),

Y = '$NULL'(17),

X \= Y.

{

}

Info: 0 tuples computed.

The built-in predicate is_null/1 tests whether its single argument is a null value:

DES> is_null(null)

{

is_null(null)

}

Info: 1 tuple computed.

DES> X=null,is_null(X)

Info: Processing:

answer(X) :-

X = null,

is_null(X).

{

answer(null)

}

Info: 1 tuple computed.

Its counterpart predicate is also provided: is_not_null/1, which is true if its argument is not a null value.

Note that from a system implementor viewpoint, nulls can never unify because they are represented by different ground terms. On the other hand, disequality is explicitly handled in order to fail when comparing nulls.

Evaluation of a given expression including at least one null value returns another different concrete null value n. The very same expression in a further computation step receives the same null value n. For instance, X=null, X+1=X+1 succeeds, whereas neither X=null, X+1=1+X, nor X=null, Y=null, X+1=Y+1 succeeds.

4.1.11 Outer Joins

Three outer join operations are provided (cf. Section 4.7.9), following relational database query languages (SQL and extended relational algebra): left (lj/3), right (rj/3) and full (fj/3) outer join. For all these predicates, their first argument is the argument to the left for the algebra relational outer join operator, the second argument is the argument to the right, and the third argument is the condition for the join operation. For example, lj(L,R,C) represents L _C R.

Having loaded the example program relop.dl, we can submit the following queries:

DES> /c relop

DES> /listing a

a(a1).

a(a2).

a(a3).

DES> /listing b

b(a1).

b(b1).

b(b2).

DES> lj(a(X),b(Y),X=Y)

Info: Processing:

answer(X,Y) :-

lj(a(X),b(Y),X = Y).

{

answer(a1,a1),

answer(a2,null),

answer(a3,null)

}

Info: 3 tuples computed.

DES> rj(a(X),b(Y),X=Y)

Info: Processing:

answer(X,Y) :-

rj(a(X),b(Y),X = Y).

{

answer(a1,a1),

answer(null,b1),

answer(null,b2)

}

Info: 3 tuples computed.

DES> fj(a(X),b(Y),X=Y)

Info: Processing:

answer(X,Y) :-

fj(a(X),b(Y),X = Y).

{

answer(a1,a1),

answer(a1,null),

answer(a2,null),

answer(a3,null),

answer(null,a1),

answer(null,b1),

answer(null,b2)

}

Info: 7 tuples computed.

Note that the third parameter is the join condition. Be aware and do not miss a where condition with a join condition. Let´s consider the above query lj(a(X),b(Y),X=Y). Do not expect the same result as above for the following query (note the shared variable X):

DES> lj(a(X),b(X),true)

Info: Processing:

answer(X) :-

lj(a(X),b(X),true).

{

answer(a1)

}

Info: 1 tuple computed.

Here, the same variable X for the relations a and b means that tuples from a and b with the same value are to be joined, as in the next equivalent query:

DES> lj(a(X),b(Y),true),X=Y

Info: Processing:

answer(X,Y) :-

lj(a(X),b(Y),true),

X = Y.

{

answer(a1,a1)

}

Info: 1 tuple computed.

Outer join relations can be nested as well:

DES> lj(a(X),rj(b(Y),c(U,V),Y=U),X=Y)

Info: Processing:

answer(X,Y,U,V) :-

lj(a(X),rj(b(Y),c(U,V),Y = U),X = Y).

{

answer(a1,a1,a1,a1),

answer(a1,a1,a1,b2),

answer(a2,null,null,null),

answer(a3,null,null,null)

}

Info: 4 tuples computed.

Note that compound conditions must be enclosed between parentheses, as in:

DES> lj(a(X),c(U,V),(X>U;X>V))

Info: Processing:

answer(X,U,V)

in the program context of the exploded query:

answer(X,U,V) :-

lj(a(X),c(U,V),(X > U;X > V)).

{

answer(a1,null,null),

answer(a2,a1,a1),

answer(a2,a1,b2),

answer(a3,a1,a1),

answer(a3,a1,b2),

answer(a3,a2,b2)

}

Info: 6 tuples computed.

4.1.12 Aggregates

Aggregates refer to functions and predicates that compute values with respect to a collection of values instead of a single value. Aggregates are provided by means of five usual computations: sum (cumulative sum), count (element count), avg (average), min (minimum element), and max (maximum element). In addition, the less usual times (cumulative product) is also provided. They behave close to most SQL implementations, i.e., ignoring nulls.

Duplicate-free counterparts are also provided: sum_distinct, count_distinct, avg_distinct, and times_distinct. Note that for minimum and maximum, no counterparts are provided since they would compute the same results. These functions behave as the above when duplicates are disabled, which is the default mode.

Any arithmetic expression can be argument of an aggregate function.

4.1.12.1 Aggregate Functions

An aggregate function can occur in expressions and returns a value, as in R=1+sum(X), where sum is expected to compute the cumulative sum of possible values for X, and X has to be bound in the context of a group_by predicate (cf. next section), wherein the expression also occur.

4.1.12.2 Group_by Predicate

A group_by predicate encloses a query for which a given list of variables builds answer sets (groups) for all possible values of these variables. Then, these groups can be aggregated with specific aggregate functions. Let’s consider the following excerpt from the file aggregates.dl:

% employee(Name,Department,Salary)

employee(anderson,accounting,1200).

employee(andrews,accounting,1200).

employee(arlingon,accounting,1000).

employee(nolan,null,null).

employee(norton,null,null).

employee(randall,resources,800).

employee(sanders,sales,null).

employee(silver,sales,1000).

employee(smith,sales,1000).

employee(steel,sales,1020).

employee(sullivan,sales,null).

We can count the number of employees for each department with the following query:

DES> group_by(employee(N,D,S),[D],R=count)

Info: Processing:

answer(D,R) :-

group_by(employee(N,D,S),[D],R = count).

{

answer(accounting,3),

answer(null,2),

answer(resources,1),

answer(sales,5)

}

Info: 4 tuples computed.

Note that two employees are not assigned to any department yet (nolan and norton). This query behaves as an SQL user would expect, though nulls do not have to represent the same data value (in spite of this, such tuples are collected in the same bag).

If we rather want to count active employees (those with assigned salaries), we submit the following query:

DES> group_by(employee(N,D,S),[D],R=count(S))

Info: Processing:

answer(D,R) :-

group_by(employee(N,D,S),[D],R = count(S)).

{

answer(accounting,3),

answer(null,0),

answer(resources,1),

answer(sales,3)

}

Info: 4 tuples computed.

Note that null departments have no employee with assigned salary.

Counting the number of departments from the relation employee needs to discard duplicates, as in:

DES> group_by(employee(N,D,S),[],R=count_distinct(D))

Info: Processing:

answer(R) :-

group_by(employee(N,D,S),[],[],R=count_distinct(D)).

{

answer(3)

}

Info: 1 tuple computed.

Conditions including aggregates on groups can be stated as well (cf. having conditions in SQL). For instance, the following query lists departments with more than one active employee.

DES> group_by(employee(N,D,S),[D],count(S)>1)

Info: Processing:

answer(D) :-

group_by(employee(N,D,S),[D],(A = count(S),A > 1)).

{

answer(accounting),

answer(sales)

}

Info: 2 tuples computed.

Note that the number of employees can also be returned, as follows:

DES> group_by(employee(N,D,S),[D],(R=count(S),R>1))

Info: Processing:

answer(D,R) :-

group_by(employee(N,D,S),[D],(R = count(S),R > 1)).

{

answer(accounting,3),

answer(sales,3)

}

Info: 2 tuples computed.

Conditions including no aggregates on tuples of the input relation (cf. SQL FROM clause) can also be used (cf. WHERE conditions in SQL). For instance, the following query computes the number of employees whose salary is greater than 1,000.

DES> group_by((employee(N,D,S),S>1000),[D],R=count(S))

Info: Processing:

answer(D,R)

in the program context of the exploded query:

answer(D,R) :-

group_by('$p2'(S,D,N),[D],R = count(S)).

'$p2'(S,D,N) :-

employee(N,D,S),

S > 1000.

{

answer(accounting,2),

answer(sales,1)

}

Info: 2 tuples computed.

Note that the following query is not equivalent to the former, since variables in the input relation are not bound after a grouping computation. The following query illustrates this situation, which generates a syntax error.

DES> group_by(employee(N,D,S),[D],R=count(S)), S>1000

Error: Incorrect use of shared set variables in metapredicate: [N,S]

The predicate group_by admits a more compact representation than its SQL counterpart. Let's consider the following Datalog session:

DES> /assert p(1,1)

DES> /assert p(2,2)

DES> /assert q(X,C):-group_by(p(X,Y),[X],(C=count;C=sum(Y)))

DES> q(X,C)

Info: Computing by stratum of [p(A,B)].

{

q(1,1),

q(2,1),

q(2,2)

}

Info: 3 tuples computed.

An analogous SQL session follows:

DES> create table p(X int, Y int)

DES> create view q(X,C) as (select X,count(Y) as C from p group by X) union (select X, sum(Y) as C from p group by X)

DES> select * from q

answer(q.X:int, q.C:int) ->

{

answer(1,1),

answer(2,1),

answer(2,2)

}

Info: 3 tuples computed.

4.1.12.3 Aggregate Predicates

An aggregate predicate returns its result in its last argument position, as in sum(p(X),X,R), which binds R to the cumulative sum of values for X, provided by the input relation p. These aggregate predicates simply allow another way to expressing aggregates, in addition to the way explained just above. Again, with the same file, the following queries are allowed:

DES> count(employee(N,D,S),S,T)

Info: Processing:

answer(T) :-

count(employee(N,D,S),S,[],T).

{

answer(7)

}

Info: 1 tuple computed.

A group by operation is simply specified by including the grouping variable(s) in the head of a clause, as in the following view, which computes the number of active employees by department:

DES> c(D,C):-count(employee(N,D,S),S,C)

Info: Processing:

c(D,C) :-

count(employee(N,D,S),S,[D],C).

{

c(accounting,3),

c(null,0),

c(resources,1),

c(sales,3)

}

Info: 4 tuples computed.

Note that the system adds to the aggregate predicate an argument with the list of grouping variables, which are the ones occurring in the first argument of the aggregate predicate that also occur in the head. This code translation is required for the aggregate predicate to be computed, although such form has not been made available to the user.

Having conditions are also allowed, including them as another goal of the first argument of the aggregate predicate as, for instance, in the following view, which computes the number of employees that earn more than the average:

DES> count((employee(N,D,S),avg(employee(N1,D1,S1),S1,A),S>A),C)

Info: Processing:

answer(C)

in the program context of the exploded query:

answer(C) :-

count('$p2'(A,S,D,N),[],C).

'$p2'(A,S,D,N) :-

employee(N,D,S),

avg(employee(N1,D1,S1),S1,[],A),

S > A.

{

answer(2)

}

Info: 1 tuple computed.

Note that this query uses different variables in the same argument positions for the two occurrences of the relation employee. Compare this to the following query, which computes the number of employees so that each one of them earns more than the average salary of his corresponding department. Here, the same variable name D has been used to refer to the department for which the counting and average are computed:

DES> count((employee(N,D,S),avg(employee(N1,D,S1),S1,A),S>A),C)

Info: Processing:

answer(C)

in the program context of the exploded query:

answer(C) :-

count('$p2'(A,S,N),[],C).

'$p2'(A,S,N) :-

employee(N,D,S),

avg(employee(N1,D,S1),S1,[],A),

S > A.

{

answer(3)

}

Info: 1 tuple computed.

Also, as a restriction of the current implementation, keep in mind that having conditions including aggregates (as the one including the average computations above) can only occur in the first argument of an aggregate. The following query, which should be equivalent to the last one, would generate a run-time exception:

DES> v(D):-avg(employee(N1,D,S1),S1,A),count((employee(N,D,S),S>A),C)

Error: S > A will raise a computing exception at run-time.

Warning: This view is unsafe because of variable(s):

[A]

Finally, recall that expressions including aggregate functions are not allowed in conjunction with aggregate predicates, but only in the context of a group_by predicate.

4.1.12.4 Aggregates and Duplicates

When duplicates are disabled (default option), aggregate functions operate over sets, so that if the source relation for an aggregate contains duplicates, they are discarded. The following system session illustrates this:

DES> /duplicates off

DES> /assert t(1,2)

DES> count(t(X,Y),C)

Info: Processing:

answer(C) :-

count(t(X,Y),[],C).

{

answer(1)

}

Info: 1 tuple computed.

On the other hand, enabling duplicates, both tuples in the relation t are counted unless count_distinct is used:

DES> /duplicates on

DES> count(t(X,Y),C)

Info: Processing:

answer(C) :-

count(t(X,Y),[],C).

{

answer(2)

}

Info: 1 tuple computed.

DES> count_distinct(t(X,Y),C)

Info: Processing:

answer(C) :-

count_distinct(t(X,Y),[],C).

{

answer(1)

}

Info: 1 tuple computed.

Note that subtle behaviours may arise when duplicates are disabled. For instance, let's assume the relation employee from the file examples/aggregates.dl and that we want to know how many employees are above the average salary minus 20. We can submit the following goal to display the salaries that meet this condition:

DES> avg(employee(_,_,S),S,A),employee(_,_,S1),S1>A-20

Info: Processing:

answer(A,S1) :-

avg(employee(_,_,S),S,[],A),

employee(_,_,S1),

S1>A-20.

{

answer(1031.4285714285713,1020),

answer(1031.4285714285713,1200)

}

Info: 2 tuples computed.

However, if we count them:

DES> count((avg(employee(_,_,S),S,A),employee(_,_,S1),S1>A-20),C)

Info: Processing:

answer(C)

in the program context of the exploded query:

answer(C) :-

count('$p2',[],C).

'$p2' :-

avg(employee(_,_,S),S,[],A),

employee(_,_,S1),

S1>A-20.

{

answer(1)

}

Info: 1 tuple computed.

we get only one because the compilation of the query generates the predicate '$p2' for which, with duplicates disabled, at most only one tuple can be in its meaning as it has no arguments. By enabling duplicates we get the expected answer:

DES> /duplicates on

DES> count((avg(employee(_,_,S),S,A),employee(_,_,S1),S1>A-20),C)

Info: Processing:

answer(C)

in the program context of the exploded query:

answer(C) :-

count('$p2',[],C).

'$p2' :-

avg(employee(_,_,S),S,[],A),

employee(_,_,S1),

S1>A-20.

{

answer(3)

}

Info: 1 tuple computed.

Note also that there are 3 employees meeting the condition, as 2 employees have the top salary (cf. the first query of this example above):

DES> employee(_,_,S)

Info: Processing:

answer(S) :-

employee(_,_,S).

{

answer(800),

answer(1000),

answer(1020),

answer(1200),

answer(null),

answer(null)

}

Info: 11 tuples computed.

4.1.13 Non-deterministic Functions and Function Predicates

Functions that return several values for the same input are known as non-deterministic. An example is rand (cf. Section 4.7) and its counterpart function predicate $rand/1, which returns a random number between 0 and 1 each time it is evaluated. For example, the next call to the recursive predicate r/1 retrieves the first 5 random numbers from the current seed:

DES> /assert r(X) :- '$rand'(X) ; r(_), '$rand'(X)

DES> top(5,r(X))

Info: Processing:

answer(X) :-

top(5,r(X)).

{

answer(4.5938383287736436E-06),

answer(0.2690426096337411),

answer(0.5255980535933436),

answer(0.7701105651790878),

answer(0.7899237996741693)

}

Info: 5 tuples computed.

Since the deductive engine may solve the same call several times until it detects the fixpoint, it has been adapted for dealing with this expected behaviour. Otherwise, different values might be retrieved for the same call. This problem is avoided as illustrated in the following example, where each different call is associated to an ascending integer, receiving the same random number:

DES> r(N,X):-N=1,'$rand'(X);r(N1,_),N1<5,N=N1+1,'$rand'(X)

Info: Processing:

r(N,X)

in the program context of the exploded query:

r(N,X) :- N=1,'$rand'(X).

r(N,X) :- r(N1,_),N1<5,N=N1+1,'$rand'(X).

{

r(1,0.2540546440998382),

r(2,0.13463473483802407),

r(3,0.5466512676458092),

r(4,0.19447782913947345),

r(5,0.6709759087495082)

}

Info: 5 tuples computed.

(Former DES versions sticked to each call in a rule and random numbers where repeated for different calls.)

Currently, the following non-deterministic functions (and corresponding function predicates) are provided: rand, current_date, current_time, and current_timestamp. Predicates depending on these functions are not cached along user inputs.

4.1.14 Impure Deterministic Functions and Function Predicates

Some deterministic functions may reveal non-functional collateral effects such as rand(Seed) (as well as its couterpart predicate $rand/2). Each time this function is called, a seed is (collateraly) set for the next calls to the rand function, therefore adding a notion of state associated to a computation. Thus, for this kind of functions, each call is only evaluated once, such as in:

DES> '$rand'(1,X),'$rand'(Y),'$rand'(2,U),'$rand'(V)

Info: Processing:

answer(X,Y,U,V) :- '$rand'(1,X),'$rand'(Y),'$rand'(2,U),'$rand'(V).

{

answer(1.932677162839319E-12,6.127357483089879E-05,3.865354325678638E-12,0.00012254714966179758)

}

Info: 1 tuple computed.

Note that in the next example there are two goals with the same seed '$rand'(1,X) and '$rand'(1,U), but at different call points, so both become evaluated:

DES> '$rand'(1,X),'$rand'(Y),'$rand'(1,U),'$rand'(V)

Info: Processing:

answer(X,Y,U,V) :- '$rand'(1,X),'$rand'(Y),'$rand'(1,U),'$rand'(V).

{

answer(1.932677162839319E-12,6.127357483089879E-05,1.932677162839319E-12,6.127357483089879E-05)

}

Info: 1 tuple computed.

This can be used in recursive predicates to generate different random numbers starting from the same seed, as in:

DES> /assert r(X) :- '$rand'(1,X) ; r(_), '$rand'(X)

DES> top(5,r(X))

Info: Processing:

answer(X) :- top(5,r(X)).

{

answer(1.932677162839319E-12),

answer(1.6402455177678477E-05),

answer(6.127357483089879E-05),

answer(0.007813457399610257),

answer(0.5010417145987278)

}

Info: 5 tuples computed.

This exact series of random numbers will be reproduced in any further call r(X). Another example involves two different calls with the same seed in a recursive predicate. The seed is set in entry 1, and again in entry 6, so that the same series of random numbers are associated to entries starting at 1 and 6:

DES> /assert r(1,X):-'$rand'(1,X)

DES> /assert r(N,X):-r(N1,_),N1<5,N=N1+1,'$rand'(X)

DES> /assert r(N,X):-r(N1,_),N1=5,N=N1+1,'$rand'(1,X)

DES> /assert r(N,X):-r(N1,_),N1>5,N1<10,N=N1+1,'$rand'(X)

DES> r(N,X)

{

r(1,1.932677162839319E-12),

r(2,6.127357483089879E-05),

r(3,0.5010417145987278),

r(4,0.007813457399610257),

r(5,1.6402455177678477E-05),

r(6,1.932677162839319E-12),

r(7,6.127357483089879E-05),

r(8,0.5010417145987278),

r(9,0.007813457399610257),

r(10,1.6402455177678477E-05)

}

Info: 10 tuples computed.

Because of similar reasons as in the previous subsection, in this case, the function predicate rand(Seed) is evaluated once for each call, but retrieving only its first (and only one) solution as opposed to the function predicate rand, which returns a value for each different call. Otherwise, the seed might be reset on fixpoint computation without need, dealing to unexpected results. That function is solved by applying a tabled aggreation committed to the first result.

Currently, this is the only one impure deterministic function. Predicates depending on these functions can be cached along user inputs.

4.1.15 Disjunctive Bodies

As introduced in Section 4.1.1, rule bodies can contain disjunctions, such as the one contained in the program family.dl:

parent(X,Y) :-

father(X,Y)

;

mother(X,Y).

This clause is equivalent to:

parent(X,Y) :-

father(X,Y).

parent(X,Y) :-

mother(X,Y).

If you list the database contents via the command /listing you will get the first form when development listings are disabled (via the command /development off). Otherwise, you get the second one (command /development on).

Datalog views and autoviews containing disjunctive bodies are allowed, and the system informs about the program transformation performed to compute them. For instance, you can directly submit the rule above as a temporary view at the prompt:

DES> parent(X,Y) :- father(X,Y) ; mother(X,Y)

Info: Processing:

parent(X,Y)

in the program context of the exploded query:

parent(X,Y) :-

father(X,Y).

parent(X,Y) :-

mother(X,Y).

{

parent(amy,fred),

parent(carolI,carolII),

parent(carolII,carolIII),

parent(fred,carolIII),

parent(grace,amy),

parent(jack,fred),

parent(tom,amy),

parent(tony,carolII)

}

Info: 8 tuples computed.

4.1.16 Relational Division in Datalog

The relational division operation for Datalog provided in DES follows the original proposal of Codd [Codd72] but, instead of comparing schemas based on column names, comparing schemas based on variable names. Given a left operand L and a right operand R in a division operator, the result is a relation with as many arguments as variables are in vars(L)-vars(R), where vars(R)Ìvars(L) and vars(T) returns the variables in a term T.

For example, given the database:

t(1,1).

t(1,2).

t(2,1).

s(1).

s(2).

Then, the query:

t(X,Y) division s(Y)

returns:

{answer(1)}

Now, let's consider that the relations to be divided contain other arguments that are not relevant for the division operator. For instance, let's consider the relation work(employee,project,hours), under an intuitive meaning. If we want to know the name of each employee who is working on each project on which employee smith is working, we have to project the division operands for the appropriate arguments. For instance:

DES> /assert np_work(N,P) :- work(N,P,_)

DES> np_work(N,P) division np_work(smith,P)

However, by using anonymous variables, it is possible to omit the non-relevant variables (by using an anonymous annotation '_' for them) for the division operator, without needing to project the relevant ones. Following the same example, the same query can be submitted as simply as:

DES> work(N,P,_) division work(smith,P,_)

Division can be nested as well. For instance, let's consider the relation team(team_nbr, employee). If we want to know whether the employees for the last query do form a complete team, then:

DES> team(T,N) division (work(N,P,_) division work(smith,P,_))

As a caveat, note that variables in the right operand of the division operator are demanded if they occur in another goal, similar to what happens with built-ins as comparison operators. For instance, the variable Y in the following query is demanded and, therefore, the query is not valid:

DES> (t(X,Y) division s(Y)),p(Y)

By switching both goals, the query becomes valid:

DES> p(Y),(t(X,Y) division s(Y))

If, on the contrary, Y does not occur in any other subgoal (and neither in the head, if considering a rule) there is no such demandness requirement. This issue breaks the declarative nature of the division operator. In addition, this is not warned to the user, yet, and will be part of future enhancements.

4.1.17 Existential Quantification

Variables occurring in a clause body that do not occur in the clause head are implicitly and existentially quantified. Given said this, existential quantifiers can be explicitly used at programmer's will with a couple of purposes: First, for explicitly denoting which are the existential variables in a rule (as a syntax recall for this kind of variables). Second, for allowing more powerful uses of the existential quantifier when coupled with negation.

The syntax for an existential quantification is exists(Vars,Goal), where Vars is the list (delimited by square brackets) of existential variables with their scope in Goal.

Next is an example of a safe query (even when X is not rangerestricted; cf. Section 5.3.1):

exists([X],not p(X))

A universal quantification can be expressed with the logic equivalence "xP(x) º Ø$xØP(x). As an example, consider the relation products including the total (including taxes) and the net (excluding taxes) prices. Checking if all the products (a relation with arguments: id, name, net and total) satisfy total ³ net can be stated as follows:

not exists([Net,Total], (products(_,_,Net,Total), Total<Net))

i.e., there is not the case of finding a net price greater than the grand total for any product. This query is a syntactic sugaring equivalent to:

not exists([Id,Name,Net,Total], (products(Id,Name,Net,Total), Total<Net))

where, in the first query, underscored variables are existentially quantified by default.

An existentially quantified variable cannot occur out of the quantification. Incorrect uses are rejected, as in:

DES> t(X), exists([X],not p(X))

Error: (DL) Quantified variable [X] cannot occur outside its scope.

As well, an unused existentially quantified variable makes the input to be rejected, as in:

DES> exists([X,Y],not p(X))

Error: Variables in the first argument of 'exists' must occur in its second argument: exists([X,Y],not p(X))

Finally, duplicated variables in the quantifier are not allowed, as in:

DES> exists([X,X],not p(X))

Error: (DL) Quantified variable [X] can occur only once in the quantifier's variable list.

4.1.18 Integrity Constraints

Integrity constraints allow the user to specifying valid values for tuples in relations. DES provides several predefined constraints stemmed from SQL: type, primary key and foreign key. In addition, a predefined functional integrity constraint is also provided. Users can also define their own integrity constraints, which are called user-defined integrity constraints from now on. All of them can be declared and the system monitors their fulfilment, which is the default behaviour. However, the command /check off allows to disable constraint checking. All predefined integrity constraints apply to facts, except type constraints, which also apply to rules. Also, user-defined constraints apply to facts and rules.

A comma-separated sequence of predefined integrity constraints is allowed to specifying multiple constraints in a single input.

4.1.18.1 Type

A type constraint specifies the values in a domain a predicate argument (table column) may take. An example of a type constraint declaration at the command prompt is as follows:

DES> :- type(p,[int,string])

This is equivalent to the following alternative syntax:

DES> :- type(p(int,string))

Allowed types include the following (where each cell in the first column contains type synonyms):

Type	Meaning
varchar string	String of unbounded length
char(N) varchar(N)	String with length up to N
char	String with length 1
integer int	Integer number
float real	Real number
date	Date expressed as date(Year,Month,Day)
time	Time expressed as time(Hour,Minute,Second)
datetime timestamp	Timestamp expressed as datetime(Year,Month,Day,Hour,Minute,Second)

Precision and range depend on the underlying Prolog system. Strings are represented with constants (cf. Section 4.1.1). A number with a dot between two digits is considered as a float and an integer otherwise.

Subsequent type declarations are allowed for the same predicate and arity, where the last declaration for a given predicate is the one to persist, overriding previous type declarations for such predicate. The following session is possible, and thus the second declaration persists:

DES> :- type(p,[string,string])

DES> :- type(p,[int,int])

Several type declarations can be submitted in a single assertion as in:

DES> :- type(p(a:int)), type(q(b:string))

As well, columns can be given names:

DES> :- type(p,[a:int,b:string])

which is equivalent to the following alternative syntax:

DES> :- type(p(a:int,b:string))

However, a type declaration for a relation already typed with a different arity is not allowed. As it will be seen in further sections, SQL statements can refer to Datalog relations, and SQL does not allow relations of the same name and different arities.

DES> :- type(p,[a:int])

Error: Cannot add types to a relation with several arities.

Relation: p

A Datalog type declaration is analogous to the creation of an SQL table, with the same outcome (defining metadata for a relation: relation name, column names and types).

DES> /dbschema p

Info: Table:

* p(a:int,b:string)

DES> drop table p

DES> /dbschema p

Info: No table or view found with that name.

DES> create table p(a int, b string)

DES> /dbschema p

Info: Table:

* p(a:int,b:string)

As already seen in previous examples, it is also possible to omit column names. In this case, they are automatically provided (with names '$1', '$2', and so on).

DES> :- type(p,[int,string])

DES> /dbschema p

Info: Table:

* p($1:int,$2:string)

Let's consider the following session, where it can be seen that the system monitors type constraints in both Datalog and SQL queries:

DES> :-type(p,[int,string])

DES> /assert p(a,b)

Error: Type mismatch p.$1:number(integer) vs. string(char(1)).

p($1:number(integer),$2:string(varchar))

DES> /assert p(1,a)

DES> p(X,Y)

{

p(1,a)

}

Info: 1 tuple computed.

DES> select * from p

answer(p.$1:int,p.$2:string) ->

{

answer(1,a)

}

Info: 1 tuple computed.

DES> insert into p values('a','b')

Error: Type mismatch p.$1:number(integer) vs. string(char(_6937)).

p($1:number(integer),$2:string(varchar))

Info: 0 tuples inserted.

Note that columns with automatically given names can be accessed from an SQL statement, but enclosed as special user identifiers. ISO delimiters (double quotes "", supported by Oracle and SQL Server) are supported as well as other vendor-specific delimiters: MS Access (square brackets []) and MySQL (back quotes ``). Otherwise, an error is raised:

DES> /sql select $1 from p

Error: (SQL) Invalid SELECT list or (SQL) Expected valid SQL expression near '/sql select '

DES> select "$1" from p

answer(p.$1:int) ->

{

answer(1)

}

Info: 1 tuple computed.

A relation already defined is checked for consistency when trying to assert a new type constraint:

DES> /assert t(1)

DES> /assert t(a)

DES> :-type(t,[int])

Error: No type tuple covers all the loaded rules for t/1:

t(1).

t(a).

Info: 2 rules listed.

Should any other constraint remains asserted (other than a type constraint), a type constraint cannot be changed:

DES> :-type(p,[a:int,b:string])

Error: Cannot change type assertion while other constraints remain.

Such constraints can be inspected in the database schema (command /dbschema).

4.1.18.1.1 Types on the Intensional Database

Types can also be declared for predicates of the intensional database, i.e., those predicates defined at least with rules, not only with facts. So, asserting a new type constraint over an intensional relation will trigger type checking, inferring types along the predicate dependency graph restricted to the typed predicate. Let's consider the following situation as an example:

DES> /listing

s(a).

t(1).

t(X) :-

s(X).

Info: 3 rules listed.

DES> :-type(t,[int])

Error: No type tuple covers all the loaded rules for t/1:

t(1).

t(X) :-

s(X).

Info: 2 rules listed.

4.1.18.1.2 Types on Propositional Relations

Finally, propositional relations are also subject of being typed, of course with an empty list of arguments:

DES> :-type(a,[])

DES> /dbschema a

Info: Table:

* a

The alternative syntax becomes shorter in this case indeed:

DES> :-type(a)

4.1.18.1.3 Type Casting

A value of a type can be converted to a value of another type for selected type combinations, either automatically or manually. The following table shows the possible type combinations:

From	To
Number Type	Number Type
Number Type	String Type
String Type	Number Type
String Type	String Type
String Type	Datetime Type
Datetime Type	String Type
date	datetime
datetime	date
datetime	time

where:

*Number Type*	*String Type*	*Datetime Type*
integer	char	date
float	char(N)	time
int	varchar(N)	datetime
real	string

Automatic type casting allows you to automatically applying a type conversion to a value in order to match the declared type along tuple insertions. By default, type casting is disabled and can be enabled with the command /type_casting on. For instance, let's consider the following example:

DES> /type_casting on

DES> :-type(t(a:int,b:float,c:string,d:varchar(2)))

DES> /assert t(1.5,1,2,123)

DES> /listing

t(2,1.0,'2','12').

Info: 1 rule listed.

Here, a round function (closest integer) has been applied to the first argument, the integer 1 has been converted the float 1.0, the integer 2 has been converted to a string, and so the last argument, which in addition has been truncated to fit the type string length constraint. Also, strings can be converted to numbers if they are read as a valid number (following the syntax in Section 4.1.1), as in:

DES> /assert t('4','5.0E10','','')

DES> /listing

t(4,5.0E+10,'','').

Info: 1 rule listed.

If a conversion is not possible, an error is raised:

DES> :-type(p(a:int))

DES> /assert p('foo')

Error: Impossible conversion of 'foo' to number(integer).

Note that the conversion proceeds only on tuple (facts) insertions, but neither on retractions nor on rules:

DES> /retract t(1.5,1,2,123)

Warning: Nothing retracted.

DES> /assert p(X) :- X='1'

Error: Type mismatch number(integer) vs. string(varchar(1)).

p(a:number(integer)) (declared types).

A manual type casting can be applied in the context of an expression with the function cast, and in the context of a goal with the predicate '$cast'/3. The function cast(Value, Type) returns Value in the type Type. For instance:

DES> X=cast(date(2016,8,31),datetime)-datetime(2016,8,30,23,59,59)

Info: Processing:

answer(X) :-

'$cast'(date(2016,8,31),datetime(datetime),A),

'$datetime_sub'(A,datetime(2016,8,30,23,59,59),B),

X=B.

{

answer(1)

}

Info: 1 tuple computed.

4.1.18.2 Nullability (Existence Constraint)

Columns can be imposed to contain a concrete value rather than a null. The next system session shows an example:

DES> :-type(p,[a:int,b:string])

DES> :-nn(p,[a])

The list of column names specifies the columns for which null values are not allowed. Thus, trying to assert a tuple such as the following, will raise an error:

DES> /assert p(null,'')

Error: Not null violation p.[a]

Subsequent existency constraints are allowed for the same predicate and arity; the last declaration is the one to persist, overriding previous declarations for such predicate.

4.1.18.3 Primary Key

A primary key constraint specifies that no two tuples have the same values for a given set of columns. Next, a system session illustrates the use of a primary key assertion:

DES> :-type(p,[a:int,b:string])

DES> :-pk(p,[a])

Primary key constraints are trivially satisfied when duplicates are disabled, as relations are considered as sets, irrespective of the current database instance, that may contain duplicates for the arguments in the primary key.

Several primary key declarations are allowed for the same predicate and arity; the last declaration is the one to persist, overriding previous type declarations for such predicate:

DES> :-pk(p,[a])

DES> :-pk(p,[c])

Error: Unknown column c.

DES> :-pk(p,[a,a])

A relation already defined with facts or rules is checked for consistency when trying to assert a new primary key constraint:

DES> :-type(q,[a:int,b:int])

DES> /assert q(1,1)

DES> /assert q(2,2)

DES> /assert q(1,2)

DES> :-pk(q,[a])

Error: Primary key violation q.[a]

Offending values in database: [pk(1)]

Info: Constraint has not been asserted.

4.1.18.4 Candidate Key (Uniqueness Constraint)

As a primary key, a candidate key constraint specifies that no two tuples have the same values for a given set of columns. Next, a system session illustrates the use of a candidate key assertion:

DES> :-type(p,[a:int,b:string])

DES> :-ck(p,[a])

Candidate key constraints are trivially satisfied when duplicates are disabled, as relations are considered as sets, irrespective of the current database instance, that may contain duplicates for the arguments in the candidate key.

Several candidate key declarations are allowed for the same predicate and arity. By contrast to primary keys, several candidate key constraints are allowed for the same predicate:

DES> :-ck(p,[b])

DES> :-ck(p,[a,b])

DES> /dbschema p

Info: Table:

* p(a:int,b:string)

- NN: [a]

- CK: [a]

- CK: [b]

- CK: [a,b]

4.1.18.5 Foreign Key

A foreign key constraint specifies that the values in a given set of columns of a relation must exist already in the columns declared in the primary key constraint of another (or even the same) relation. Next, an example of a foreign key assertion is shown:

DES> :-type(p(a:int)),type(q(b:int)),pk(q,[b])
DES> :-fk(p,[a],q,[b])

However, if the relations do not exist, an error is raised:

DES> :-fk(p,[a],q,[b])

Error: Relation p has not been typed yet.

DES> :-type(p,[a:int]), type(q,[b:int])

Trying to impose a foreign key with a referenced table which does not have a primary key for matching columns raises an error:

DES> :-fk(p,[a],q,[b])

Error: Referenced column list q.[b] is not a primary key.

DES> :-pk(q,[b])

DES> :-fk(p,[a],q,[b])

The same constraint cannot be reasserted:

DES> :-fk(p,[a],q,[b])

Error: Trying to reassert an existing constraint.

DES> /dbschema

Info: Table(s):

* p(a:int)

- FK: p.[a] -> q.[b]

* q(b:int)

- PK: [b]

Info: No views.

DES> /assert p(1)

Error: Foreign key violation p.[a]->q.[b]

when trying to insert: p(1)

DES> /assert q(1)

DES> /assert p(1)

DES> /listing

p(1).

q(1).

Info: 2 rules listed.

Several foreign keys may exist for the same relation:

DES> :-type(p,[a:int])

DES> :-type(q,[b:int])

DES> :-type(r,[a:int,b:int,c:string])

DES> :-pk(p,[a]), pk(q,[b])

DES> :-fk(r,[a],p,[a]), fk(r,[b],q,[b])

DES> /dbschema r

Info: Table:

* r(a:int,b:int,c:string)

- FK: r.[a] -> p.[a]

- FK: r.[b] -> q.[b]

Referenced columns have to match the types of foreign key columns, otherwise an error is raised:

DES> :-fk(r,[c],q,[b])

Error: Type mismatch r.c:string(varchar) <> q.b:number(integer)

A relation already defined with facts or rules is checked for consistency when trying to assert a new foreign key constraint:

DES> :-type(p,[a:int])

DES> :-type(q,[a:int])

DES> /assert p(1)

DES> :-pk(q,[a])

DES> :-fk(p,[a],q,[a])

Error: Foreign key violation p.[a]->q.[a]

Offending values in database: [fk(1)]

Info: Constraint has not been asserted.

So far, this corresponds to the usual behaviour in the relational setting, but foreign keys in this deductive setting can be used not only for extensional relations, but also for intensional ones. This subject is covered in Section 4.1.20, when dealing with limited domain predicates.

4.1.18.6 Functional Dependency

A functional dependency constraint specifies that, given a set of attributes A₁ of a relation R, they functionally determine another set A₂, i.e., each tuple of values of A₁ in R is associated with precisely one tuple of values A₂ in the same tuple of R.

DES> :-fd(p,[a],[c])

Error: Relation p has not been typed yet.

DES> :-type(p,[a:int,b:int])

DES> :-fd(p,[a],[c])

Error: Unknown column c.

DES> :-fd(p,[a],[b])

DES> /dbschema p

Info: Table:

* p(a:int,b:int)

- FD: [a] -> [b]

By asserting the fact p(1,2), it must hold that any other tuple with 1 in its first attribute must have the value 2 in its second attribute.

DES> /assert p(1,2)

DES> /assert p(1,3)

Error: Functional dependency violation p.[a]->p.[b]

in table p(a,b)

when trying to insert: p(1,3)

Witness tuple : p(1,2)

Several functional dependency constraints can be imposed on a given relation. They can be deleted either with the command drop_ic or when an SQL DROP TABLE or DROP DATABASE statements are issued.

Trivial functional dependencies are rejected:

DES> :-fd(p,[a],[a])

Warning: Trivial functional dependency. Not asserted.

A relation already defined with facts or rules is checked for consistency when trying to assert a new functional dependency constraint:

DES> :-type(p,[a:int,b:int,c:int])

DES> /assert p(1,1,1)

DES> /assert p(1,2,3)

DES> :-fd(p,[a],[c])

Error: Functional dependency violation p.[a]->p.[c]

Offending values in database: [fd(1,1,1),fd(1,2,3)]

Info: Constraint has not been asserted.

4.1.18.7 User-defined Integrity Constraints

Users can also define their own integrity constraints. A user-defined integrity constraint is represented with a rule without head. The rule body is an assertion that specifies inconsistent data, i.e., should this body can be proved, an inconsistency is detected and reported to the user.

Declaring such integrity constraints implies to change your mind w.r.t. usual consistency constraints as domain constraints in SQL. For instance, to specify that a column c of a table t can take values between two integers one can use the SQL clause CHECK in the creation of the table as follows:

CREATE TABLE t(c INT CHECK (c BETWEEN 0 AND 10));

In contrast, in Datalog you can submit the following constraints:

DES> :-type(t,[c:int])

DES> :-t(X),(X<0;X>10)

Notice that the rule body succeeds for values in t out of the interval [0,10]. So, an integrity constraint specifies unfeasible values rather than feasible. Also note that whilst several predefined constraints are allowed in a constraint, only one user-defined integrity constraint is allowed. A couple of assertions to show the behaviour of the above example follow:

DES> /assert t(0)

DES> /assert t(11)

Error: Integrity constraint violation.

ic(X) :-

t(X),

X < 0

;

X > 10.

Offending values in database: [ic(11)]

Note that to be able to interpret that offending values, the integrity constraint is shown as a rule defining a new predicate ic, where the rule's head has as many variables as relevant variables in the constraint. Then, offending values are encapsulated in the meaning of the constraint relation ic.

A rule body of a constraint is any valid rule body, i.e., goals in constraints can refer to other user-defined or built-in predicates as well, including negation, aggregates, etc. Let's consider the following session, in which we are interested in specifying a directed tree (a connected graph with no cycles):

DES> /verbose on

Info: Verbose output is on.

DES> /consult paths

Info: Consulting paths...

edge(a,b).

edge(a,c).

edge(b,a).

edge(b,d).

path(X,Y) :-

path(X,Z),

edge(Z,Y).

path(X,Y) :-

edge(X,Y).

end_of_file.

Info: 6 rules consulted.

Info: Computing predicate dependency graph...

Info: Computing strata...

DES> :-path(X,X)

Info: Parsing query...

Info: Constraint successfully parsed.

Info: Checking user-defined integrity constraint over database.

path(X,X).

Info: Computing predicate dependency graph...

Info: Computing strata...

Error: Integrity constraint violation.

ic(X) :-

path(X,X).

Offending values in database: [ic(b),ic(a)]

Info: Constraint has not been asserted.

The constraint :-path(X,X) specifies that a path from a node to itself is not allowed. As the consulted program contains a cycle involving nodes a and b, the constraint is violated and therefore it is not asserted. Offending values are listed (in this case, all the values involved in any cycle; you can try out other edges and see the outcome).

Another use is to first specify the constraint and then a graph. However, don't be tempted to submit the constraint and consult the program: the constraint will be removed since consulting a program amounts to erase the existing database, including user-defined integrity constraints. Instead, use the /reconsult command:

DES> /verbose on

Info: Verbose output is on.

DES> /cd examples

Info: Current directory is:

c:/des/des6.8/examples/

DES> :-path(X,X)

Info: Parsing query...

Info: Constraint successfully parsed.

Info: Checking user-defined integrity constraint over database.

path(X,X).

Info: Computing predicate dependency graph...

Warning: Undefined predicate(s): [path/2]

Info: Computing strata...

DES> /reconsult paths

Info: Consulting paths...

edge(a,b).

edge(a,c).

edge(b,a).

edge(b,d).

Info: Checking user-defined integrity constraint over database.

path(X,X).

Info: Computing predicate dependency graph...

Info: Computing strata...

path(X,Y) :-

path(X,Z),

edge(Z,Y).

Info: Checking user-defined integrity constraint over database.

path(X,X).

Info: Computing predicate dependency graph...

Info: Computing strata...

Error: Integrity constraint violation.

ic(X) :-

path(X,X).

Offending values in database: [ic(b),ic(a)]

path(X,Y) :-

edge(X,Y).

File : c:/des/des6.8/examples/paths.dl

Lines: 10,10

end_of_file.

Info: 5 rules consulted.

Info: Computing predicate dependency graph...

Info: Computing strata...

Note that the first rule for path is not rejected because in the already consulted program it is still consistent w.r.t. to the constraint. However, trying to add the second rule for path makes it infeasible, so it is rejected. Now, only 5 rules have been asserted. If the file was not included the third fact for edge, then it would be accepted as a valid tree. Again, trying to insert such a tuple, after such a program is consulted, raises an error:

DES> /assert edge(d,a)

Info: Checking user-defined integrity constraint over database.

path(X,X).

Info: Computing predicate dependency graph...

Info: Computing strata...

Error: Integrity constraint violation.

ic(X) :-

path(X,X).

Offending values in database: [ic(a),ic(b),ic(d)]

Observe that since the path relation is now complete, all the nodes in the cycle are displayed (a, b, and c).

The considered constraint is not yet enough to ensure a directed tree defined by edge facts. Two conditions remain: First, a given node cannot have more than one incoming edge, and, second, a tree must be a connected graph. If the first condition is imposed, it suffices for the second to check that the number of nodes is the number of edges plus 1. So:

DES> /assert node(N):-edge(N,A);edge(A,N)

Info: Computing predicate dependency graph...

Info: Computing strata...

Info: Rule asserted.

DES> :-count(edge(A,B),Es), count(node(N),Ns), D is Ns-Es, D\=1.

Info: Parsing query...

Info: Constraint successfully parsed.

Info: Computing predicate dependency graph...

Info: Computing strata...

Info: Checking user-defined integrity constraint over database.

count(edge(A,B),Es),

count(node(N),Ns),

D is Ns - Es,

D \= 1.

Info: Computing by stratum of [edge(A,B),node(A)].

Info: Computing predicate dependency graph...

Info: Computing strata...

DES> /assert edge(e,f) % An unconnected component

Info: Checking user-defined integrity constraint over database.

count(edge(A,B),Es),

count(node(N),Ns),

D is Ns - Es,

D \= 1.

Info: Computing by stratum of [edge(A,B),node(A)].

Info: Computing predicate dependency graph...

Info: Computing strata...

Error: Integrity constraint violation.

ic(Es,Ns,D) :-

count(edge(A,B),Es),

count(node(N),Ns),

D is Ns - Es,

D \= 1.

Offending values in database: [ic(4,6,2)]

User-defined integrity constraints are dropped when abolishing the database or consulting a file.

4.1.18.8 Dropping Constraints

Any predefined or user-defined integrity constraint can be dropped with the command /drop_ic (see Section 5.17.1) followed by the constraint to be dropped with the same syntax as its declaration.

4.1.18.9 Caveats

Either by consulting a program, or by dropping the current database, or by abolishing the database, all integrity constraints are removed, including SQL table and view definitions.

As rules are not checked for predefined constraints, situations like the following may occur:

DES> create table t(a int primary key)

DES> insert into t values (1)

Info: 1 tuple inserted.

DES> /assert t(X):-X=1

DES> /duplicates on

DES> t(X)

{

t(1),

t(1)

}

Info: 2 tuples computed.

Nonetheless, if you also want to monitor rules, you can otherwise use a user-defined constraint such as:

DES> create table t(a int)

DES> insert into t values (1)

Info: 1 tuple inserted.

DES> :-group_by(t(X),[X],C=count(X),C>1),C>1

DES> /assert t(X):-X=1

Error: Integrity constraint violation.

ic(X,C) :-

group_by(t(X),[X],(C = count(X),C > 1)),

C > 1.

Offending values in database: [ic(1,2)]

Error: Asserting rules due to integrity constraint violation.

4.1.19 Restricted Predicates

The meaning of a predicate can be limited by defining restricting rules. A restricting rule is a rule for which its head is a restricting atom (a regular atom preceded by a minus sign, cf. Section 4.1.2). The meaning of a predicate is then the tuples deduced from its regular rules minus the tuples deduced from its restricting rules. A restricting rule does not represent true negation, but a means to discard positive tuples from the meaning of a predicate. So, both p and -p can occur in a program with no contradiction. Computing a restricted predicate p can be seen as follows: First, compute its meaning P⁺ from its regular rules. Then, compute the meaning P^- of its restricting rules and build the meaning for p as the difference P⁺ - P^-. Adding a restricting rule for a predicate involves to add a negative dependency q-p (cf. Section 4.1.8) from any other predicate q depending on p.

Let’s consider the following number generator:

DES> /assert p(X) :- X=1 ; p(Y), Y<10, X=Y+1.

DES> p(X)

{

p(1),

p(2),

...

p(10)

}

Info: 10 tuples computed.

Even numbers can be obtained by adding the following restricting rule:

DES> /assert -p(X) :- p(X), X mod 2 = 1.

DES> p(X)

{

p(2),

p(4),

p(6),

p(8),

p(10)

}

Info: 5 tuples computed.

Note that you can also request the meaning of the restricted part of the predicate. In general, a restricting atom can occur anywhere an atom is allowed, and, in particular, in a top-level query, as follows:

DES> -p(X)

{

-(p(1)),

-(p(3)),

-(p(5)),

-(p(7)),

-(p(9))

}

Info: 5 tuples computed.

Restricting rules can also be recursive. The following example looks also for even numbers:

DES> /assert -p(X) :- X=1 ; -p(Y), X=Y+2, X<10.

DES> p(X)

{

p(2),

p(4),

p(6),

p(8),

p(10)

}

Info: 5 tuples computed.

As a caveat, note that the complete meaning of a predicate can be removed if a regular atom is used incorrectly, as in:

DES> /assert -p(X) :- p(X)

DES> p(X)

{

}

Info: 0 tuples computed.

The rule -p(X) :- -p(X) represents a tautology.

All duplicates in the meaning of a restricted predicate are removed for a single tuple in the meaning of the restricting rules. For example:

DES> /assert p(1)

DES> /assert p(2)

DES> /assert -p(1)

DES> /duplicates on

DES> p(X)

{

p(2),

p(2)

}

Info: 2 tuples computed.

Restricted predicates are also useful for hypothetical reasoning, a subject covered in Section 4.1.21.

4.1.20 Limited Domain Predicates

Domains corresponding to predefined types are infinite in general. For instance, integer has associated the (non-limited) domain of integers (..., -1, 0, 1, ...). However, predicates with foreign key declarations on a set of its arguments have the domains for these arguments limited to those of the referenced predicates' primary keys. For example, let's consider the following session:

DES> :-type(my_date(day:int,month:int,year:int)),
       type(day_dom(day:int)),
       pk(day_dom,[day]),
       fk(my_date,[day],day_dom,[day]).

The argument day in my_date can only take values in the argument of day_dom, which can be defined as:

day_dom(1).

day_dom(2).

day_dom(3).

day_dom(4).

day_dom(5).

day_dom(6).

day_dom(7).

So, trying to assert an incorrect argument for day in my_date would raise an error:

DES> /assert my_date(8,10,2015)

Error: Foreign key violation my_date.[day]->day_dom.[day]

when trying to insert: my_date(8,10,2015)

Analogously, the domains for months and years can be constrained in this way. This example mimics the behaviour of a relational database but, further, in this deductive setting, the domain of the days can be intensionally defined as follows:

day_dom(X) :- X=1 ; day_dom(Y), Y<7, X=Y+1

In addition, the relation for which the functional dependency is imposed can be an intensional relation as well. Let's consider this other example:

DES> :-type(numbers(a:int)), type(even(a:int)),

pk(even,[a]), fk(numbers,[a],even,[a]).

Here, the predicate numbers can only take values in the semantics of even due to the foreign key constraint. Let's confirm this with a predicate numbers as a number generator from 1 to 10, and even as an even number generator from 0 to 20:

DES> /assert numbers(X):-X=1;numbers(Y),Y<10,X=Y+1

DES> /assert even(X):-X=0;even(Y),Y<20,X=Y+2

DES> even(X)

{

even(0),

even(2),

...

even(20)

}

Info: 11 tuples computed.

DES> numbers(X)

{

numbers(2),

numbers(4),

numbers(6),

numbers(8),

numbers(10)

}

Info: 5 tuples computed.

Since numbers is limited to have tuples in even, only the even numbers from 2 to 10 are in the meaning of numbers. Looking at the rules in the database, we find the ones for the generator predicates and one restricting rule for numbers:

DES> /listing

-numbers(A) :-

numbers(A),

not even(A).

numbers(X) :-

X=1

;

numbers(Y),

Y<10,

X=Y+1.

even(X) :-

X=0

;

even(Y),

Y<20,

X=Y+2.

Info: 3 rules listed.

This restricting rule limits the possible values that numbers can take by eliminating the tuples in numbers that are not in even. This adds a negative dependency from even to numbers in the PDG:

DES> /pdg
Nodes: [numbers/1,even/1]
Arcs : [numbers/1+numbers/1,
numbers/1-even/1,
even/1+even/1]

Foreign keys, thus, are useful devices to specify domain constraints for relations. In contrast to the relational case, where foreign key constraints can only be applied to tables (the extensional part of the database), here we admit this also for the intensional part of the deductive database. A predicate with all their arguments affected by foreign keys is called here a limited domain predicate.[6]

A limited domain predicate is safe with respect to negation because its domain is finite whenever its referenced predicates are also finite. Then, it is possible to submit an open negated call because the predicate domain is known and the complement of the positive meaning is thus known as well. For example, the following query is safe and returns the expected result:

DES> not numbers(X)

Info: Processing:

answer(X) :-

not numbers(X).

{

answer(0),

answer(12),

answer(14),

answer(16),

answer(18),

answer(20)

}

Info: 6 tuples computed.

The domain of numbers is (0), (2), (4), ... (20) and its positive semantics is defined by the positive program rules as (2), (4), ..., (10). Therefore, the complement of the positive semantics is (0), (12), (14), ..., (20), which is the intended meaning for its negation. Out of curiosity, let's see the restricted part of the predicate numbers:

DES> -numbers(X)

{

-numbers(1),

-numbers(3),

-numbers(5),

-numbers(7),

-numbers(9)

}

Info: 5 tuples computed.

It is not possible to submit a non-ground negated call to this restricted predicate:

DES> not -numbers(X)

Error: not '$p0'(X) might not be correctly computed because of the unrestricted variable: [X]

Warning: This autoview is unsafe because of variable: [X]

because the restricting rules has no limited domain[7]. Still, it is possible to submit ground negated calls as:

DES> not -numbers(0)

Info: Processing:

answer

in the program context of the exploded query:

answer :-

not '$p0'.

'$p0' :-

-numbers(0).

{

answer

}

Info: 1 tuple computed.

DES> not -numbers(1)

Info: Processing:

answer

in the program context of the exploded query:

answer :-

not '$p0'.

'$p0' :-

-numbers(1).

{

}

Info: 0 tuples computed.

Limited domain predicates are also useful for hypothetical reasoning, as shown in the next section.

4.1.21 Hypothetical Queries

Hypothetical queries are a common need in several scenarios, related mainly with business intelligence applications and the like. They are also known as "what-if" queries and help managers to take decisions on scenarios which are somewhat changed with respect to a current state. Such queries are used, for instance, for deciding which resources must be added, changed or removed to optimize some criterion (cost function - also well related to optimization technologies). Hypothetical queries in the database arena are typically used for assumptions w.r.t. a current database instance.

DES includes one form of Hypothetical Datalog queries which may serve to answer several questions. The syntax of an hypothetical query is as follows:

Rule1 /\ ... /\ RuleN => Goal

which means that, assuming that the current database is augmented with the rules Rule1, ..., RuleN, then Goal is computed with respect to this augmented database (each Rulei must be safe; see Section 5.3). Such a query is also understood as a literal in the context of a rule, so that any rule can contain hypothetical goals, as in a :- b => c. In turn, any Rulei can contain hypothetical goals. Variables in Rulei are local to it (i.e., they are neither shared with other rules nor the goal). Moreover, a hypothetical literal does neither share variables with other literals nor the head of the rule in which it occurs. Assumed rules can be either regular or restricting rules.

Borrowing an example from [Bon90][8], we consider an extended and adapted rule-based system for describing university policy: student(S) means that S is a student, course(C) that C is a course, take(S,C) that student S takes course C, and grad(S) that S is eligible for graduation. The extensional database can contain facts as:

student(adam).

student(bob).

student(pete).

student(scott).

student(tony).

course(eng).

course(his).

course(lp).

take(adam,eng).

take(pete,his).

take(pete,eng).

take(scott,his).

take(scott,lp).

take(tony,his).

The intensional database can contain rules as:

grad(S) :- take(S,his), take(S,eng).

A regular query for students that would be eligible to graduate is:

DES> grad(S)

{

grad(pete)

}

Info: 1 tuple computed.

A first hypothetical query for this database asks "If Tony took eng, would he be eligible to graduate?", which can be queried with:

DES> take(tony,eng) => grad(tony)

Info: Processing:

answer :-

take(tony,eng)=>grad(tony).

{

answer

}

Info: 1 tuple computed.

Also, if Pete did not take his, he would not be eligible to graduate (notice the restricting atom, with a preceding minus sign):

DES> -take(pete,his) => grad(S)

Info: Processing:

answer(S) :-

-(take(pete,his))=>grad(S).

{

}

Info: 0 tuples computed.

More than one assumption can be simultaneously stated, as in: "If Tony took eng, and Adam took his, what are the students that are eligible to graduate?"

DES> take(tony,eng) /\ take(adam,his) => grad(S)

Info: Processing:

answer(S) :-

take(tony,eng)/\take(adam,his)=>grad(S).

{

answer(adam),

answer(pete),

answer(tony)

}

Info: 3 tuples computed.

Another query is "Which are the students which would be eligible to graduate if his and lp were enough to get it?":

DES> (grad(S) :- take(S,his), take(S,lp)) => grad(S)

Info: Processing:

answer(S) :-

(grad(S):-take(S,his),take(S,lp))=>grad(S).

{

answer(pete),

answer(scott)

}

Info: 2 tuples computed.

Note that, although S occurs in both the antecedent and the consequent, they are not actually shared, and they simply act as different variables.

Considering also information about course prerequisites as:

pre(eng,lp).

pre(hist,eng).

pre(Pre,Post) :-

pre(Pre,X),

pre(X,Post).

One might wonder whether adding a new prerequisite implies a cycle (so that students cannot fulfil prerequisites at all for the courses in a cycle):

DES> pre(lp,hist)=>pre(X,X)

Info: Processing:

answer(X) :-

pre(lp,hist)=>pre(X,X).

{

answer(eng),

answer(hist),

answer(lp)

}

Info: 3 tuples computed.

The answer includes those nodes in the graph that are in a cycle (i.e., a course becomes a prerequisite of itself).

Following the example for even numbers in Section 4.1.19, and given the regular rule for p is asserted, we can use the following assumption for computing those numbers:

DES> /assert p(X) :- X=1 ; p(Y), Y<10, X=Y+1.

DES> (-p(X) :- p(X), X mod 2 = 1) => p(X)

Info: Processing:

answer(X) :-

(-(p(X)):-p(X),X mod 2=1)=>p(X).

{

answer(2),

answer(4),

answer(6),

answer(8),

answer(10)

}

Info: 5 tuples computed.

4.1.21.1 Hypothetical Queries and Integrity Constraints

Assumptions can be used in combination with any of the features of DES; in particular, integrity constraints. Following the previous example, you can even express it with the aid of integrity constraints. Avoiding cycles can be forced by:

DES> :-pre(X,X)

Then, if you want to list prerequisites assuming pre(lp,hist) as before:

DES> pre(lp,hist)=>pre(X,Y)

Info: Processing:

answer(X,Y) :-

pre(lp,hist)=>pre(X,Y).

Error: Integrity constraint violation.

ic(X) :-

pre(X,X).

Offending values in database: [ic(lp),ic(eng),ic(hist)]

Info: The following rule cannot be assumed:

pre(lp,hist).

{

answer(eng,lp),

answer(hist,eng),

answer(hist,lp)

}

Info: 3 tuples computed.

So, the system informs that there is an inconsistency when trying to assert such offending fact (pre(lp,hist)), which makes prerequisites to form a cycle (as shown in the offending value list [ic(lp),ic(eng),ic(hist)]). The system informs about the rules that cannot be assumed but continues its processing. This is also useful to know the result for the admissible assumptions. Note that, in general, offending facts can be a subset of the meaning of an assumed rule in the context of the current database. To illustrate this, let's consider the following program for throwing a coin:

% Tails win:

:- win, heads.

win :- heads ; tails.

Predicate win states that one wins if either heads or tails are got, and the constraint states that you have to get tails to win. Then, the following hypothetical goal states whether assuming heads or tails leads to win.

DES> heads /\ tails => win

Info: Processing:

answer :-

heads/\tails=>win.

Error: Integrity constraint violation.

ic :-

win,

heads.

Info: The following rule cannot be assumed:

heads.

{

answer

}

Info: 1 tuple computed.

As it is informed, heads cannot be assumed in order to win.

4.1.21.2 Hypothetical Queries and Duplicates

Duplicates can also be used along computations involving assumptions. Let's consider a variation of the classical Nim game, known as the subtraction game. Here, there is only one heap from which a player can take one or two tokens in his turn. A player wins if there is only one token in other player's turn (misère game). This can be formulated with the next program:

win_nim :-

take => one_left.

win_nim :-

take/\take => one_left.

win_nim :-

take => enough, win_nim.

win_nim :-

take/\take => enough, win_nim.

one_left :-

total(N),

count(take,C),

N-C=1.

enough :-

total(N),

count(take,C),

N-C>0.

total(4).

The predicate win_nim states that I win if I take one or two tokens and there is one left for you. Otherwise, if there are enough tokens (after taking one or two) to continue playing, then let's see if I can win.

Each occurrence of take in the left hand side of => is an assumed fact that can be counted if duplicates are enabled (otherwise, the counting will be 0 - if there is no one - or 1 - if there is one or more, as duplicates are discarded). So, the predicate one_left determines whether there is exactly one token left, and enough determines if there is one token left at least. The predicate total states the total number of tokens which are available for a game.

For more than 2 tokens there is always both winning and loosing paths for the player in turn. For exactly 2 tokens there is no loosing path (because the player cannot take 2 as the heap would be empty). And for 1 token, there is no winning path:

DES> win_nim

{

}

Info: 0 tuples computed.

Note that enabling duplicates can lead to non-terminating queries. For instance, let's consider:

DES> /duplicates off

DES> /assert p:-p=>p

DES> p

{

}

Info: 1 tuple computed.

DES> /duplicates on

DES> p

... Non-terminating

Here, the hypothesis p is recursively added to the database with no end as there is no terminating condition.

4.1.21.3 Hypothetical Queries and Negation

Implication can also be used in conjunction with negation. Let's consider the following example, which states flight links (flight/2 for origin and destination) between airports (airport}), and where flight travels (flight_travel/2 also for origin and destination) are possible if involved airports are not closed:

flight_travel(X,Y) :-

flight(X,Y),

not closed(X),

not closed(Y).

flight_travel(X,Y) :-

flight_travel(X,Z),

flight_travel(Z,Y).

flight(a,b).

flight(b,c).

flight(c,d).

A regular query for consulting possible travels is:

DES> flight_travel(X,Y)

{

flight_travel(a,b),

flight_travel(a,c),

flight_travel(a,d),

flight_travel(b,c),

flight_travel(b,d),

flight_travel(c,d)

}

Info: 6 tuples computed.

Assuming that airport b is closed, we ask for the possible travels with this assumption:

DES> closed(b) => flight_travel(X,Y)

Info: Processing:

answer(X,Y) :-

closed(b)=>flight_travel(X,Y).

{

answer(c,d)

}

Info: 1 tuple computed.

where negated calls to closed/1 occur in the first rule of flight_travel/2.

We can also ask for the opposite: Which are the flight travels which are not possible for that assumption:

DES> flight_travel(X,Y),(closed(b)=>not flight_travel(X,Y))

Info: Processing:

answer(X,Y) :-

flight_travel(X,Y),

closed(b)=>not flight_travel(X,Y).

{

answer(a,b),

answer(a,c),

answer(a,d),

answer(b,c),

answer(b,d)

}

Info: 5 tuples computed.

Note that, first, we ask for all the possible flights (first goal flight_travel(X,Y)) and, then, we restrict to those flights which are not possible under the assumption. The first goal is needed for the query to be safe. Recall that Datalog with negation is not constructive (variables in the negated goal are not instantiated unless their values are already provided by a positive goal), and answers must be ground. Note, also, that the meaning of the first occurrence of goal flight_travel(X,Y) in this last query is the very same as the meaning of the first query. However, the meaning of the second occurrence of that goal restricts the answer to those flights for which involved airports are not closed because of the assumption.

Another alternative for such assumption would be to discard those flights with either its origin or destination at airport b, and then assuming the transitive closure of the relation flight with travel:

DES> (-flight(X,Y):-flight(X,Y),(X=b;Y=b)) /\

( travel(X,Y):-flight(X,Y);flight(X,Z),travel(Z,Y)) =>

travel(X,Y).

Info: Processing:

answer(X,Y) :-

(-(flight(X,Y)):-flight(X,Y),(X=b;Y=b))/\(travel(X,Y):-flight(X,Y);flight(X,Z),travel(Z,Y))=>travel(X,Y).

{

answer(c,d)

}

Info: 1 tuple computed.

But notice that this is not equivalent to overloading the relation flight with its transitive closure, as follows:

DES> (-flight(X,Y):-flight(X,Y),(X=b;Y=b)) /\

( flight(X,Y):-flight(X,Y);flight(X,Z),flight(Z,Y)) =>

flight(X,Y).

Info: Processing:

answer(X,Y) :-

(-(flight(X,Y)):-flight(X,Y),(X=b;Y=b))/\(flight(X,Y):-flight(X,Y);flight(X,Z),flight(Z,Y))=>flight(X,Y).

{

answer(a,c),

answer(a,d),

answer(c,d)

}

Info: 3 tuples computed.

Indeed, for computing the meaning of flight, first the meaning of its regular rules are computed (which deliver its transitive closure including flights involving airport b), and then, the meaning of its restricting rules, therefore removing from the transitive closure those flights leaving from or arriving at airport b.

4.1.22 Fuzzy Datalog

Datalog implements Logic Programming with crisp relations, as opposed to uncertainty as found in some real-world applications that require approximate relations. Relations between objects cannot be always precisely specified. As an example, think of the relations near, cold, and tall. Usually, in a fuzzy setting they are given an approximation degree δ for a given pair of related objects, stating that the first one is related to the second one with confidence δ.

Fuzzy theory comes as early as [Zade65] and it was applied to logic programming in the seventies, with the seminal work of R. Char Tung Lee [Lee72]. A relevant work [Sess02] introduces the notion of syntactic similarity and a weak SLD-resolution for fuzzy logic programs. In DES, we follow the approach of Bousi~Prolog (BPL) [JR10], which modifies the classical resolution procedure by replacing the unification algorithm by a fuzzy unification one, based on proximity relation (a broader kind of binary fuzzy relations that subsumes similarity relations). In addition, we extend it with approximation degrees for rules (known as graded rules).

Fuzzy Datalog in DES is a new system mode that must be enabled with the command:

DES> /system_mode fuzzy

FDES>

which changes the default prompt DES> to FDES>. This command resets the database.

4.1.22.1 Fuzzy Relations and Approximation Degrees

[JR10] defines a proximity/similarity binary relation ~ relating either two predicates or two function symbols. Here, function symbols are restricted to constant symbols because DES does not allow user compound terms as data. Fuzzy relations are extensionally defined by proximity equations, and intensionally by properties (cf. Section 4.1.22.2). For example, the proximity equation:

so_much ~ very_much = 0.6.

between the constants so_much and very_much states that they are similar with a degree of 0.6. For this relation, (by default) it is intensionally defined that a symbol is similar to itself with a degree of 1.0 (reflexivity). Also that very_much ~ so_much = 0.6 (symmetry), cf. Section 4.1.22.2.

By taking an example from that work, let us consider the following program (in the distribution directory examples/fuzzy/cookies.dl):

% Facts

likes(john, cookies, a_little).

likes(mary, cookies, very_much).

likes(peter, cookies, so_much).

likes(paul, cookies, does_not).

% Rules

buy(X,P) :- likes(X, P, very_much).

For the query buy(X,cookies) about people prone to buying cookies, a classical Datalog system (eliding proximity equations) would return the single answer buy(mary, cookies). However, john and peter are also reasonable candidates to buy cookies from a real-world interpretation of the relation likes. Hence, if we are looking for a flexible query answering procedure, more approximate to the real-world setting, john and peter should appear as answers. So, by adding the next proximity equations:

% Proximity Equations relating Constants

does_not ~ a_little = 0.5.

a_little ~ very_much = 0.2.

does_not ~ so_much = 0.1.

so_much ~ very_much = 0.6.

a_little ~ so_much = 0.4.

then, the query above would return these answers:

FDES> buy(X,cookies)

Info: Processing:

answer(X) :-

buy(X,cookies).

{

answer(mary),

answer(peter)with 0.6,

answer(john)with 0.4,

answer(paul)with 0.4

}

Info: 4 tuples computed.

Any fuzzy query is considered as an autoview (cf. Section 4.1.6), and the answer is built with the relevant variables in the query. In this example, X is the relevant variable for which matching values are looked for in the database. Thus, while mary is surely expected to buy cookies (i.e., with an approximation degree of 1.0 -an approximation degree which is omitted in the output), both john and paul would buy cookies with an approximation degree of 0.4, and peter with 0.6 (denoted with the keyword with).

As a second way to state approximation degrees, proximity equations can be stated between predicates as well. To this end, each predicate symbol in an equation must be accompanied by its arity. The next example (in the distribution directory examples/fuzzy/sizes.dl) classifies people on their height as tall, medium and short, specifying that a medium (resp. short) person can be understood as a tall (resp. medium) one with a degree of 0.4:

:- t_norm(product).

tall/1 ~ medium/1 = 0.4.

medium/1 ~ short/1 = 0.4.

tall(magic_johnson).

tall(paul).

medium(john).

medium(ava).

short(bob).

short(eve).

Looking for tall people, we get:

FDES> tall(X)

Info: Processing:

answer(X) :-

tall(X).

{

answer(magic_johnson),

answer(paul),

answer(ava)with 0.4,

answer(john)with 0.4,

answer(bob)with 0.16,

answer(eve)with 0.16

}

Info: 6 tuples computed.

Notice that the assertion :- t_norm(product) in this program selects a specific t-norm. A t-norm (represented with the operator D) is the extension of the first-order logic conjunction for the fuzzy setting, and applies to approximation degrees. Usual t-norms include: minimum (Göedel), product and Łukasiewicz, where the first one is the default in DES. Also note that the answer is ordered first by approximation degree, and then, by tuples.

For the last example, it turns out to be more appropriate a product t-norm because, by transitivity, if the approximation degree between tall and medium is 0.4, and between medium and short is 0.4, then the approximation degree between tall and short is computed as 0.4 D_product 0.4 = 0.16 (the minimum t-norm would return 0.4, which does not seem appropriate in this case).

The third and last way to express approximation degrees is for rules in predicates. Each rule in a predicate may receive a degree to express its confidence in the context of the predicate. Such rules are known as graded rules. As an example in the stock market, let us consider the following rules (in the distribution directory examples/fuzzy/stock.dl):

stock_up(google) with 0.9.

stock_up(greek_bonds) with 0.2.

shareholder(paul,google).

shareholder(paul,greek_bonds).

keep_stock(Name,Stock) :-

shareholder(Name,Stock),

stock_up(Stock).

where google stock is expected to raise with a degree of 0.9 and greek_bonds with 0.2. Then, the query keep_stock(Name,Stock) would return the stocks that are profitable to keep for each shareholder:

FDES> keep_stock(N,S)

Info: Processing:

answer(N,S) :-

keep_stock(N,S).

{

answer(paul,google)with 0.9,

answer(paul,greek_bonds)with 0.2

}

Info: 2 tuples computed.

In this example, it might be wise to set a degree threshold for the outcome, which can be done with a l-cut value. For example, we can be interested in keeping stocks with a degree greater than or equal to 0.8:

FDES> /lambda_cut 0.8

FDES> keep_stock(Name,Stock).

Info: Processing:

answer(N,S) :-

keep_stock(N,S).

{

answer(paul,google)with 0.9

}

Info: 1 tuple computed.

The command /lambda_cut sets this threshold, which can be alternatively stated in a program as an assertion, with :- lambda_cut(0.8).

Contrary to proximity equations, a graded rule is not overwritten by the same rule but with a different grade, and the prevailing grade is the maximum when fuzzy answer subsumption is enabled. For example:

FDES> /assert stock_up(google) with 0.6

FDES> /listing stock_up(google)

stock_up(google) with 0.6.

stock_up(google) with 0.9.

Info: 2 rules listed.

FDES> stock_up(google)

Info: Processing:

answer :-

stock_up(google).

{

answer with 0.9

}

Info: 1 tuple computed.

Both rules are still in the database, as it can be checked by either listing the rules or disabling fuzzy answer subsumption:

FDES> /listing stock_up(google)

stock_up(google) with 0.6.

stock_up(google) with 0.9.

Info: 2 rules listed.

FDES> /fuzzy_answer_subsumption off

FDES> stock_up(google)

Info: Processing:

answer :-

stock_up(google).

{

answer with 0.9,

answer with 0.6

}

Info: 2 tuples computed.

4.1.22.2 Fuzzy Relations and Properties

A crisp binary relation R relates values of two domains D₁ and D₂ as a subset of D₁ × D₂, so it can be specified as a characteristic function as well:

For a binary fuzzy relation R: D × D, this function admits values in the interval [0,1] and, as classical relations, may enjoy several properties, including:

· Reflexive: R(x,x) = 1 for all x Î D.

· Symmetric: R(x,y) = R(y,x) for all x,y Î D.

· Transitive: R(x,z) ≥ R(x,y) D R(y,z) for all x,y,z Î D.

One can extensionally specify fuzzy relations with a set of proximity equations, and properties that intensionally provide all the tuples in its meaning (all the entries that define the fuzzy relation). This meaning is computed as a D-closure (also referred to as t-closure), which is somewhat similar to a transitive closure by replacing the conjunction by a t-norm operator D.

Let us consider the following example:

FDES> /abolish

FDES> /assert a~b=0.4

FDES> /assert b~c=0.3

These two proximity equations define the relation ~, which by default has attached the properties reflexive, symmetric and transitive, and the t-norm Gödel. The complete meaning of the fuzzy relation can be inspected with the following command:

FDES> /list_t_closure

a~a=1.0.

a~b=0.4.

a~c=0.3.

b~a=0.4.

b~b=1.0.

b~c=0.3.

c~a=0.3.

c~b=0.3.

c~c=1.0.

Info: 9 equations listed.

where equations such as a~a=1.0 are deduced by reflexivity, b~a=0.4 by symmetry, and a~c=0.3 by transitivity. So, users are not obliged to specify the equations that are intensionally deduced by properties.

Asserting an proximity equation between two symbols for which there is already another equation results in overwritting the existing equation:

FDES> /abolish

FDES> /assert a~b=0.4

FDES> /assert a~b=0.3

FDES> /list_fuzzy_equations

a~b=0.3.

Info: 1 equation listed.

Typical relations are collected in the following table with respect to their properties:

Relation	Reflexive	Symmetric	Transitive
Strict Order	no	no	yes
Partial Order	yes	no	yes
Proximity	yes	yes	maybe
Similarity	yes	yes	yes

Properties (reflexive, symmetric and transitive) for the (default) relation ~ can be stated with the command:

/fuzzy_relation ~ [comma-separated property names]

However, the default fuzzy relation ~ is not intended to be modified because it plays a fundamental role in the so-called weak unification recalled in next subsection (if changed, unexpected results may occur). Instead, one can define arbitrary fuzzy relations, as for example the proximity relation near, which can be specified as follows:

/fuzzy_relation near [reflexive,symmetric]

You can specify as many fuzzy relations as needed, which can coexist with the default ~. We speak of relationship equations referring to equations of user-defined fuzzy relations. But note that weak unification only works for this relation.

Properties can be consulted with the same command with no arguments:

FDES> /fuzzy_relation

Info: Properties of '~' are [reflexive,symmetric,transitive]

As already introduced, the operator D represents the t-norm, where typical ones and included in DES are:

· Minimum/Göedel (min/goedel): x D y = min(x,y)

· Product (product): x D y =x∙y

· Łukasiewicz (luka/lukasiewicz): x D y = max(0,x+y-1)

· Hamacher Product (hamacher):

· Nilpotent Minimum (nilpotent):

These t-norms can be stated and consulted with the command:

/t_norm ~ t-norm_name

As a matter of portability with BPL programs, the t-norm can be stated in the command /fuzzy_relation as a parameter (between parentheses) of the transitive property (to this end, also the command synonym /fuzzy_rel is provided). For example:

FDES> /fuzzy_relation ~ [reflexive,symmetric,transitive(product)]

Submitting the goal X~Y in the last example results in obtaining the whole meaning of the relation ~:

FDES> X~Y

Info: Processing:

answer(X,Y) :-

X~Y.

{

answer(a,a),

answer(b,b),

answer(c,c),

answer(a,b)with 0.4,

answer(b,a)with 0.4,

answer(a,c)with 0.3,

answer(b,c)with 0.3,

answer(c,a)with 0.3,

answer(c,b)with 0.3

}

Info: 9 tuples computed.

Note that this result is valid for a l-cut less or equal to 0.3. If the l-cut value of 0.8 which was specified in an earlier example remains, then the answer in this case consists only of the first three answers. If you want to be sure of obtaining the whole meaning, use the command /list_t_closure instead.

Replacing a variable by any of the constants in the fuzzy relation results in an appropriate filtering of the relation, as in:

FDES> X~a

Info: Processing:

answer(X) :-

X~a.

{

answer(a),

answer(b)with 0.4,

answer(c)with 0.3

}

Info: 3 tuples computed.

where the outcome shows that the constant a is related to itself with an approximation degree d of 1.0, with b with d of 0.4, and with c with d of 0.3.

By removing both the reflexive and transitive properties, this goal now outputs:

FDES> /fuzzy_relation ~ [symmetric]

FDES> X~a

Info: Processing:

answer(X) :-

X~a.

{

answer(b)with 0.4

}

Info: 1 tuple computed.

If the symmetric property would also be removed, no result tuple would be output in this last query. But recall that unexpected results can occur with respect to the weak unification and resolution procedures if the default properties of ~ are changed. So, if other properties are needed, better define a new fuzzy relation.

4.1.22.3 Weak Unification and Weak Unification Operator

Classical logic programming unification is replaced by weak unification in which syntactically-different symbols may match with a certain approximation degree. In Datalog, only constants and variables can be unified because it implements function-free first-order logic. In the fuzzy setting, two constants are unifiable is they are similar with an approximation degree greater than or equal to the current l-cut.

Weak unification implicitly occurs when matching query (or goal) arguments, as in the following example (taken from Section 4.1.22.1): likes(X,P,very_much). Also, whereas the operator = implements classical (crisp) equality, the operator ~~ implements an explicit fuzzy weak unification. The following are examples of explicit weak unification between Datalog terms (either variables or constants):

FDES> % Next goal delivers an approximation degree 0.4 because it was specified with a proximity equation

FDES> a~~b

Info: Processing:

answer :-

a~~b.

{

answer with 0.4

}

Info: 1 tuple computed.

FDES> % Due to the reflexive property, the following is true with an approximation degree 1.0 (which is omitted in the displays)

FDES> a~~a

Info: Processing:

answer :-

a~~a.

{

answer

}

Info: 1 tuple computed.

FDES> % Due to the transitive property, the following is true with an approximation degree 0.3

FDES> a~~c

Info: Processing:

answer :-

a~~c.

{

answer with 0.3

}

Info: 1 tuple computed.

FDES> % Weak unification provides a representative of unifiers:

FDES> X~~a

Info: Processing:

answer(X) :-

X~~a.

{

answer(a)

}

Info: 1 tuple computed.

Note that the result of a weak unification is a representative of the class of all possible weak most general unifiers. In the last example, in addition to X/a with 1, other unifiers include X/b with 0.4 and X/c with 0.3. Notably, the representative is the best (w.r.t. the computed unification degree) among the possible weak most general unifiers.

Alternatives for different degrees are only possible for alternative program rules. For example, given the same proximity equations, we can add the rules p(a), p(b) and p(c)to the database. Then:

FDES> p(a)

Info: Processing:

answer :-

p(a).

{

answer,

answer with 0.4,

answer with 0.3

}

Info: 3 tuples computed.

4.1.22.4 Fuzzy Expressions

A fuzzy expression Term1 FuzzyRelationOperator Term2 returns the approximation degree between Term1 and Term2, where FuzzyRelationOperator can be ~ or any other user-defined fuzzy relation operator. Evaluating a fuzzy expression returns its approximation degree. Thus, a fuzzy expression can occur at any point in an expression for which a numeric value is expected. For instance, following the previous example:

FDES> 1-a~b>0.2

Info: Processing:

answer :-

1-sim(~,a,b)>0.2.

{

answer

}

Info: 1 tuple computed.

4.1.22.5 Accessing Approximation Degrees

By default, approximation degrees are automatically displayed along answers. They are hidden from the user when, in its compiled form, each goal in either a conjunctive query or rule body contains an approximation degree. This degree is internally used to build the outcome approximation degree, as seen in previous example.[9] Sometimes, it is needed to access its value to reasoning in terms of it. To this end, we provide the metapredicate approx_degree/2, which returns in its second argument the approximation degree of the goal in its first argument.

As an application example, this can be used to emulate a dynamic l-cut in which the computation can proceed if it is above a (dynamic) value. The following example shows this, given the same equations as before:

FDES> approx_degree(X~Y,D), D>0.3

Info: Processing:

answer(X,Y,D) :-

approx_degree(X~Y,D),

D>0.3.

{

answer(a,a,1.0),

answer(a,b,0.4),

answer(b,a,0.4),

answer(b,b,1.0),

answer(c,c,1.0)

}

Info: 5 tuples computed.

4.1.22.6 An Application: Recommender Systems

This application is reproduced from [JS18]. Recommender systems are an effective way to assist people by offering advice on finding suitable products and services to facilitate online decision-making [CW14]. Subjective information (such as how a person evaluates a product or service, and how another person trusts an opinion depending on its confidence) can be specified with linguistic, fuzzy information. This idea is applied to modelling a small recommender system for restaurants in Madrid.

We consider people interested in asking questions relating the location of the restaurant with respect to its own location, the quality of the restaurant in terms of other's opinions, and the type of food served. Thus, we can distinguish two fuzzy relations: A proximity relation near (reflexive and symmetric) for representing walking distances, and a predefined similarity relation ~ (which is, in addition, transitive) for representing quality degrees. These are defined in the next code excerpt (located in the distribution directory at examples/fuzzy/recommender.dl).

:-fuzzy_relation(near,[reflexive,symmetric]).

sol near callao = 0.6.

sol near cruz = 0.5.

callao near plaza_españa = 0.4.

:-fuzzy_relation(~,[reflexive,symmetric,transitive]).

plain~good=0.5.

good~very_good=0.5.

very_good~excellent=0.3.

The first assertion fuzzy_relation defines the operator near as a proximity relation for a walking distance with the reflexive and symmetric properties. Analogously, a similarity relation ~ is explicitly defined next (in fact, its assertion can be removed from the program since it is defined as such by default).

A fuzzy predicate confidence/1 defines the degree of reliability (in the opinion) which a given type of user deserves. For example, a local guide is assumed to be a person including serious comments in the database where normal and casual users may not, all of them with different confidences:

confidence(local_guide) with 0.9.

confidence(normal_user) with 0.5.

confidence(casual_user) with 0.3.

Next, several relations are defined with facts in the database: The relation restaurant/3 relates the name of a restaurant, its location, and food served. Users and their types are related in the relation user/3. Finally, user comments are represented in the relation comment/3 relating user, restaurant, and comment.

restaurant(don_oso,cruz,burguer).

restaurant(rodilla,callao,snacks).

restaurant(roque,sol,rice).

restaurant(tagliatella,benavente,italian).

user(juan,local_guide).

user(sara,normal_user).

user(pepe,casual_user).

comment(juan,don_oso,plain).

comment(juan,rodilla,good).

comment(pepe,roque,excellent).

comment(sara,tagliatella,very_good).

A recommendation relies on the quality of a restaurant, which is defined with a single rule that takes into account the comment a user has provided, the type of this user, and its confidence:

quality(Restaurant,Quality) :-

comment(User,Restaurant,Quality),

user(User,Type),

confidence(Type).

So, in order to provide recommendations, the rule recommend relates restaurants (Restaurant) with the location of the user (Origin), serving certain food (Food) with an acknowledged quality (Quality):

recommend(Origin,Food,Quality,Restaurant) :-

restaurant(Restaurant,Location,Food),

Location near Origin,

quality(Restaurant,Quality).

As an example of a query for this database, the following system session returns recommendations for a user located at sol:

DES> /system_mode fuzzy

FDES> /consult recommender

Info: 22 rules consulted.

FDES> recommend(sol,Food,Quality,Restaurant)

Info: Processing:

answer(Food,Quality,Restaurant) :-

recommend(sol,Food,Quality,Restaurant).

{ answer(snacks,good,rodilla)with 0.6,

answer(burguer,plain,don_oso)with 0.5,

answer(rice,excellent,roque)with 0.3 }

In this session, after switching the deductive system to the fuzzy setting, the command /consult loads the database located in the given file (with default extension .dl). The query returns all possible restaurants indicating the type of food served, quality and the recommended restaurant. Each answer tuple is ordered by default with respect to descending approximation degrees. The first tuple indicates that rodilla has a support degree of 0.6, which is a value constructed by taking into account that the restaurant is located at callao, which is near sol. Also, there is a comment from the local guide juan (with a support of 0.9) stating that the restaurant is good. The next tuple in the answer set refers to the restaurant don_oso, receiving a support degree of 0.5 with quality plain, because the same local guide commented on this restaurant with this quality level for a restaurant located at cruz, near sol. The last tuple receives a small support because the comment was raised by a user whose type is scored rather low. We can interactively add information about the type of the food served with, e.g.:

FDES> /assert burguer~fast_food=0.7.

FDES> /assert snacks~fast_food=0.9.

Then, a similar query but looking for good fast food near sol (with no need to reload the database) would retrieve:

FDES> recommend(sol,fast_food,good,Restaurant)

Info: Processing:

answer(Restaurant) :-

recommend(sol,fast_food,good,Restaurant).

{ answer(rodilla)with 0.6,

answer(don_oso)with 0.5 }

Actually, there are two tuples for don_oso fulfilling the question, with the same support degree (one for plain and other for good quality). Due to the default set-oriented behavior of the system, duplicates are removed.

Finally, a query for the predicate recommend with variables in all its arguments would return all possible recommendations. (The reader is encouraged to try the system with different queries.)

4.1.22.7 Fuzzy Restricted Predicates

The notion of restricted predicates (cf. Section 4.1.19) in the crisp setting can be extrapolated to the fuzzy setting. While a crisp restricted predicate removes certain tuples (as defined by the corresponding restricting rules) from its meaning, a fuzzy restricted predicate lowers the support of selected tuples as defined by the restricting rules. For example, let us suppose that we were mostly convinced in the current database that Paula was brunette, which is a knowledge stated with the fact paula(brunette) with 0.8. But, under another light, we are not so convinced anymore, and we can add the fact -paula(brunette) with 0.2 (note the minus sign at the beginning) to lower this perception degree. So:

FDES> /assert paula(brunette) with 0.8

FDES> /assert -paula(brunette) with 0.2

FDES> paula(X)

Info: Processing:

answer(X) :-

paula(X).

{

answer(brunette)with 0.6

}

Info: 1 tuple computed.

Thus, the computed approximation degree for the query results from the approximation degree of the (positive) predicate minus the approximation degree of its restricted rules (0.8-0.2 = 0.6 in the example). A result degree less than or equal to zero for a given tuple leads to rejecting it from the result. Therefore, using a restricted rule -G (which is equivalent to -G with 1.0) removes all tuples from the meaning of G.

Restricting rules can be added to both extensional and intensional predicates. Following the recommender example in Section 4.1.22.6, we want to decrease the confidence on the quality of don_oso because it seems too high for a food critic. Then, we can add the rule:

-quality(don_oso,Q) :- quality(Q) with 0.1.

Where the predicate quality/1 simply states the different qualities (not shown in Section 4.1.22.6, and defined by the rule quality(Q):-comment(_U, _R, Q))[10].

Then, the (computed[11]) quality is accordingly lowered:

FDES> quality(R,Q)

Info: Processing:

answer(Q,R) :-

quality(R,Q).

{

answer(good,rodilla)with 0.9,

answer(plain,don_oso)with 0.8,

answer(excellent,roque)with 0.3

}

Info: 3 tuples computed.

There may be several identical rules (either restricting or not) for the same predicate with different grades. In this case, the computed approximate degree of the predicate corresponds to the maximum of the positive meaning minus the maximum of the negative meaning, as illustrated next:

FDES> /listing stock_up(google)

stock_up(google) with 0.6.

stock_up(google) with 0.9.

Info: 2 rules listed.

FDES> /listing -stock_up(google)

-stock_up(google) with 0.1.

-stock_up(google) with 0.05.

Info: 2 rules listed.

FDES> stock_up(google)

Info: Processing:

answer :-

stock_up(google).

{

answer with 0.8

}

Info: 1 tuple computed.

Usefulness of fuzzy restricted predicates mainly belongs to decision-making applications, which can be easily modelled with Fuzzy Hypothetical Datalog, as explained in the next section.

4.1.22.8 Fuzzy Hypothetical Datalog

Assumptions, as in Hypothetical Datalog (c.f. Section 4.1.21), can be stated in Fuzzy Datalog as well. In this case, not only rules and facts can be assumed, but also graded rules and proximity equations.

Recalling the example in the stock market (Section 4.1.22.1), let us assume that Paul is willing to buy Amazon shares with a stock up expectation of 0.7. Then, under this assumption, the query for determining what stocks are wise to keep returns the following:

FDES> stock_up(amazon) with 0.7 /\ shareholder(paul,amazon) => keep_stock(N,S)

Info: Processing:

answer(N,S) :-

stock_up(amazon) with 0.7

shareholder(paul,amazon)

keep_stock(N,S).

{

answer(paul,google)with 0.9,

answer(paul,amazon)with 0.7,

answer(paul,greek_bonds)with 0.2

}

Info: 3 tuples computed.

As well, we can tune existing information in the database. For example, the confidence in Greek bonds can be raised:

FDES> stock_up(greek_bonds) with 0.5 => keep_stock(N,S)

Info: Processing:

answer(N,S) :-

stock_up(greek_bonds) with 0.5

keep_stock(N,S).

{

answer(paul,google)with 0.9,

answer(paul,greek_bonds)with 0.5

}

Info: 2 tuples computed.

If we want to test a decreasing confidence in Google, it is not appropriate to simply assume something as stock_up(google) with 0.6, because there is already a fact (stock_up(google) with 0.9) with higher grade in the database, a fact that is not overwritten by this assumption. Let us try it:

FDES> stock_up(google) with 0.6 => stock_up(google)

Info: Processing:

answer :-

stock_up(google) with 0.6

stock_up(google).

{

answer with 0.9

}

Info: 1 tuple computed.

Instead, restricted predicates can be used to tune decreasing confidence grades:

FDES> -stock_up(google) with 0.3 => keep_stock(N,S)

Info: Processing:

answer(N,S) :-

-stock_up(google) with 0.3

keep_stock(N,S).

{

answer(paul,google)with 0.6,

answer(paul,greek_bonds)with 0.2

}

Info: 2 tuples computed.

As expected, the database has not been changed, i.e., the expectations about Google remain the same after all these assumptions:

FDES> stock_up(google)

Info: Processing:

answer :-

stock_up(google).

{

answer with 0.9

}

Info: 1 tuple computed.

Thus, both fuzzy hypothetical reasoning and restricted predicates makes it possible to consider a changing scenario for decision-making in this very tiny and simple stock market example.

As an example of assuming proximity equations, let us consider a fuzzy relation near that states how "near" are two cities by train (railways are generally not straight, and two cities can be connected by a much more train distance than it might been expected):

:- fuzzy_relation(near,[reflexive,symmetric,transitive(product)]).

madrid near ciudad_real = 0.6.

ciudad_real near badajoz = 0.4.

badajoz near lisboa = 0.5.

Indeed, the train connection between madrid and badajoz is deceptive, but a new high-speed rail is under discussion. If built, reaching lisboa would be faster:

FDES> madrid near lisboa

Info: Processing:

answer :-

madrid near lisboa.

{

answer with 0.12

}

Info: 1 tuple computed.

FDES> madrid near badajoz = 0.4 => madrid near lisboa

Info: Processing:

answer :-

madrid near badajoz=0.4

madrid near lisboa.

{

answer with 0.2

}

Info: 1 tuple computed.

In this example, the new (explicit) equation madrid near badajoz = 0.4 has been considered. Before it was, the link between madrid and badajoz was still available because near is transitive, and its t-closure included madrid near badajoz = 0.24:

FDES> /list_t_closure near

...

madrid near badajoz=0.24.

...

By recomputing the t-closure of near in the presence of the new explicit equation, it includes the implicit equation madrid near lisboa = 0.2, which is the one used to compute the answer.

In addition, it is also possible to replace an existing explicit equation with an assumption. Recall that only one proximity equation between two given nodes is allowed in a database (adding a new one overwrites the older one). So, assuming an existing equation with a different approximation degree amounts to remove it in the assumption context and add the new equation. Out of this context, the original equation remains. In the same example, we can just consider that a new high-speed railway has been built between ciudad_real and badajoz (so that both cities are "closer"):

FDES> ciudad_real near badajoz = 0.6 => madrid near lisboa

Info: Processing:

answer :-

ciudad_real near badajoz=0.6

madrid near lisboa.

{

answer with 0.18

}

Info: 1 tuple computed.

Note that the assumed equation is only applicable in its hypothetical context, and it has no sense outside:

FDES> (ciudad_real near badajoz = 0.6 => madrid near lisboa), ciudad_real near badajoz = Degree

Info: Processing:

answer(Degree) :-

(ciudad_real near badajoz=0.6

madrid near lisboa),

sim(near,ciudad_real,badajoz)=Degree.

{

answer(0.4)with 0.18

}

Info: 1 tuple computed.

So, the corresponding approximation degree out of such context remains the same (0.4).

4.1.22.9 Fuzzy Datalog Caveats

Several non-classical Datalog features are not supported, such as:

· Most built-in predicates (such as division, exists, ...)

· Null values (thus neither do outer joins).

In a nutshell, only expect classical features to work in this fuzzy setting (in addition to the non-classical ones explicitly described in this manual).

4.2 SQL

This section describes the main limitations, features, and decisions taken in adding SQL to DES as a query language, which coexists with Datalog. We describe four parts of the supported subset of the SQL language: DDL (Data Definition Language, for defining the database schema), DQL (Data Query Language, for listing contents of the database) and DML (Data Manipulation Language, for inserting and deleting tuples)[12], and ISL (Information Schema Language). Section 4.2.13 resumes the SQL grammar. As ODBC connections are allowed, some DBMS specific features have been added, as well as features in ISL which are not covered in the SQL standard.

The syntax recognized by the interpreter is borrowed from the SQL standard. However, the SQL dialect supported by DES includes features which are not in this standard, as hypothetical views and the division relational algebra operator. Section names include the notice (Non-Standard) to refer to such extra features.

4.2.1 Main Limitations

· No insertions/deletions/updates into views.

· Strings in displayed outputs are not enclosed between apostrophes unless they begin with upper case.

· DCL (Data Control Language, for controlling access rights) is not provided in DES.

4.2.2 Main Features

As main features, we highlight:

· Data query, data definition, data manipulation, and information schema language parts provided.

· Subqueries (nested queries without depth limits).

· Correlated queries (tables and relations in nested subqueries can be referenced by the host query). For example: SELECT * FROM t,(SELECT a FROM s) s WHERE t.a=s.a.

· Subqueries in expressions, as SELECT a FROM t WHERE t.a > (SELECT a FROM s).

· Table, relation, column, and expression aliases.

· Support for duplicates and duplicate elimination (which must be explicitly enabled with the command /duplicates on by contrast to usual DBMS's, in which this is the default and only one mode).

· Linear, non-linear and mutual recursive queries (not all current DBMS's support linear queries and no one support non-linear and mutual recursive ones). In contrast to some current DBMS's, these queries can be located anywhere a query is allowed.

· Simplified recursive queries are allowed (Non-Standard): Although supported, there is no need for using a WITH clause.

· Hypothetical queries (Non-Standard).

· Set operators build relations, which can be used wherever a data source is expected (FROM clause).

· Null values are supported, along with outer joins (full, left and right).

· Aggregate functions allowed in expressions at the projection list and HAVING conditions. GROUP BY clauses are also allowed.

· View support. Any relation built with an SQL query can be defined as a view.

· Supported database integrity constraints include type constraints, existence (nullability), primary keys, candidate keys, referential integrity, check constraints, functional dependencies (non-standard), and user-defined constraints.

· Parentheses can be used elsewhere they are needed and also for easing the reading of statements. Also, they are not required when they are not needed (in contrast to some current DBMS systems).

· Suggestions are provided for misspelled table, view and column names when similar entries are found.

· Type casting is disabled by default. Enabling this (with /type_casting on) provides the usual behaviour of current DBMS's allowing, for instance, to insert a string (representing a number) into a numeric field.

· SQL statements can end with a semicolon (;) but it is not compulsory unless /multiline on is enabled.

· Any identifier is valid as an user identifier. For instance, the following statements are valid in DES, but rejected in most DBMS's.

CREATE TABLE from(from INT, dest INT);

SELECT * FROM from JOIN from using;

Note that using stands for a renaming for the second from table reference (user identifiers are shown in lowercase whereas system identifiers are shown in uppercase).

· Syntax error reports for both the local database and ODBC connections.

· Semantic error reports for the local database (future work include applying this to external databases).

4.2.3 Datalog vs. SQL

With respect to Datalog, some decisions have been taken:

· As in Datalog, user identifiers are case-sensitive (table and attribute names, ...). This is not the usual behaviour of current DBMS's.

· In contrast to Datalog, built-in identifiers are not case-sensitive. This conforms to the normal behaviour of current DBMS's.

4.2.4 Data Definition Language

This part of the language deals with creating (or replacing), and dropping tables and views. The schema can be consulted with the command /dbschema.

4.2.4.1 Creating Tables

The first form of this statement is as follows:

CREATE [OR REPLACE] TABLE TableName(Column1 Type1 [ColumnConstraints1], ..., ColumnN TypeN [ColumnConstraintsN] [, TableConstraints])

This statement defines the table schema with name TableName and column names Column1, ..., ColumnN., with types Type1, ..., TypeN, respectively. If the optional clause OR REPLACE is used, the table is dropped if existed already, deleting all of its tuples.

A second form of this statement creates a table with the same schema of an existing table, following SQL standard optional feature T171:

CREATE TABLE TableName [(] LIKE ExistingTableName [)]

This version copies the complete schema, including all integrity constraints (both predefined and user-defined).

A third, last form of this statement creates a table with a SQL statement as data and schema generator:

CREATE TABLE TableName [(] AS SQLStatement [)]

In this case, a table with name TableName is created with the schema and data returned by the query SQLStatement.

As indicated by the optional meta-symbols [], parentheses in these two last forms are not mandatory.

There is provision for several column constraints:

· NOT NULL. Existency constraint forbiding null values.

· PRIMARY KEY. Primary key constraint for only one column.

· UNIQUE. Uniqueness constraint for only one column (Also allowed the alternative syntax: CANDIDATE KEY).

· REFERENCES TableName[(Column)]. Referential integrity constraint for only one column.

· DEFAULT Expression. Makes the value resulting from evaluating Expression the value assigned to a column for which no value is provided in an INSERT statement

· DETERMINED BY Column. Functional dependency. If this constraint is applied to the column Column1, then: Column → Column1 (Non-Standard).

· CHECK Condition. Check constraint for columns as in a WHERE clause.

Also, there is provision for several table constraints:

· PRIMARY KEY (Column,..., Column). Primary key constraint for one or more columns.

· UNIQUE (Column,..., Column). Uniqueness constraint for one or more columns (Also allowed the non-standard alternative syntax: CANDIDATE KEY (Column,..., Column)

· FOREIGN KEY (Column1,..., ColumnN) REFERENCES TableName[(Column1,..., ColumnN)])]. Referential integrity constraint for one or more columns.

· NOT NULL Column. Non-standard existence constraint for Column.

· CHECK CheckConstraint. Check constraint, as listed next.

Check constraints:

· Condition. As in a WHERE clause

· (ColumnR1,..., ColumnRN) DETERMINED BY (ColumnL1,..., ColumnLN). Functional dependency: ColumnL1,...,ColumnLN → ColumnR1,...,ColumnRN (Non-Standard)

Allowed types include:

· CHAR. Fixed-length string of 1.

· CHAR(n). Fixed-length string of n characters.

· VARCHAR(n) (or VARCHAR2(n) or TEXT(n)). Variable-length string of up to n characters.

· VARCHAR (or STRING). Variable-length string of up to the maximum length of the underlying Prolog atom.

· INTEGER (or INT or SMALLINT or NUMERIC or DECIMAL). Integer number.

· REAL (or FLOAT). Real number.

· NUMERIC(n) (or DECIMAL(n)). Integer number of up to n digits.

· NUMERIC(p,s) (or DECIMAL(p,s)). Decimal number with precision p and scale s.

· DATE. Date (year-month-day).

· TIME. Date (hour:minute:second).

· TIMESTAMP (or DATETIME). Timestamp (year-month-day hour:minute:second).

Numeric types rely on the underlying Prolog system (see Section 4.1.18.1). Precision and scale are ignored. Automatic type casting is disabled by default but can be enabled with /type_casting on to behave similar to SQL systems. By default, strong typing is applied.

Examples:

CREATE TABLE t(a INT PRIMARY KEY, b STRING)

CREATE OR REPLACE TABLE s(a INT, b INT REFERENCES t(a), PRIMARY KEY (a,b))

Note in this last example that if the column name in the referential integrity constraint is missing, the referred column of table t is assumed to have the same name that the column of s where the constraint applies (i.e., b). So, an error is thrown because columns s.b and t.b have different types:

DES> CREATE OR REPLACE TABLE s(a INT, b INT REFERENCES t, PRIMARY KEY (a,b))

Error: Type mismatch s.b:number(int) <> t.b:string(varchar).

Error: Imposing constraints.

A declared primary key or foreign key constraint is checked whenever a new tuple is added to a table, following relational databases. Recall, first, that the same database is shared for Datalog and SQL, and second, that asserting production rules (i.e., those defining the intensional database) from the Datalog side is allowed but primary key and foreign key constraints are not checked for them (they are only checked for facts). Then, the following scenario is possible:

DES> create or replace table t(a int, b int, c int, d int, primary key (a,c))

DES> insert into t values(1,2,3,4)

Info: 1 tuple inserted.

DES> % The following is expected to raise an error:

DES> insert into t values(1,1,3,4)

Error: Primary key violation when trying to insert: t(1,1,3,4)

Info: 0 tuples inserted.

DES> % However, the following is allowed:

DES> /assert t(X,Y,Z,U) :- X=1,Y=2,Z=3,U=4.

DES> /listing

t(1,2,3,4).

t(X,Y,Z,U) :-

X = 1,

Y = 2,

Z = 3,

U = 4.

A Datalog rule should be viewed as a component of the intensional database. Current DBMS's avoid to define a view with the same name as a table and, therefore, there is no way of unexpected behaviours such as the one illustrated above.

Note that it is possible to have tuples already stored in the database prior to its corresponding table creation. This means that the CREATE TABLE statement can fail if any of those tuples does not meet all the constraints stated for the table. For instance, let's consider:

DES> /assert t(null)

DES> create table t(a int primary key)

Error: Null values found for t.[a]

Offending values in database: [nn($NULL(0))]

Info: Constraint has not been asserted.

DES> /dbschema

Info: Database '$des'

Info: No tables.

Info: No views.

Info: No integrity constraints.

Next, a very simple example is reproduced to illustrate basic constraint handling:

DES> create or replace table u(b int primary key,c int)

DES> create or replace table s(a int,b int, primary key (a,b))

DES> create or replace table t(a int,b int,c int,d int, primary key (a,c), foreign key (b,d) references s(a,b), foreign key(b) references u(b))

DES> insert into t values(1,2,3,4)

Error: Foreign key violation t.[b,d]->s.[a,b] when trying to insert: t(1,2,3,4)

Info: 0 tuples inserted.

DES> insert into s values(2,4)

Info: 1 tuple inserted.

DES> insert into t values(1,2,3,4)

Error: Foreign key violation t.[b]->u.[b] when trying to insert: t(1,2,3,4)

Info: 0 tuples inserted.

DES> insert into u values(2,2)

Info: 1 tuple inserted.

DES> insert into t values(1,2,3,4)

Info: 1 tuple inserted.

DES> /listing

s(2,4).

t(1,2,3,4).

u(2,2).

4.2.4.2 Creating Views

CREATE [OR REPLACE] VIEW ViewName[(Column1, ..., ColumnN)]

AS SQLStatement

This statement defines the view schema in a similar way as defining tables. The view is created with the SQL statement SQLStatement as its definition. If the optional clause OR REPLACE is used, the view is firstly dropped if existed already. Other tuples or rules asserted (with the command /assert) are not deleted, as the next example shows:

DES> /assert v(1)

DES> create or replace view v(a) as select 2

DES> select * from v

answer(v.a:int) ->

{

answer(1),

answer(2)

}

Info: 2 tuples computed.

Note that column names are not mandatory.

Examples:

DES> CREATE VIEW v(a,b,c,d) AS

SELECT * FROM t WHERE a>1;

DES> CREATE OR REPLACE VIEW w(a,b) AS

SELECT t.a,s.b FROM t,s WHERE t.a>s.a;

DES> /dbschema

Info: Table(s):

* s(a:int,b:int)

- PK: [a,b]

* u(b:int,c:int)

- PK: [b]

* t(a:int,b:int,c:int,d:int)

- PK: [a,c]

- FK: t.[b,d] -> s.[a,b]

- FK: t.[b] -> u.[b]

Info: View(s):

* v(a:int,b:int,c:int,d:int)

- Defining SQL Statement:

SELECT ALL *

FROM

WHERE a > 1;

- Datalog equivalent rules:

v(A,B,C,D) :-

t(A,B,C,D),

A > 1.

* w(a:int,b:int)

- Defining SQL Statement:

SELECT ALL t.a, s.b

FROM

WHERE t.a > s.a;

- Datalog equivalent rules:

w(A,B) :-

t(A,C,D,E),

s(F,B),

A > F.

Info: No integrity constraints.

Note that primary key constraints follow the table schema, and inferred types are in the view schema.

4.2.4.3 Dropping Tables

DROP TABLE OptionalClauses TableName OptionalClauses

This statement drops the table schema corresponding to TableName, deleting all of its tuples (whether they were inserted with INSERT or with the command /assert) and rules (which might have been added via /assert). Any referential integrity constraint pointing to TableName is dropped. OptionalClauses includes IF EXISTS and CASCADE. If the clause IF EXISTS is included, dropping an inexistent table does not raise an error. If the clause CASCADE is included, dropping a table implies dropping all views depending on TableName.

Example:

DROP TABLE t

4.2.4.4 Dropping Views

DROP VIEW OptionalClauses ViewName OptionalClauses

This statement drops the view with name ViewName, deleting all of its tuples (inserted with the command /assert) and rules (which might have been added via /assert). OptionalClauses includes IF EXISTS and CASCADE. If the clause IF EXISTS is included, dropping an inexistent view does not raise an error. If the clause CASCADE is included, dropping a view implies dropping all views depending on ViewName.

Example:

DROP VIEW v

4.2.4.5 Renaming Tables

RENAME TABLE TableName TO NewTableName

This non-standard statement (following IBM DB2) allows to change the name of table TableName to NewTableName. Foreign keys referring to this table are modified accordingly. Also, views including referenes to this table are modified to refer to the new name.

4.2.4.6 Renaming Views

RENAME VIEW ViewName TO NewViewName

This non-standard statement (following IBM DB2) allows changing the name of view ViewName to NewViewName. Also, views including references to this view are modified to refer to the new name.

4.2.4.7 Modifying Tables

There are three main ways for modifying (altering) a table: either adding/dropping constraints, or redefining a column (both its data type and constraints) or only changing its data type. The last two are not in the SQL standard.

The first alternative is:

ALTER TABLE TableName [ADD|DROP] CONSTRAINT TableConstraint

This statement allows adding and dropping constraints. Syntax of TableConstraint is as of table constraints, where a constraint specification is expected (instead of a constraint name).

For instance:

DES> create table t(a int primary key check(a>0))

DES> /dbschema

Info: Database '$des'

Info: Table(s):

* t(a:int)

- PK: [a]

- IC:

+ SQL Check:

a > 0

+ Datalog Check:

'$ic_t0'(A) :-

t(A),

A=<0.

Info: No views.

Info: No integrity constraints.

DES> alter table t drop constraint primary key

Error: (SQL) Expected sequence of column names between parentheses after 'alter table t drop constraint primary key'.

DES> alter table t drop constraint primary key(a)

DES> /development on

DES> /dbschema

Info: Database '$des'

Info: Table(s):

* t(a:int)

- IC:

+ SQL Check:

a > 0

+ Datalog Check:

'$ic_t0'(A) :-

t(A),

A=<0.

Info: No views.

Info: No integrity constraints.

DES> alter table t drop constraint check(a>0)

DES> /dbschema

Info: Database '$des'

Info: Table(s):

* t(a:int)

Info: No views.

Info: No integrity constraints.

Note here that a column constraint as primary key is not allowed, and the equivalent table constraint must be used instead.

The second alternative is:

ALTER TABLE TableName ALTER [COLUMN] Column Type [ColumnConstraints]

This statement redefines Column with data type Type and constraints ColumnConstraints (if provided). Any older constraint referring to this column is removed (even table constraints). If table data can be kept for the new column definition, executing this statement succeeds. Otherwise, its execution is rejected. The following example shows this:

DES> create table t(a int primary key, b string, check (a>0))

DES> alter table t alter column a string default ''

DES> /describe t

Info: Database '$des'

Info: Table:

* t(b:string,a:string)

- DE: a <- ''

Note that both the column and table constraints are removed, and only the new default constraint remains. Further, any other foreign key constraint referencing the altered table will be removed:

DES> /dbschema

Info: Database '$des'

Info: Table(s):

* s(a:int)

- FK: s.[a] -> t.[a]

* t(a:int,b:string)

- PK: [a]

Info: No views.

Info: No integrity constraints.

DES> alter table t alter column a string default ''

DES> /dbschema

Info: Database '$des'

Info: Table(s):

* s(a:int)

* t(a:string,b:string)

- DE: a <- ''

Info: No views.

Info: No integrity constraints.

Whether existing data can be kept depends on the current type casting setting: If enabled (with the command /type_casting on), more opportunities of keeping data are expected. For example:

DES> create table t(a int primary key, b string, check (a>0))

DES> insert into t values(1,'a')

Info: 2 tuples inserted.

DES> alter table t alter column a string default ''

Error: Type mismatch $_t.a:string(varchar) vs. number(integer).

$_t(a:string(varchar),b:string(varchar)) (declared types).

Info: 0 tuples inserted.

DES> /type_casting on

DES> alter table t alter column a string default ''

Info: 1 tuple inserted.

DES> select * from t

answer(t.a:string,t.b:string) ->

{

answer('1',a)

}

Info: 1 tuple computed.

Finally, the third alternative is:

ALTER TABLE TableName ALTER [COLUMN] Column SET [DATA] TYPE Type

This alternative is almost equivalent to the second one by specifying only the data type. As a difference, existing constraints are not removed. For example:

DES> create table t(a int primary key determined by b, b string default '', check (a>0))

DES> alter table t alter column b set data type varchar(10)

DES> /describe t

Info: Database '$des'

Info: Table:

* t(a:int,b:varchar(10))

- PK: [a]

- DE: b <- ''

- FD: [b] -> [a]

- IC:

a > 0

4.2.4.8 Dropping Databases

DROP DATABASE

This statement drops the current database, dropping all tables, views, and rules (this includes Datalog rules and constraints that may have been asserted or consulted). It behaves exactly as the command /abolish except that it asks for user confirmation.

Example:

DES> drop database

Info: This will drop all views, tables, constraints and Datalog rules.

Do you want to proceed? (y/n) [n]:

4.2.5 Data Manipulation Language

This part of the language deals with inserting, deleting and updating tuples in tables. SQL insertions, deletions and updates are not allowed for views.

4.2.5.1 Inserting Tuples

There are two forms of inserting tuples. The first one explicitly states what tuples are to be inserted:

INSERT INTO TableName[(Col1,…,ColN)] VALUES (Expr1,...,ExprN) [, ..., (Expr1,...,ExprN)]

This statement inserts into the table TableName as many tuples as those built with each tuple of expressions Expr1, ..., ExprN, and Col1 to ColN are non-repeated column names of the table. Expressions are evaluated before inserting the tuple. If no column names are given, N is expected to be the number of columns of the table. If column names are given, each expression Expri corresponds to column name Coli. For those column names which are not provided in a column name sequence, nulls are inserted. The keyword DEFAULT can be used instead of a constant (this makes to select either null or the value defined with the DEFAULT constraint in the CREATE TABLE statement).

The next example inserts a single tuple:

CREATE TABLE t(a int, b int DEFAULT 0)

INSERT INTO t VALUES (1,1)

The next one inserts a single tuple into the same table (automatically applying a null value for the non-provided column a):

INSERT INTO t(b) VALUES (2)

Which is equivalent to:

INSERT INTO t(b,a) VALUES (2,null)

and represents the tuple (null,2). Note that the order of provided column names represent the order of corresponding values; in this example, the columns are reversed with respect to the table definition.

For inserting several tuples at a time:

INSERT INTO t VALUES (1,1),(null,2)

The default value defined for the column b can be used in these two sentences:

INSERT INTO t(a) VALUES (1)

INSERT INTO t(a,b) VALUES (2,DEFAULT)

The first one inserts the tuple (1,0), and the second one the tuple (2,0).

Default values for all columns can be expressed as in:

INSERT INTO t DEFAULT VALUES

Expressions for default values can be used instead of just values in the table definition. For instance:

DES> CREATE TABLE t(a int, b time DEFAULT CURRENT_TIME+30)

DES> INSERT INTO t(a) VALUES (1)

Info: 1 tuple inserted.

DES> SELECT CURRENT_TIME

answer($a0:datetime(time)) ->

{

answer(time(19,44,20))

}

Info: 1 tuple computed.

DES> SELECT * FROM t

answer(t.a:int,t.b:datetime(time)) ->

{

answer(1,time(19,44,50))

}

Info: 1 tuple computed.

It is possible to specify expressions instead of values when inserting tuples, as:

INSERT INTO t(a) VALUES (sqrt(5)^2);

The second form of the INSERT statement allows to inserting tuples which are the result of a SELECT statement:

INSERT INTO TableName[(Col1,…,ColN)] SQLStatement

This statement inserts into the table TableName as many tuples as returned by the SQL statement SQLStatement. This statement has to return as many columns as either the columns of TableName, if no column names are given, or the number of provided column names (N), otherwise.

Examples:

INSERT INTO t SELECT * FROM s

You can also insert tuples into a table coming directly (or indirectly) from the table itself for duplicating rows, as in:

INSERT INTO t SELECT * FROM t

Note that there is no recursion in this query as the source table t is not changed during solving the SELECT statement.

For testing the new (duplicated) contents of t, you can use /listing t, instead of a SELECT statement, since this statement always returns a set (no duplicates) when duplicates are disabled (cf. Section 4.1.9).

As in the first form, you can specify columns of the target table as in:

INSERT INTO t(b) SELECT a FROM t

which inserts as many rows in t as it had before insertion, and for each row, a new tuple is built with the value of the source column a in the target column b, and null in the target column a.

4.2.5.2 Deleting Tuples

DELETE FROM TableName [[AS] Identifier] [WHERE Condition]

This statement deletes all the tuples of the table TableName that fulfil Condition. It does not delete production rules asserted via /assert.

Examples:

DELETE FROM t

which deletes all tuples from table t.

DELETE FROM t WHERE a>0

which only deletes tuples from the table t such that the value for the column a is greater than 0.

Aliases can be used in correlated subqueries, as in:

DELETE FROM Contracts C

WHERE NOT EXISTS (SELECT *

FROM Contains

WHERE Reference = C.Reference);

4.2.5.3 Updating Tuples

UPDATE TableName [[AS] Identifier] SET Att1=Expr1,...,AttN=ExprN [WHERE Condition]

This statement updates each column Atti with the values computed for each Expri for all the tuples of the table TableName that fulfil Condition.

Example:

UPDATE Employees SET Salary=Salary*1.1 WHERE Id IN

(SELECT Id from Promoted WHERE Year='2025');

which increases in a 10% the salaries of the employees which have been promoted in 2025.

4.2.6 Data Query Language

There are three main types of SQL query statements: SELECT statements, set statements (UNION, INTERSECT, and EXCEPT), and WITH statements (for building recursive queries).

4.2.6.1 Basic SQL Queries

The syntax of the basic SQL query statement is:

SELECT [DISTINCT|ALL] ProjectionList

[FROM Relations

[WHERE Condition]

[ORDER BY OrdExpressions] ]

Where:

· Square brackets indicate that the enclosed text is optional. Also, the vertical bar is used to denote alternatives.

· ProjectionList is a list of comma-separated columns or expressions that will be returned as a tuple result. Wildcards are allowed, as * (for referring to all the columns in the data source) and Relation.* (for referring to all the columns in the relation Relation). The name Relation can be the name of a table, view or an alias (for a table or subquery). The clause DISTINCT discards duplicates whereas the clause ALL does not (this is only noticeable when duplicates are enabled with the command /duplicates on).

· Condition is a logical condition built from comparison operators (=, <>, !=, <, >, >=, and <=), Boolean operators (AND, OR, XOR, and NOT), Boolean constants (TRUE, FALSE), the existence operator (EXISTS) and the membership operator (IN). See the grammar description in Section 4.2.13 for details. Subqueries are allowed with no limitations.

· Relations is a list of comma-separated relations. A relation can be either a table name, or a view name, or a subquery, or a join relation. They can be renamed via aliases. If no FROM clause is provided, the built-in DUAL relation is used as a data source (cf. Section 4.2.6.1.2).

· OrdExpressions is a list of comma-separated ordering expressions. An ordering expression can be either simply an expression or an expression followed by the ordering criterion (ASC -or ASCENDING- for ascending order, and DESC -or DESCENDING- for descending order). Answers are ordered by default (see /order_answer) but this order is overridden if the ORDER BY clause is either directly used in a query or in the definition of a view the query refers to. The order is based on the standard order of terms of the underlying Prolog system (see Section 0). An ordering expression can include both an alias as defined in ProjectionList and aggregate functions. Positional notation (such as in DB2 and PostgreSQL) is also allowed (though its use is commonly discouraged).

Examples:

Given the tables:

CREATE TABLE s(a int, b int);

CREATE TABLE t(a int, b int);

CREATE TABLE v(a int, b int);

We can submit the following queries:

SELECT distinct a

FROM t

SELECT t.*, s.b

FROM t,s,v

WHERE t.a=s.a AND v.b=t.b

SELECT t.a, s.b, t.a+s.b

FROM t,s

WHERE t.a=s.a

SELECT *

FROM (SELECT * from t) as r1,

(SELECT * from s) as r2

WHERE r1.a=r2.b;

SELECT *

FROM s

WHERE s.a NOT IN SELECT a FROM t;

SELECT *

FROM s

WHERE EXISTS

SELECT a

FROM t

WHERE t.a=s.a;

SELECT *

FROM s

WHERE s.a > (SELECT a FROM t);

SELECT 1, a1+a2, a+1 AS a1, a+2 AS a2

FROM t;

SELECT 1;

SELECT a FROM t ORDER BY -a;

SELECT CAST(MONTH(CURRENT_DATE) AS STRING) || ' - ' || CAST(YEAR(CURRENT_DATE) AS STRING);

Notes:

· SQL expressions follow the same syntax as Datalog.

· An SQL expression can be renamed and used in other expressions.

· Circular definitions will yield exceptions at run-time, as in a+a3 AS a3

· Terms in expressions in the select list are first tried as built-in constants and functions. This may lead to confusion. For example:, creating a table with a column with name e, and selecting e from this table renders:

DES> CREATE TABLE t(e int);

DES> INSERT INTO t VALUES (1);

Info: 1 tuple inserted.

DES> SELECT e FROM t;

answer($a1:float) ->

{

answer(2.718281828459045)

}

Info: 1 tuple computed.

That is, e represents the Euler arithmetic constant, and in this query, its numerical value is returned. If you want to access the column name e, then use qualification, as follows:

DES> SELECT t.e FROM t;

answer(t.e:int) ->

{

answer(1)

}

Info: 1 tuple computed.

A join relation is either of the form:

Relation NATURAL JoinOp Relation

or:

Relation JoinOp Relation [JoinCondition]

where Relation is as before (without any limitation), JoinOp is any join operator (including [INNER] JOIN, LEFT [OUTER] JOIN, RIGHT [OUTER] JOIN, and FULL [OUTER] JOIN), and JoinCondition can be either:

ON Condition

or:

USING (Column1,...,ColumnN)

where Condition is as described in the WHERE clause, and Column1, ..., ColumnN are common column names of the joined relations. Omitting the condition in a non-natural join is equivalent to a true condition. Note that the clause USING does not apply to NATURAL joins, but like them, arguments for the equijoin occur only once in the result.

Examples:

Given the tables:

CREATE TABLE s(a int, b int);

CREATE TABLE t(a int, b int);

CREATE TABLE v(a int, b int);

We can submit the following queries:

SELECT *

FROM t INNER JOIN s ON t.a=s.a AND t.b=s.b;

SELECT *

FROM t NATURAL INNER JOIN s;

SELECT *

FROM t INNER JOIN s USING (a,b);

SELECT * FROM t INNER JOIN s USING (a);

SELECT *

FROM t INNER JOIN s USING (b);

SELECT *

FROM (t INNER JOIN s ON t.a=s.a) AS s, v

WHERE s.a=v.a;

SELECT *

FROM (t LEFT JOIN s ON t.a=s.a) RIGHT JOIN v ON t.a=v.a;

SELECT * FROM t FULL JOIN s ON t.a=s.a;

Notes:

- The default keyword ALL following SELECT retains duplicates whenever duplicates are enabled (command /duplicates on). In turn, DISTINCT discards duplicates. But note that if duplicates are disabled, both ALL and DISTINCT behave the same (i.e., discarding duplicates).

- The column list for USING must be enclosed between parentheses; otherwise, the name USING can be used as an alias.

4.2.6.1.1 Top-N Queries

The number of computed tuples for a select statement can be limited with the so-called Top-N queries. ISO 2008 includes this as a final clause in the SELECT statement:

SELECT [DISTINCT|ALL] ProjectionList

FROM Rels

…

FETCH FIRST Integer ROWS ONLY

However, DES also provides another non-standard, but common form in other RDBMS's of such queries:

SELECT [TOP Integer] [DISTINCT|ALL] ProjectionList

…

You can switch the order of the TOP and DISTINCT clauses, and even the weird case of simultaneously specifying both forms of Top-N queries in the same statement, as long as they express the same limit.

Results of top-N queries may not follow the order in which tuples were asserted in the database, because their processing depends on the tabled deductive engine, which keeps results from former computations.

4.2.6.1.2 The dual table

The dual table is a special one-row, one-column table present by default in Oracle databases. It is suitable for computing expressions and selecting a pseudo column with no data source. As propositional relations are also allowed in DES, dual does not need a column at all, and it is therefore defined as a single fact without arguments. This table can be used to compute arithmetic expressions as, e.g.:

DES> select sqrt(2) from dual

answer($a0:float) ->

{

answer(1.4142135623730951)

}

Info: 1 tuple computed.

As in MySQL, DES also allows to omit the FROM clause in theses cases (the compilation from SQL to Datalog adds the dual table as data source):

DES> select sqrt(2)

answer($a0:float) ->

{

answer(1.4142135623730951)

}

Info: 1 tuple computed.

Although this table is not displayed with the command /dbschema, it can be nevertheless dropped with a DROP TABLE SQL statement. If it is deleted, the just described behaviour is no longer possible. In addition, it cannot be re-declared with a CREATE TABLE SQL statement, but with a type declaration, as :-type(dual). Both the statement DROP DATABASE and the command /abolish restore this table.

4.2.6.2 A More Developed SQL Query Description

The syntax of the basic SQL query statement is:

SELECT [TOP Integer] [[ALL|DISTINCT]] ProjectionList

[INTO TargetList]

[FROM Relations

[WHERE WhereCondition]

[GROUP BY GroupExpressions]

[HAVING HavingCondition]

[ORDER BY OrderDescription]

[OFFSET Integer [LIMIT Integer]]

[FETCH FIRST Integer ROWS ONLY]]

Where:

· SelectTargetList is the list of comma-separated system/user variable names which receives the values from ProjectionList. This allows to communicate SQL return values with the basic scripting system. For example, SELECT 1 INTO v stores the number 1 in the user variable v. Note that the other way round of communication is by including variables surrounded by $ signs for injecting values from the scripting system to SQL (as, e.g., SELECT * FROM t WHERE a=$v$, where v is a variable defined with the command /set).

· TOP N selects the first N returned rows from the query.

· GROUP BY groups tuples by the criterion specified by GroupExpressions

· HAVING applies a condition on groups.

· OFFSET returns a number of tuples (those specified by LIMIT or all otherwise) starting at a given displacement (0 for the first tuple).

· FETCH behaves as TOP, and both can be used in recursive definitions.

Refer to Section 4.2.13 to inspect the full SQL grammar supported by DES.

4.2.6.2.1 TOP, OFFSET, LIMIT and FETCH

The following query limits the result set to the first n computed rows:

select top n ... from ...

and is equivalent to the following others:

select ... from ... offset 0 limit n

select ... from ... limit n

select ... from ... fetch first n rows only

These are alternative syntactic forms to support the syntax of different SQL systems.

Note that setting n to 0 produces no rows and the system warns about it as in:

DES> select top 0 'Test' from dual

Warning: [Sem] LIMIT/TOP 0 returns nothing.

Warning: [Sem] Inconsistent condition.

answer($a0:string) ->

{

}

Info: 0 tuples computed.

The system also warns for a 0-offset, which does nothing, as in:

DES> select 'Test' from dual offset 0

Warning: [Sem] OFFSET 0 does nothing.

answer($a0:string) ->

{

answer('Test')

}

Info: 1 tuple computed.

Imposing an offset implies to add a stratum; so, a view with an offset cannot be part of a recursive cycle (unless a 0-offset).

4.2.7 String Operations

This section lists string predicates and functions which can be used for testing strings and building string expressions, respectively.

4.2.7.1 CONCAT (Non-ISO)

The function concat(String1, String2) returns a string as the concatenation of String1 and String2. The infix operators || (ISO) and + (Non-ISO) can also be used to concatenate strings.

4.2.7.2 INSTR (Non-ISO)

The function instr(String, Substring) return the first numeric position (1 base index) in String of the searched Substring.

4.2.7.3 LENGTH (Non-ISO)

The function length(String) returns the number of characters of String.

4.2.7.4 LIKE (ISO)

The predicate like is used for pattern matching on strings, where patterns are built with constants and two special characters:

Percent (%), which matches any substring.
Underscore (_), which matches any character.

Patterns are case sensitive. The following example retrieves the employees whose names start with 'N':

DES> select employee from works where employee like 'N%'

answer(works.employee:string) ->

{

answer('Nolan'),

answer('Norton')

}

Info: 2 tuples computed.

It is possible to provide an escape character should the pattern must include one of the special character. For example, the next query retrieves e-mail addresses containing at least one underscore:

DES> select email from employees where email like '%_%' escape '_'

answer(employees.email:string) ->

{

answer('a_nolan@gmail.com')

}

Info: 1 tuple computed.

Values, patterns and the escape character can be formed as expressions involving constants, columns, and other string operations.

4.2.7.5 LOWER (ISO)

The function lower(String) returns the lower case version of String.

4.2.7.6 LPAD (Non-ISO)

The function lpad(String, Width [, Fill]) appends either spaces or Fill (if specified) to the left of String for a total width Width.

4.2.7.7 LTRIM (Non-ISO)

The function ltrim(String) removes leading spaces from String.

4.2.7.8 REPLACE (Non-ISO)

The function replace(String, Find, Replace) replaces the string Find by Replace in the given string String.

4.2.7.9 REVERSE (Non-ISO)

The function reverse(String) reverses the string String.

4.2.7.10 RPAD (Non-ISO)

The function rpad(String, Number [, Fill]) appends either spaces or Fill (if specified) to the right of String for a total width Width.

4.2.7.11 RTRIM (Non-ISO)

The function rtrim(String) removes trailing spaces from String.

4.2.7.12 SUBSTR (Non-ISO)

The function substr(String, Offset [, Length]) returns a string that consists of Length characters from String starting at the Offset position. An offset ranges from 1 (first position of the string) up to the length of the string. An offset greater than this length makes the result to be an empty string. As well, an empty string is returned for a length less than 1. If Offset is negative and Length is greater than -Offset, then the first Length+Offset+1 characters are returned (up to the length of the string).

If Length is not provided, it returns all the string characters starting at the Offset position.

4.2.7.13 TRIM (Non-ISO)

The function trim(String) removes both leading and trailing spaces from String.

4.2.7.14 UPPER (ISO)

The function upper(String) returns the upper case version of String.

4.2.8 Conversion Functions

SQL is a strong typed language (to an extent). Thus, it provides several functions to convert data from one type to another.

4.2.8.1 EXTRACT (ISO)

The function extract(field from datetime) extracts the given field (year, month, day, hour, minute, or second) from a datetime value (date, time or timestamp/datetime). See also Section 4.7.6 for functions extracting parts of a datetime type.

4.2.8.2 CAST (ISO)

The function cast(value as type) converts the data value to a type type. It can be used with the alternative syntax cast(value,type).

4.2.8.3 TO_CHAR (Non-ISO)

The function to_char(Datetime [, Format]) converts a Datetime to a string for the given Format if specified; otherwise, the current date and time formats are assumed.

4.2.8.4 TO_DATE (Non-ISO)

The function to_date(String [, Format]) converts a String to a datetime for the given Format if specified; otherwise, the current date and time formats are assumed.

4.2.8.5 Automatic Type Casting

By enabling automatic type casting with the command /type_casting on, similar results to current DBMS are got. DES tries to convert to the more general type when solving SQL queries. For example:

DES> create table t(a date, b varchar(10))

DES> insert into t values('2020-01-01','2020-01-01')

DES> select * from t where a=b

answer(t.a:datetime(date),t.b:varchar(10)) ->

{

answer('2020-01-01','2020-01-01')

}

Info: 1 tuple computed.

However, systems such as PostgreSQL returns an error in this case:

DES> select * from t where a=b

Error: ODBC Code 1: ERROR: operator does not exist: date = character varying;

Error while executing the query

4.2.9 (Multi)Set Expressions (Non-Standard)

Expressions in the projection list and conditions (in having and where clauses) are scalar following the standard. However, DES allows non-scalar expressions dealing to multisets (sets, if duplicates are disabled as by default).

In the following example, the table t will contain values 1 and 2 for its single field a. By selecting the sum of a from two instances of t, we get the different summations (1+1, 1+2, 2+1, and 2+2):

DES> create table t(a int)

DES> insert into t values (1),(2)

Info: 2 tuples inserted.

DES> select (select a from t)+(select a from t) from dual

answer($a4:int) ->

{

answer(2),

answer(3),

answer(4)

}

Info: 3 tuples computed.

DES> /duplicates on

DES> select (select a from t)+(select a from t) from dual

answer($a4:int) ->

{

answer(2),

answer(3),

answer(4)

}

Info: 4 tuples computed.

If the multiset expression is located at a condition, this condition is examined for each value of the expression, giving as many alternatives as true condition instances:

DES> select 1 from dual where (select a from t)>0

answer($a2:int) ->

{

answer(1),

answer(1)

}

Info: 2 tuples computed.

In this example, following the previous one, there are two values for a in t that makes true the select condition. Thus, two answers are returned. If more multiset expressions are included, the possible alternatives are the product of their cardinalities, as in:

DES> select 1 from dual where (select a from t)>=(select a from t)

answer($a4:int) ->

{

answer(1),

answer(1)

}

Info: 3 tuples computed.

Future work includes to include a flag to commit to SQL standard.

4.2.9.1 Relational Division in SQL (Non-Standard)

The division operation was originally introduced as a relational operation in Codd's paper about relational model. Although it seems to be a practical operation, it is not included in current DBMS's. However, DES includes a novel DIVISION operator that can be used in the FROM clause of a SELECT statement. The next system session illustrates its use:

DES> create table t(a int, b int)

DES> create table s(a int)

DES> insert into t values (1,1)

Info: 1 tuple inserted.

DES> insert into t values (1,2)

Info: 1 tuple inserted.

DES> insert into t values (2,1)

Info: 1 tuple inserted.

DES> insert into s values (1)

Info: 1 tuple inserted.

DES> insert into s values (2)

Info: 1 tuple inserted.

DES> select * from t division s

answer(t.b:int) ->

{

answer(1)

}

Info: 1 tuple computed.

4.2.9.2 Set SQL Queries

The three set operators defined in the standard are available: UNION, EXCEPT, and INTERSECT. (Also, Oracle's MINUS is allowed as a synonymous for EXCEPT.) The first one also admits the form UNION ALL for retaining duplicates. The syntax of a set SQL query is:

SQLStatement

SetOperator

SQLStatement

Where SQLStatement is any SQL statement described in the data query part (without any limitation). SetOperator is any of the abovementioned set operators.

Examples:

(SELECT * FROM s) UNION (SELECT * FROM t);

(SELECT * FROM s) UNION ALL (SELECT * FROM t);

(SELECT * FROM s) INTERSECT (SELECT * FROM t);

(SELECT * FROM s) EXCEPT (SELECT * FROM t);

Note that parentheses are not mandatory in these cases and are only used for readability.

4.2.9.3 WITH SQL Queries

The WITH clause, as introduced in the SQL:1999 standard and available in several RDBMS as DB2, Oracle and SQL Server, is intended in particular to define recursive queries. Its syntax is:

WITH LocalViewDefinition1,

...,

LocalViewDefinitionN

SQLStatement

Where SQLStatement is any SQL statement, and LocalViewDefinition1, ..., LocalViewDefinition1 are (local) view definitions that can only be used in any of these definitions and in SQLStatement. These local views are not stored in the database and are rather computed by demand when executing SQLStatement. Although such definitions are local, they can have the same names as existing objects (tables or views). In such a case, the semantics of the object is overloaded with the semantics of the local definition.

The syntax of a local view definition is as follows:

[RECURSIVE] ViewName(Column1, ..., ColumnN) AS SQLStatement

Here, the keyword RECURSIVE for defining recursive views is not mandatory.

Examples[13]:

CREATE TABLE flights(airline string, from string, to string);

WITH

RECURSIVE reaches(from,to) AS

(SELECT from,to FROM flights)

UNION

(SELECT r1.from,r2.to

FROM reaches AS r1, reaches AS r2

WHERE r1.to=r2.from)

SELECT * FROM reaches;

WITH

Triples(airline,from,to) AS

SELECT airline,from,to

FROM flights,

RECURSIVE Reaches(airline,from,to) AS

(SELECT * FROM Triples)

UNION

(SELECT Triples.airline,Triples.from,Reaches.to

FROM Triples,Reaches

WHERE Triples.to = Reaches.from AND

Triples.airline=Reaches.airline)

(SELECT from,to FROM Reaches WHERE airline = 'UA')

EXCEPT

(SELECT from,to FROM Reaches WHERE airline = 'AA');

In addition, shorter definitions for recursive views are allowed in DES. The next view delivers the same result set as the first example above:

CREATE VIEW reaches(from,to) AS

(SELECT from,to FROM flights)

UNION

(SELECT r1.from,r2.to

FROM reaches AS r1, reaches AS r2

WHERE r1.to=r2.from);

Defining a local view v with the same name as an existing view or table in DBMS's as SQL Server and DB2 results in computing the WITH main statement with respect to the new (local and temporary) definition of v, disregarding the contents of the already-defined, non-local relation v. DES, by contrast, considers the local definition as overloading the existing relation. The following session shows this:

DES> create table s(a int)

DES> insert into s values (2)

Info: 1 tuple inserted.

DES> with s(a) as select 1 select * from s

answer(s.a:int) ->

{

answer(1),

answer(2)

}

Info: 2 tuples computed.

DES> /open_db db2

DES> with s(A) as (select 1 from dual) select * from s

answer(A:INTEGER(4)) ->

{

answer(1)

}

Info: 1 tuple computed.

DES> select * from s;

answer(A:INTEGER(4)) ->

{

answer(2)

}

Info: 1 tuple computed.

4.2.9.4 Hypothetical SQL Queries (Non-Standard)

A novel addition to SQL in DES includes hypothetical queries. Such queries are useful, for instance, in decision support systems as they allow submitting a query by assuming either some knowledge which is not in the database or some knowledge which must not taken into account.

Syntax of hypothetical queries is proposed as:

ASSUME

LocalAssumption1,

...,

LocalAssumptionN

SQLStatement

Where SQLStatement is any SQL DQL statement, and LocalAssumption1, ..., LocalAssumptionN are of the form:

DQLStatement [NOT] IN Relation

SQLStatement is solved under the local assumptions LocalAssumptioni. A Relation is either a name or a complete schema (including attribute names) of either an existing relation or a new relation. So, both tables and views can be overloaded with such local assumptions.

As an example, let's consider a flight database defined by the following:

CREATE TABLE flight(origin string, destination string, time real);

INSERT INTO flight VALUES('lon','ny',9.0);

INSERT INTO flight VALUES('mad','par',1.5);

INSERT INTO flight VALUES('par','ny',10.0);

CREATE OR REPLACE VIEW travel(origin,destination,time) AS

WITH connected(origin,destination,time) AS

SELECT * FROM flight

UNION

SELECT flight.origin,connected.destination,

flight.time+connected.time

FROM flight,connected

WHERE flight.destination = connected.origin

SELECT * FROM connected;

Here, the relation flight represents possible direct flights between locations, and travel represents possible connections by using one or more direct flights. Both include flight time. By querying the relation travel, we get:

DES> SELECT * FROM travel;

answer(travel.origin:string,travel.destination:string,travel.time:float) ->

{

answer(lon,ny,9.0),

answer(mad,ny,11.5),

answer(mad,par,1.5),

answer(par,ny,10.0)

}

Info: 4 tuples computed.

Now, if we assume that there is a tuple flight('mad','lon',2.0), we can query the database with this assumption with the following query (with multi-line input enabled):

DES> ASSUME

SELECT 'mad','lon',2.0

flight(origin,destination,time)

SELECT * FROM travel;

answer(travel.origin:string,travel.destination:string,travel.time:float) ->

{

answer(lon,ny,9.0),

answer(mad,lon,2.0),

answer(mad,ny,11.0),

answer(mad,ny,11.5),

answer(mad,par,1.5),

answer(par,ny,10.0)

}

Info: 6 tuples computed.

Note that the SELECT statement following the keyword ASSUME simply stands for the construction of a single tuple for the table flight (such statement can be otherwise stated as SELECT 'mad','lon',2.0 FROM dual, where dual is the built-in table described in Section 4.2.6.1.2).

In addition, not only tuples can be extensionally assumed, but any SQL DQL statement, i.e., tuples intensionally assumed. As an example, let's suppose that the relation flight is as previously defined, and a view connect that displays locations connected by direct flights:

DES> CREATE VIEW connect(origin,destination) AS

SELECT origin,destination FROM flight;

DES> SELECT * FROM connect;

answer(connect.origin:string,connect.destination:string) ->

{

answer(lon,ny),

answer(mad,par),

answer(par,ny)

}

Info: 3 tuples computed.

Then, if we assume that connections are allowed with transits, we can submit the following hypothetical query (note that the assumed SQL statement is recursive):

DES> ASSUME

(SELECT flight.origin,connect.destination

FROM flight,connect

WHERE flight.destination = connect.origin)

connect(origin,destination)

SELECT * FROM connect;

answer(connect.origin:string,connect.destination:string) ->

{

answer(lon,ny),

answer(mad,ny),

answer(mad,par),

answer(par,ny)

}

Info: 4 tuples computed.

In addition to this, one can use a WITH statement instead of an ASSUME statement by simply stating an existing relation in the definition of the local view. For instance, for the last example, we can write:

DES> WITH

connect(origin,destination) AS

(SELECT flight.origin,connect.destination

FROM flight,connect

WHERE flight.destination = connect.origin)

SELECT * FROM connect;

answer(connect.origin:string,connect.destination:string) ->

{

answer(lon,ny),

answer(mad,ny),

answer(mad,par),

answer(par,ny)

}

Info: 4 tuples computed.

One can use several assumptions in the same query, but only one for a given relation. If needed, you can assume several rules by using UNION. For example:

WITH

flight(origin,destination,time) AS

SELECT 'mad','lon',2.0

UNION

SELECT ‘par’,’ber’,3.0

SELECT * FROM travel;

which is equivalent to:

ASSUME

SELECT 'mad','lon',2.0

UNION

SELECT ‘par’,’ber’,3.0

flight(origin,destination,time)

SELECT * FROM travel;

Both can be alternatively formulated as follows, where several assumptions are made for the same relation and attribute names are dropped:

WITH

flight AS

SELECT 'mad','lon',2.0,

flight AS

SELECT ‘par’,’ber’,3.0

SELECT * FROM travel;

ASSUME

SELECT 'mad','lon',2.0

IN flight,

SELECT ‘par’,’ber’,3.0

IN flight

SELECT * FROM travel;

Note that an assumption for a non-existing relation requires its complete schema:

DES> ASSUME SELECT 1 IN p SELECT * FROM p

Error: Complete schema required for local view definition: p

DES> ASSUME SELECT 1 IN p(a) SELECT * FROM p

answer(p.a:int) ->

{

answer(1)

}

Info: 1 tuple computed.

It is also possible to assume that some tuples are not in a relation (either a table or a view) and then submit a query involving such relation. The following example illustrates this, where we assume that the flight from Madrid to Paris is not available but another flight to London does. Then, we query what travels are possible in this new scenario:

DES> ASSUME

SELECT 'mad','lon',2.0 IN flight,

SELECT 'mad','par',1.5 NOT IN flight

SELECT * FROM travel;

answer(travel.origin:string,travel.destination:string,travel.time:float) ->

{

answer(lon,ny,9.0),

answer(mad,lon,2.0),

answer(mad,ny,11.0),

answer(par,ny,10.0)

}

Info: 4 tuples computed.

Finally, the command /hypothetical Switch allows enabling (on) and disabling (off) the redefinition of relations in WITH and ASSUME queries. If it is enabled, reusing an existing relation causes to overload its definition with the new query. Otherwise, a redefinition error is raised.

4.2.10 Information Schema Language (ISL)

Several non-standard statements are provided to display schema information:

· SHOW TABLES; List table names. TAPI enabled.

· SHOW VIEWS; List view names. TAPI enabled.

· SHOW DATABASES; List database names. TAPI enabled.

· DESCRIBE Relation; Display schema for Relation, as /dbschema Relation.

4.2.11 Transaction Management Language (ISL)

Several standard statements are provided to manage transaction states:

· COMMIT [WORK]; Save the current database. TAPI enabled.

· SAVEPOINT Name; Save the current database to savepoint Name. TAPI enabled.

· ROLLBACK [WORK] [TO SAVEPOINT Name]; Restore database either to the last commit or to the savepoint Name. TAPI enabled.

4.2.12 SQL Syntax and Semantic Checking

Since DES is targetted towards teaching, a reasonable effort has been done to emit detailed error and warning messages, by contrast to most database systems. To this end, both syntax and semantic checking have been coupled with meaningful messages. Syntax checking deals with highlighting the source(s) of incorrect statements, while semantic checking applies to correct statements (from a syntactical point-of-view) but highlights possible error sources.

4.2.12.1 SQL Syntax Checking

Syntax checking proceeds by parsing the input as far as possible until there is no way to detect a correct statement. In this case, both the location of the error and the reason (or reasons if there are several alternatives to end a correct statement) are pointed out, preceded by the assumed language for the error (SQL). Sometimes, possible alternatives are also suggested as expected continuations.

If user identifiers for tables, views and columns are not found, possible alternatives are also suggested by following a "Do What I Mean" (DWIM) approach. For identifiers with 4 characters or more, the following identifiers are suggested: those either equal up to case, or equal up to one char, or equal but one char; and for 2 or more characters: those either equal but swapped characters, or containers.

4.2.12.2 SQL Semantic Checking

After the syntax checking stage, a semantic analysis can point out possible incorrect statements (e.g., missing or incorrect tuples in the actual outcome). By contrary to other approaches (assessment tools, test case generation, data provenance... [JESA12]), we avoid actual execution of statements to inspect query outcome. Instead, we target at the compile-time stage and use CLP to partially solve queries independently from the table instances.

There are some indicators of bad statement design which can be used to raise semantic warnings. In particular, we focus on SQL semantic errors as described in [BG06] that can be caught independently of the database instance. There are many possible errors and, among them, the following are included: inconsistent, tautological and simplifiable conditions, uncorrelated relations in joins, unused tuple variables, constant output columns, duplicate output columns, unnecessary general comparison operators, and several others.

Next, all the supported semantic errors (identified by numbers in [BG06]) in our implementation are described. The analysis incorporates the bindings produced along a successful CLP program solving.

· Error 1: Inconsistent condition. If the evaluation of the CLP program fails, a warning is issued.

· Error 2: Unnecessary DISTINCT. A warning is issued if the query returns no duplicates and includes this modifier with respect to the primary keys in the involved relations.

· Error 3: Constant output column. As a consequence of CLP solving, a column can become ground.

· Error 4: Duplicated column values. Two or more columns can be assigned to the same logical variable representing its output.

· Error 5: Unused tuple variable. An unaccessed single relation in the FROM list from the root query (Error 27 captures all other cases).

· Error 6: Unnecessary join. Check if no column in a join is used in addition to its correlation, if any. Foreign keys are taken into account, otherwise, false positives might be raised.

· Error 7: Tuple variables are always identical. A warning is issued if two or more relations produce the same tuples. This is accomplished by testing if the same goal occurs more than once with the same variables.

· Error 8: Implied or tautological condition. The original Error 8 included an inconsistent condition, which is checked in Error 1 above. Checking this is based on testing whether the complement of the condition fails, meaning that the condition is trivially true.

· Error 9: Comparison with NULL. This is performed in the SQL syntax tree by looking for comparisons with null values.

· Error 11: Unnecessary general comparison operator. A warning is issued if LIKE '%' occurs, which is equivalent to IS NOT NULL by inspecting the SQL syntax tree. Additionally it issues a warning about trivially true (resp. false) conditions as cte LIKE '%' (resp. NOT LIKE).

· Error 12: LIKE without wildcards. Again, this error is straightforwardly checked by inspecting the SQL syntax tree.

· Error 13: Unnecessarily complicated SELECT in EXISTS-subquery. Detect patterns different from SELECT * as the root in an existential subquery.

· Error 16: Unnecessary DISTINCT in aggregation function. A warning is issued if either MIN or MAX is used with a DISTINCT argument, as well as if other aggregate is used with a DISTINCT expression involving key columns.

· Error 17: Unnecessary argument of COUNT. A warning is issued if COUNT is applied to an argument that cannot be null as a primary key. Metadata is used to determine non-null arguments.

· Error 18: Inefficient HAVING (conditions without aggregation function). These conditions should be moved to the WHERE clause, prefiltering tuples.

· Error 27: Missing join condition. A warning is issued if two relations are not joined by a criterium. This includes Error 5 for a single unused relation.

· Error 32: Strange HAVING. A warning is issued if a SELECT with HAVING does not include a GROUP BY.

· Error 33: SUM(DISTINCT ...) or AVG(DISTINCT ...). A warning is issued if duplicate elimination is included for the argument of either SUM or AVG. If included, this might not be an error, but it is suspicious because duplicates are usually relevant for these aggregates.

4.2.13 SQL Grammar

This grammar follows an EBNF-like syntax. Here, terminal symbols are: Parentheses, commas, semicolons, single dots, asterisks, and apostrophes. Other terminal symbols are completely written in capitals, as SELECT. Alternations are grouped with brackets instead of parentheses. Percentage symbols (%) start line comments. User identifiers must start with a letter and consist of letters and numbers; otherwise, a user identifier can be enclosed between quotation marks (both square brackets and double quotes are supported) and contain any character. Next, SQLstmt stands for a valid SQL statement.

SQLstmt ::=

DDLstmt[;]

DMLstmt[;]

DQLstmt[;]

ISLstmt[;]

TMLstmt[;]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% DDL (Data Definition Language) statements

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

DDLstmt ::=

CREATE [OR REPLACE] TABLE CompleteConstrainedSchema

CREATE [OR REPLACE] TABLE TableName [(] LIKE TableName [)]

CREATE [OR REPLACE] TABLE TableName [(] AS DQLstmt [)]

CREATE [OR REPLACE] VIEW Schema AS DQLstmt

CREATE DATABASE DatabaseName % Unsupported up to now

ALTER TABLE TableName [ADD|DROP] | [[COLUMN] Att | CONSTRAINT [ConstraintName] TableConstraint]

ALTER TABLE TableName ALTER [COLUMN] Att [AttDefinition | SET [DATA] TYPE Type]

RENAME TABLE TableName TO TableName

RENAME VIEW ViewName TO ViewName

DROP TABLE DropTableClauses TableName{,TableName} DropTableClauses % Extended syntax following MySQL, SQL Server and others

DROP VIEW DropViewClauses ViewName DropViewClauses

DROP DATABASE [DatabaseName]

CompleteSchema := DQLstmt % Addition to support HR-SQL syntax

DropTableClauses ::=

[IF EXISTS] [CASCADE [CONSTRAINTS]]

DropViewClauses ::=

[IF EXISTS] [CASCADE]

Schema ::=

RelationName

RelationName(Att,...,Att)

CompleteConstrainedSchema ::=

RelationName(AttDefinition {,AttDefinition} [, TableConstraintDefinitions])

AttDefinition ::=

Att Type [ColumnConstraintDefinition {ColumnConstraint}]

CompleteSchema ::=

RelationName(Att Type {,...,Att Type})

Type ::=

CHAR(n) % Fixed-length string of n characters

CHARACTER(n) % Equivalent to CHAR(n)

CHAR % Fixed-length string of 1 character

VARCHAR(n) % Variable-length string of up to n characters

VARCHAR2(n) % Oracle's variable-length string of up to n characters

TEXT(n) % MS Access' variable-length string of up to n characters

VARCHAR % Variable-length string of up to the maximum length of the underlying Prolog atom

STRING % Equivalent to VARCHAR

% CHARACTER VARYING(n) % Equivalent to the former

% |

INT

INTEGER % Equivalent to INT

SMALLINT

NUMERIC(p,d) % A total of p digits, where d of those are in the decimal place

NUMERIC(p) % An integer with a total of p digits

NUMERIC % An integer

DECIMAL(p,d) % Synonymous for NUMERIC

DECIMAL(p) % Synonymous for NUMERIC

DECIMAL % Synonymous for NUMERIC

NUMBER(p,d) % Synonymous for NUMERIC. For supporting Oracle NUMBER

NUMBER(p) % Synonymous for NUMERIC

NUMBER % Synonymous for NUMERIC

REAL

FLOAT % Synonymous for REAL

% |

% DOUBLE PRECISION % Equivalent to FLOAT

% |

FLOAT(p) % FLOAT with precision of at least p digits

DECIMAL % Synonymous for REAL (added to support DECIMAL LogiQL Type). Not SQL standard

DATE % Year, month and day

TIME % Hours, minutes and seconds

TIMESTAMP % Combination of date and time

ConstraintNameDefinition ::=

CONSTRAINT ConstraintName

ColumnConstraintDefinition ::=

[ConstraintNameDefinition] ColumnConstraint

ColumnConstraint ::=

[NOT] NULL % NULL is not in the standard

PRIMARY KEY

UNIQUE

CANDIDATE KEY % Not in the standard, but supported in DB2 for functional dependencies

REFERENCES TableName[(Att)]

DEFAULT Expression

CHECK CheckConstraint

TableConstraintDefinitions ::=

TableConstraintDefinition{,TableConstraintDefinition}

TableConstraintDefinition ::=

[ConstraintNameDefinition] TableConstraint

TableConstraint ::=

NOT NULL Att % Not in the standard

UNIQUE (Att {,Att})

CANDIDATE KEY (Att {,Att}) % Not in the standard

PRIMARY KEY (Att {,Att})

FOREIGN KEY (Att {,Att}) REFERENCES TableName[(Att {,Att})]

CHECK CheckConstraint

CheckConstraint ::=

WhereCondition

(Att {,Att}) DETERMINED BY (Att {,Att}) % Not in the standard, but supported in DB2 for functional dependencies

RelationName is a user identifier for naming tables, views and aliases

TableName is a user identifier for naming tables

ViewName is a user identifier for naming views

Att is a user identifier for naming relation attributes

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% DML (Data Manipulation Language) statements

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

DMLstmt ::=

INSERT INTO TableName[(Att {,Att})] VALUES (ExprDef {,ExprDef}) {, (ExprDef {,ExprDef})}

INSERT INTO TableName DEFAULT VALUES

INSERT INTO TableName[(Att {,Att})] DQLstmt

DELETE FROM TableName [[AS] Identifier] [WHERE Condition]

UPDATE TableName [[AS] Identifier] SET Att=Expr {,Att=Expr} [WHERE Condition]

% ExprDef is either a constant or the keyword DEFAULT

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% DQL (Data Query Language) statements:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

DQLstmt ::=

(DQLstmt)

UBSQL

UBSQL ::=

SELECTstmt

DQLstmt UNION [ALL] DQLstmt

DQLstmt EXCEPT DQLstmt

DQLstmt MINUS DQLstmt

DQLstmt INTERSECT [ALL] DQLstmt

WITH LocalViewDefinition {,LocalViewDefinition} DQLstmt

ASSUME LocalAssumption {,LocalAssumption} DQLstmt % Not in the standard

LocalViewDefinition ::=

[RECURSIVE] Schema AS DQLstmt

[RECURSIVE] DQLstmt NOT IN Schema

LocalAssumption ::=

DQLstmt [NOT] IN Schema

SELECTstmt ::=

SELECT [TOP Integer] [[ALL|DISTINCT]] SelectExpressionList

[INTO SelectTargetList]

[FROM Rels

[WHERE WhereCondition]

[GROUP BY Atts]

[HAVING HavingCondition]

[ORDER BY OrderDescription]

[OFFSET Integer [LIMIT Integer]]

[FETCH FIRST Integer ROWS ONLY]]

Atts ::=

Att {,Att}

OrderDescription ::=

Att [OrderDirection] {,Att [OrderDirection]}

OrderDirection ::=

ASC|DESC|ASCENDING|DESCENDING

SelectExpressionList ::=

SelectExpression {,SelectExpression}

SelectExpression ::=

UnrenamedSelectExpression

RenamedExpression

UnrenamedSelectExpression ::=

Att

RelationName.Att

RelationName.*

Expression

DQLstmt

RenamedExpression ::=

UnrenamedExpression [AS] Identifier

Expression ::=

Op1 Expression

Expression Op2 Expression

Function(Expression{, Expression})

Att

RelationName.Att

Cte

DQLstmt

Op1 ::=

- | \

Op2 ::=

^ | ** | * | / | // | rem | \/ | # | + | - | /\ | << | >> | div

Function ::=

sqrt/1 | ln/1 | log/1 | log/2 | sin/1 | cos/1 | tan/1 | cot/1

| float/1 | integer/1 | sign/1 | gcd/2 | min/2 | max/2 | mod/2

| float_integer_part/1 | float_fractional_part/1

| datetime_add/2 | datetime_sub/2 | add_months/2

| current_time/0 | current_date/0 | current_datetime/0 | sysdate/0

| extract-from

| coalesce/N | greatest/N | iif/3 | least/N | nvl/2 | nvl2/3 | nullif/2

| case-when-then-end

SelectTargetList ::=

HostVariable {, HostVariable}

% Aggregate Functions:

% The argument may include a prefix "distinct" for all but "min" and "max":

% avg/1 | count/1 | count/0 | max/1 | min/1 | sum/1 | times/1

ArithmeticConstant ::=

pi | e

Rels ::=

Rel {,Rel}

Rel ::=

UnrenamedRel

RenamedRel

UnrenamedRel ::=

TableName

ViewName

DQLstmt

JoinRel

DivRel

RenamedRel ::=

UnrenamedRel [AS] Identifier

JoinRel ::=

Rel [NATURAL] JoinOp Rel [JoinCondition]

JoinOp ::=

INNER JOIN

LEFT [OUTER] JOIN

RIGHT [OUTER] JOIN

FULL [OUTER] JOIN

JoinCondition ::=

ON WhereCondition

USING (Atts)

DivRel ::=

Rel DIVISION Rel % Not in the standard

WhereCondition ::=

BWhereCondition

UBWhereCondition

HavingCondition

% As WhereCondition, but including aggregate functions

BWhereCondition ::=

(WhereCondition)

UBWhereCondition ::=

TRUE

FALSE

EXISTS DQLstmt

NOT (WhereCondition)

(AttOrCte{,AttOrCte}) [NOT] IN [DQLstmt|(Cte{,Cte})|((Cte{,Cte}){,(Cte{,Cte})})] % Extension for lists of tuples

WhereExpression IS [NOT] NULL

WhereExpression [NOT] IN DQLstmt

WhereExpression ComparisonOp [[ALL|ANY]] WhereExpression

WhereCondition [AND|OR|XOR] WhereCondition

WhereExpression BETWEEN WhereExpression AND WhereExpression

WhereExpression ::=

Att

Cte

Expression

DQLstmt

AggrExpression ::=

[AVG|MIN|MAX|SUM]([DISTINCT] Att)

COUNT([*|[DISTINCT] Att])

AttOrCte ::=

Att

Cte

ComparisonOp ::=

= | <> | != | < | > | >= | <=

Cte ::=

Number

'String'

DATE 'String' % String in format '[BC] Int-Int-Int'

TIME 'String' % String in format 'Int:Int:Int'

TIMESTAMP 'String' % String in format '[BC] Int-Int-Int Int:Int:Int'

NULL

% Number is an integer or floating-point number

% Int is an integer number

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ISL (Information Schema Language) statements

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

ISLstmt ::=

SHOW TABLES

SHOW VIEWS

SHOW DATABASES

DESCRIBE [TableName|ViewName]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% TML (Transaction Management Language) statements

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

TMLstmt ::=

COMMIT [WORK]

ROLLBACK [WORK] [TO SAVEPOINT SavepointName]

SAVEPOINT SavepointName

Note that this grammar includes the following syntax for DDL statements:

CompleteSchema := DQLstmt

This allows to write typed view definitions in the form:

view(col1 type1, ..., coln typen) := DQLstmt;

which is the syntax needed to support HR-SQL [NSS20] relation definitions.

4.3 (Extended) Relational Algebra

Following the original proposal [Codd70,Codd72] there have been some extensions to its operators (basic, additional and extended). Here, we include all the original and extended operators for dealing with outer joins, duplicate elimination, recursion, and grouping with aggregates. Further, we provide recursion in this setting, as well as other operators for Top-N queries and ordering.

With respect to the textual syntax, we follow [Diet01], where arguments of functions are enclosed between parentheses (as relations), and subscripts and superscripts are delimited between blanks. Arguments in infix operators are not required to be enclosed between any delimiters. Also, parentheses can be used to enhance reading. Conditions and expressions are built with the same syntax as in SQL.

The equivalent Datalog rules and SQL statements for a given RA query can be inspected with the commands /show_compilations on and /show_sql on, respectively. For instance, assuming that the relations in examples/aggregates.ra have been processed already:

DES> /show_compilations on

DES> /show_sql on

DES> project employee.name (employee njoin parking)

Info: Equivalent SQL query:

SELECT ALL employee.name

FROM ((

employee

NATURAL INNER JOIN

parking

));

Info: RA expression compiled to:

answer(A) :-

employee(A,_B,_C),

parking(A,_D).

...

Info: 4 tuples computed.

Examples below refer to the database defined in either examples/relop.ra. (relations a, b, and c) or examples/aggregates.ra (relations employee and parking) .

4.3.1 Operators

This section includes descriptions for basic, additional and extended operators.

4.3.1.1 Basic operators

§ Selection σ_q(R). Select tuples in relation R matching condition q.

Concrete syntax:

select Condition (Relation)

Example:

select a<>'a1' (c);

§ Projection π_A_1,...,An(R). Return all tuples in R only with columns A₁,...,A_n.

Concrete syntax:

project A1,...,An (Relation)

Example:

project b (c);

Note: Columns can be qualified when ambiguity arises, as in:

project a.a (a product c)

If no qualification is provided in presence of ambiguity, then a syntax error is raised.

§ Set union R₁ È R₂.

Concrete syntax:

Relation1 union Relation2

Example:

a union b;

§ Set difference R₁ - R₂.

Concrete syntax:

Relation1 difference Relation2

Example:

a difference b;

§ Cartesian product R₁ ´ R₂.

Concrete syntax:

Relation1 product Relation2

Example:

a product b;

§ Renaming r_R_2(A1,...,An)(R₁). Rename R₁ to R₂, and also arguments of R₁ to A₁,...,A_n.

Concrete syntax:

rename Schema (Relation)

Example:

project v.b (rename v(b) (select true (a)));

Note:

The new name of a renamed relation must be different from the relation.

§ Assignment R₁(A1,...,An) ¬ R₂. Create a new relation R₁ with argument names A1,...,An as a copy of R₂. It allows defining new views.

Concrete syntax:

Relation1 := Relation2

Example:

v(c) := select true (a);

Note:

Easy relation copying is supported by simply specifying relation names (no need to specify their arguments unless you want to change the destination argument names), as in:

u := v; -- Same argument schema for u and v

u(b) := v; -- Renamed schema for u w.r.t. v

4.3.1.2 Additional operators

These operators can be expressed in terms of basic operators, and include:

§ Set intersection R₁ Ç R₂.

Concrete syntax:

Relation1 intersect Relation2

Example:

a intersect b;

§ Theta join R₁ _qR₂. Equivalent to σ_q(R₁ ´ R₂).

Concrete syntax:

Relation1 zjoin Condition Relation2

Example:

a zjoin a.a<b.b b;

§ Natural (inner) join R₁ R₂. Return tuples of R₁ joined with R₂ such that common attributes are pair-wise equal and occur only once in the output relation.

Concrete syntax:

Relation1 njoin Relation2

Example:

a njoin c;

§ Division R₁ ÷ R₂. Return restrictions of tuples in R₁ to the attribute names of R₁ which are not in the schema of R₂, for which it holds that all their combinations with tuples in R₂ are present in R₁. The attributes in R₂ form a proper subset of attributes in R₁.

Concrete syntax:

Relation1 division Relation2

Example:

a division c;

4.3.1.3 Extended operators

Extended operators cannot be expressed in terms of former operators, and include:

§ Extended projection (expressions and renamings) π_E_{1 A1,...,En An}(R). Return tuples of R with a new schema R(A₁,...,A_n) with columns E₁,...,E_n where each E_i is an expression built from constants, attributes of R, and built-in operators. If a given A_i is not provided, the name for the column is either the column E_i, if it is a column, or it is given an arbitrary new name.

Concrete syntax:

project E1 A1,...,En An (Relation)

Examples:

:-type(d(a:string,b:int)).

project b+1 (d);

project incb (project b+1 incb (d))

project sqrt(2) (dual)

§ Duplicate elimination d(R). Return tuples in R, discarding duplicates.

Concrete syntax:

distinct (Relation)

Example:

distinct (project a (c));

Notes:

1) The effect of duplicate elimination is observable when duplicates are enabled with the command /duplicates on.

2) As distinct is also a Datalog (meta)predicate, the query distinct (c) from the Datalog prompt would be solved as a Datalog query, instead of an RA one. Then, if you have to ensure your query will be evaluated by the RA processor, you can either switch to RA with /ra, or prepend the query with /ra, as follows:

DES> % Either switch to RA:

DES>/ra

DES-RA> distinct (project a (c));

DES> /datalog

DES> % Or simply add /ra

DES>/ra distinct (project a (c));

§ Left outer join R₁ _q R₂. Includes all tuples of R₁ joined with matching tuples of R₂ w.r.t. the condition q. Those tuples of R₁ which do not have matching tuples of R₂ are also included in the result, and columns corresponding to R₂ are filled with null values.

Concrete syntax:

Relation1 ljoin Condition Relation2

Example:

a ljoin a=b b;

§ Right outer join R₁ _q R₂. Equivalent to R₂ _q R₁. R₁ _q R₂

Concrete syntax:

Relation1 rjoin Condition Relation2

Example:

a rjoin a=b b;

§ Full outer join R₁ _q R₂. Equivalent to R₁ _q R₂ È R₁ _q R₂.

Concrete syntax:

Relation1 fjoin Condition Relation2

Example:

a fjoin a=b b;

§ Natural left outer join R₁ R₂. Similar to the left outer join but with no condition. Return tuples of R₁ joined with R₂ such that common attributes are pair-wise equal and occur only once in the output relation.

Concrete syntax:

Relation1 nljoin Relation2

Example:

a nljoin c;

§ Natural right outer join R₁ R₂. Equivalent to R₂ R₁.

Concrete syntax:

Relation1 nrjoin Relation2

Example:

a nrjoin c;

§ Natural full outer join R₁R₂. Equivalent to R₁ R₂ È R₁ R₂.

Concrete syntax:

Relation1 nfjoin Relation2

Example:

a nfjoin c;

§ Grouping with aggregations _G_1,...,Gn V^E^1,...,En _q (R). Build groups of tuples in R so that: first, each tuple t in the group have the same values for attributes G₁,...,G_n , second, t matches the condition q (possibly including aggregate functions) and, third, t is projected by the expressions E₁,...,E_n (also possibly including aggregate functions). An empty list of grouping attributes G₁,...,G_n is denoted by an opening and a closing bracket ([]).

Concrete syntax:

group_by GroupingAtts ProjectingExprs HavingCond (Relation)

Examples:

% Number of employees

group_by [] count(*) true (employee);

% Employees with a salary greater than average salary,

% grouped by department

group_by dept id salary > avg(salary) (employee);

§ Sorting τ_L (R). Sort the relation R with respect to the sequence L [GUW02]. This sequence contains expressions which can be annotated by an ordering criterion, either ascending or descending (respectively abbreviated by asc and desc).

Concrete syntax:

sort Sequence (Relation)

Examples:

sort salary (employee);

sort dept desc, name asc (employee);

§ Top φ_N (R). Return the first N tuples of the relation R.

Concrete syntax:

top N (Relation)

Example:

top 10 (hits);

As in SQL, results of top-N queries may not follow the order in which tuples were asserted in the database, because their processing depends on the tabled deductive engine, which keeps results from former computations.

4.3.2 Recursion in RA

Recursion in RA expressions can be specified by simply including the name of the view which is being defined in its definition body. Solving recursion in RA has been proposed as the application of a fixpoint operator to an RA expression (see, for instance, [Agra88, HA92]). DES compiles RA expressions to Datalog programs and uses the (fixpoint-based) deductive engine to solve them.

As an example of recursion in RA, let's consider the following classic program for finding paths in a graph:

create table edge(origin string, destination string);

paths(origin, destination) :=

select true (edge)

union

project paths.origin, edge.destination

(select paths.destination=edge.origin (edge product paths));

select true (paths);

As illustrated in this example, non-linear recursion is allowed as the relation paths is called twice in its definition. Note also that the complete schema must be provided in the left hand side of the assignment operator (otherwise, an unknown relation is raised).

As well, mutually recursive definitions can be specified. However, the schema of the relations must be known before their use in a recursive RA expression. As there is no available an RA context within two or more mutual recursive relations can be encapsulated and defined (similar to the WITH SQL clause), one has to define the schema of each involved mutually recursive relation prior to its definition. This can be done with a CREATE TABLE statement or submitting void definitions. Let's consider the mutually recursive definition for even and odd integers.

With the first alternative:

DES> create table odd(x int);

DES> even(x):= project 0 (dual) union project x+1 (odd);

DES> odd(x) := project x+1 (even);

With the second alternative:

DES> even(x):= project 0 (dual)

DES> odd(x) := project x+1 (even);

DES> even(x):= project 0 (dual) union project x+1 (odd);

This is possible because the assignment operator rewrites any previous definition.

4.3.3 RA Grammar

Here, terminal symbols are: Parentheses, commas, semicolons, single dots, asterisks, and apostrophes. Other terminal symbols are completely written in capitals, as SELECT. However, they are not case-sensitive (though relation names do). Percentage symbols (%) start comments. User identifiers must start with a letter and consist of letters and numbers; otherwise, a user identifier can be enclosed between quotation marks (both square brackets and double quotes are supported) and contain any characters. Next, RAstmt stands for a valid RA statement.

This grammar is built following [Diet01], so that RA files accepted by WinRDBI (a tool described in that book) are also accepted by DES. DES grammar extends WinRDBI grammar in providing support also for: Theta join operator, division, outer join operators, duplicate elimination (distinct operator), grouping (group_by operator), recursive queries, and renaming operator (this avoids to resort to building new relations with the assignment operator :=, although it is supported, too). Also, there is no need to define views and simple queries can be directly submitted to the system.

RAstmt ::=

SELECT WhereCondition (RArel) % Selection (sigma)

PROJECT SelectExpressionList (RArel) % Projection (pi)

RENAME Schema (RArel) % Renaming (rho)

DISTINCT (RArel) % Duplicate elimination

RArel PRODUCT RArel % Cartesian Product

RArel DIVISION RArel % Division

RArel UNION RArel % Set union

RArel DIFFERENCE RArel % Set difference

RArel INTERSECT RArel % Set intersection

RArel NJOIN RArel % Natural join

RArel ZJOIN WhereCondition RArel % Zeta join

RArel LJOIN WhereCondition RArel % Left outer join

RArel RJOIN WhereCondition RArel % Right outer join

RArel FJOIN WhereCondition RArel % Full outer join

RArel NLJOIN RArel % Natural left outer join

RArel NRJOIN RArel % Natural right outer join

GROUP_BY GAtts SelectExpressionList HavingCondition (RArel)

% Grouping

SORT OrderDescription (RArel) % Sorting

TOP Integer (RArel) % Top-N query

RArel ::=

RAstmt

Relation

View definition (assignment statement):

RAview ::=

[Schema | ViewName] := [RAstmt | ViewName]

Schema ::=

ViewName

ViewName(ColName,...,ColName)

GAtts :=

[]

Atts

Where Atts, Condition, SelectExpressionList, HavingCondition and OrderDescription are as in the SQL grammar.

4.4 Tuple Relational Calculus

Relational calculus was proposed by E.F. Codd in [Codd72] as a relational database sublanguage, together with a relational algebra (cf. previous section) with the same purpose. In that paper, he introduced what we know today as Tuple Relational Calculus (TRC) with a positional notation for relation arguments instead of the named notation more widely used nowadays. TRC is closer to SQL than DRC.

Textual syntax of TRC statements in DES follows [Diet01] (with named notation) but relaxing some conditions to ease the writing of queries. For instance, parentheses are not required unless they are really needed, but nonetheless they can be used sparingly to help reading. Furthermore, there are several additions included in DES w.r.t. [Diet01]:

· Implicit references to the dual table are supported, which allows the user to write not only variables but also constants in the target list (following [Codd72] nomenclature for the comma-separated sequence of variables that conforms the output).

· Classical implication is supported, both with the keyword implies as suggested in [Diet01] and the infix operator ->.

· The membership operator in (and its negation not in) supported as an addition for range restriction. So, several syntaxes proposed by different textbooks are supported.

· Wider support of formulae: Order of terms is not relevant for safe formulas, e.g., a comparison can precede the reference to the relation which is the data provider (range restriction).

· Support for propositional relations.

· More detailed syntax and safety error messages.

· Strong type checking. For instance, trying to compare a numeric constant with a string constant is not allowed.

· In addition to (DDL) relation definition queries, DML queries for selecting data are also supported.

The basic syntax of a TRC query (alpha expression in [Codd72]) is:

{ VarsAttsCtes | Formula }

where VarsAttsCtes is known as the target list: a comma-separated sequence of either tuple variables, or attributes, or constants. Tuple variables start with either uppercase or an underscore. A tuple attribute is denoted by r.a, where r is the relation name, and a is an attribute name of the relation r. String constants are delimited by single quotes ('). Identifiers for relations and attributes start either with lowercase or are delimited by double quotes (").

A query can be optionally ended with a semicolon (;). This semicolon is only required when multiline input is enabled (with the command /multiline on).

The following are TRC formulas:

o A monadic atom A

o A comparison built with constants, built-in comparison symbol and variables

Moreover, if F, F1 and F2 are formulae, Vars is a comma-separated sequence of tuple variables, Var is a tuple variable, and Rel is a relation name, then the following are also formulae:

not F -- Negation

F1 and F2 -- Conjunction

F1 or F2 -- Disjunction

F1 -> F2 -- Implication

exists Vars F -- Existential quantifier

forall Vars F -- Universal quantifier

-- The following are alternative syntax sugarings

F1 implies F2 -- Logical implication

Var in Rel -- An atom: Rel(Var)

Var not in Rel -- A negated atom: not Rel(Var)

Tuple variables starting with an underscore are existentially quantified by default ([Diet01] only allows this in DRC). Parentheses can be used sparingly to encapsulate and enhance reading. The alternative syntax sugaring is redundant and intended for user convenience. Operators are not case-sensitive.

The original proposal [Codd72] included range terms of the form p_jR, where p_j is a monadic predicate followed by a tuple variable R, indicating that R has relation r_j in its range. This is expressed in DES as either rj(R) (as in [Diet01]) or rj in R, thus removing the need for p_j.

TRC queries must be safe and legal:

· Each tuple variable in a negated formula must occur in a positive atom (data provider) out of the formula.

· A quantified tuple variable cannot occur out of the formula to which the quantifier is applied.

· Tuple variables and attributes cannot occur duplicated in the target list.

Assuming the relations in examples/jobs.trc, the following are valid TRC queries:

DES> -- Name of employees working for 'IBM':

DES> {W.employee | works(W) and W.company='IBM'}

answer(employee:string) ->

{

answer('Anderson'),

answer('Andrews'),

answer('Arlington'),

answer('Bond')

}

Info: 4 tuples computed.

DES> -- Name of employees not working for 'IBM':

DES> {W.employee | works(W) and not exists U (works(U) and U.company='IBM' and U.employee=W.employee)};

answer(employee:string) ->

{

answer('Nolan'),

answer('Norton'),

answer('Sanders'),

answer('Silver'),

answer('Smith'),

answer('Steel'),

answer('Sullivan')

}

Info: 7 tuples computed.

A tuple variable occurring at different places of a formula (that is, shared tuple variables) means an additional constraint on the result: tuples in each relation for a shared tuple variable must match, therefore easing formulations by removing the need for introducing new equalities. For example, the following query for the database defined in examples/empTraining.trc returns the employees that are either managers or coaches, where the tuple variable T is shared by the relations managers and coaches:

DES> /trc { T | managers(T) or coaches(T) };

answer(eID:string) ->

{

answer('654'),

...

}

Info: 7 tuples computed.

The relations with shared tuple variables must be compatible, i.e., they must have the same number of attributes and the same types (but can have different attribute names). If one of these tuple variables is referenced in the target list, the output schema is built from the first relation occurrence in the formula. Correspondingly, any reference to an attribute of a shared variable corresponds to the name of the attribute of the first relation in the formula with that shared variable. This means that attribute names of a further relations for the same shared variable cannot be accessed. For instance:

DES> create table p(a int)

DES> create table q(b int)

DES> {X|p(X) and q(X) and X.b>0}

Error: Unknown column 'X.b' in statement.

Though types are enforced to be equal for relations referred by the same shared tuple variable, it is however possible to relax this requirement à la SQL, i.e., by allowing compatible types (see Section 4.1.18.1.3), as illustrated in the next example:

DES> create table p(a int)

DES> create table q(b float)

DES> {X|p(X) or q(X)}

Error: Type mismatch q.b:number(float) vs. number(integer).

DES> /type_casting on

DES> {X|p(X) or q(X)}

answer(a:int) ->

{

answer(2.0),

answer(1)

}

Info: 2 tuples computed.

Relations can be defined with the assignment operator (:=) with two possibilities:

· Relation definition: Schema := TRCQuery

· Relation copying: RelationName1 := RelationName2

A schema can be either a relation name or an atom. In the first case, i.e., when attribute names are not provided for defining a relation, an attribute name in the target list becomes the attribute name for the relation. If an attribute name is duplicated in the target list (when it comes from different relations), its name is preceded (qualified) with varname_, where varname is the (first letter being down cased) name of the tuple variable it belongs to. For instance, in the following query, each duplicated attribute name is automatically qualified in the schema as follows:

DES> {E1.employee, E2.employee |

lives(E1) and lives(E2) and E1.city=E2.city and

E1.street=E2.street and E1.employee<E2.employee} ;

answer(e1_employee:string,e2_employee:string) ->

{

answer('Steel','Sullivan')

}

Info: 1 tuple computed.

Recursive definitions are allowed when the relation name to be defined occurs in its definition. For example, let us consider a relation knows(who:string, whom:string) stating that a person identified in its first attribute directly knows a person identified in the second one, and its instance { knows(a,b), knows(b,c), knows(c,d) }. Following the link of related people can be expressed in TRC as the union of the base case (knows) and the inductive case (indc) as follows:

DES> :-type(knows(who:string, whom:string))

DES> insert into knows values ('a','b'), ('b','c'), ('c','d');

DES> :-type(indc(who:string, whom:string))

DES> :-type(link(who:string, whom:string))

DES> indc := { K.who, I.whom | K in knows and I in link and K.whom=I.who };

DES> link := { L | L in knows or L in indc };

Note that it is needed to provide the schema of link before the recursive definition for indc because indc refers to the relation link[14]. Otherwise, an undefined relation error is raised.

This can be queried from the TRC prompt with:

DES-TRC> { L | L in link };

{

linked(a,b), linked(a,c), linked(a,d),

linked(b,c), linked(b,d),

linked(c,d)

}

Info: 6 tuples computed.

Non-linear recursive definitions (i.e., the defined relation occurs more than once in its definition) are also allowed, as the following equivalent formulation to the previous one, which also retrieves the same tuples:

DES> indc := { L1.who, L2.whom | L1 in link and L2 in link and L1.whom=L2.who };

Note that termination is ensured even when there may be cycles in the graph represented by the relation knows, as adding the tuple knows(d,a) to its instance. In this case, 16 tuples would be retrieved (each person would be linked with any other person including itself). Termination control is due to the fixpoint the deductive engine implements (fixpoint iterations are repeated until no more tuples are deduced).

However, it is not possible to devise the link length between two individuals because arithmetic expressions are not yet supported. This feature would be interesting to add for applications requiring such data (as social networks in particular and length of paths in general).

Duplicates are also allowed in TRC. For example, the following session shows the difference when dealing with sets and multisets:

DES> -- Duplicates disabled by default (set operations)

DES> z := { 0 | exists T dual(T) }

DES> { T | z(T) or z(T) }

answer(a:int) ->

{

answer(0)

}

Info: 1 tuple computed.

DES> -- Enabling duplicates (multiset operations)

DES> /duplicates on

DES> { T | z(T) or z(T) }

answer(a:int) ->

{

answer(0),

answer(0)

}

Info: 2 tuples computed.

As an example of propositional relations, the following one can be considered:

DES> /assert p

DES> {'true' | p -> q}

Warning: Undefined predicate: [q/0]

answer($a0:boolean) ->

{

}

Info: 0 tuples computed.

DES> /assert q

DES> {'true' | p -> q}

answer($a0:boolean) ->

{

answer(true)

}

Info: 1 tuple computed.

DES translates TRC queries to DRC queries, which in turn are compiled to Datalog, and eventually processed by the deductive engine. The equivalent Datalog rules for a given TRC query can be inspected by enabling compilation listings with the command /show_compilations on. The final executable Datalog form can be inspected alternatively by enabling development listings with the command /development on. The next session, which considers the relations defined in examples/jobs.trc, shows this:

DES> {E1.employee | works(E1) and not exists E2 (works(E2) and E1.employee=E2.employee and E2.company='IBM')};

Info: TRC statement compiled to:

answer(Employee) :-

works(Employee,_E1_company,_E1_salary),

not exists([_E2_employee,_E2_company,_E2_salary],

(works(_E2_employee,_E2_company,_E2_salary),

Employee=_E2_employee,_E2_company='IBM')).

answer(employee:string) ->

{ ... }

Info: 7 tuples computed.

DES> /development on

DES> {E1.employee | works(E1) and not exists E2 (works(E2) and E1.employee=E2.employee and E2.company='IBM')};

Info: TRC statement compiled to:

answer(Employee) :-

works(Employee,_E1_company,_E1_salary),

not '$p4'(Employee).

'$p4'(Employee) :-

works(Employee,A,B),

works(Employee,'IBM',_E2_salary).

answer(employee:string) ->

{ ... }

Info: 7 tuples computed.

4.4.1 TRC Grammar

% Tuple Relational Calculus statement:

TRCstmt ::=

{ VarsAttsCtes | Formula }

Formula ::=

Formula AND Formula

Formula OR Formula

Formula IMPLIES Formula

Formula -> Formula % Synonymous for IMPLIES

(Formula)

Relation (Var)

Var [NOT] IN Relation

NOT Formula

Condition

QuantifiedFormula

QuantifiedFormula ::=

Quantifier Formula

Quantifier QuantifiedFormula

Quantifier ::=

EXISTS Vars

FORALL Vars

Condition ::=

AttCte RelationalOp AttCte

AttCte ::=

Variable.Attribute

Constant

VarAttCte ::=

Variable

AttCte

VarsAttsCtes ::=

VarAttCte

VarAttCte, VarsAttsCtes

Vars ::=

Variable

Variable, Vars

RelationalOp ::=

| >

| <

| <>

| !=

| >=

| <=

% View definition (assignment statement):

TRCview ::=

[Schema | ViewName] := [TRCstmt | ViewName]

Schema ::=

ViewName

ViewName(ColName,...,ColName)

4.5 Domain Relational Calculus

Domain Relational Calculus (DRC) was proposed in [LP77] and includes domain variables instead of the tuple variables as found in the Tuple Relational Calculus (TRC) [Codd72]. Both calculi are acknowledged as more declarative than their counterpart algebra because while the algebra require to specify the operations needed to compose the output data, the calculi do not, expressing queries with logic constructs (conjunction, disjunction, negation, implication, and existential and universal quantifications). DRC is closer to Datalog than TRC.

Textual syntax of DRC statements in DES follows [Diet01] and, as in TRC, relaxing some conditions to ease the writing of queries and providing several additions. Besides the additions already introduced in the TRC introduction in previous section, for DRC:

· Domain variables starting with an underscore are existentially quantified by default (in addition to the anonymous variables).

The basic syntax of a DRC query is:

{ VarsCtes | Formula }

where VarsCtes is known as the target list, i.e., a comma-separated sequence of either domain variables or constants. Domain variables start with either uppercase or an underscore. String constants are delimited by single quotes ('). Identifiers for relations and attributes start either with lowercase or are delimited by double quotes (").

A query can be optionally ended with a semicolon (;). This semicolon is only required when multiline input is enabled (with the command /multiline on).

The following are TRC formulas:

o An atom A

o A comparison A B C, where A and C can be either constants or variables, and C a built-in infix comparison symbol (=, <, <=, ...)

Moreover, if F, F1 and F2 are formulae, Vars is a comma-separated sequence of domain variables and Rel is a relation name, then the following are also formulae:

not F -- Negation

F1 and F2 -- Conjunction

F1 or F2 -- Disjunction

F1 -> F2 -- Implication

exists Vars F -- Existential quantifier

forall Vars F -- Universal quantifier

-- The following are alternative syntax sugarings

F1 implies F2 -- Logical implication

Vars in Rel -- An atom: Rel(Vars)

Vars not in Rel -- A negated atom: not Rel(Vars)

Domain variables starting with an underscore are existentially quantified by default. Parentheses can be used sparingly to encapsulate and enhance reading. The alternative syntax sugaring is redundant and intended for user convenience. Operators are not case-sensitive.

DRC queries must be safe and legal:

· Each domain variable in a negated formula must occur in a positive atom (data provider) out of the formula.

· A quantified domain variable cannot occur out of the formula on which the quantifier is applied.

· Domain variables must not occur duplicated in the target list.

Assuming the relations in examples/jobs.drc, the following is a valid DRC query:

DES> -- Name of employees working for 'IBM':

DES> {E | works(E,'IBM',_)}

answer(e:string) ->

{

answer('Anderson'),

answer('Andrews'),

answer('Arlington'),

answer('Bond')

}

Info: 4 tuples computed.

This query is equivalent to the following one, where the quantification has been made explicit:

{E | exists Co,S (works(E,Co,S) and Co='IBM')}

Another example for the same database is:

DES> -- Name, street and city of employees earning more than 1000 in a given company:

DES> {E,St,C | lives(E,St,C) and exists Co,S (works(E,Co,S) and S>1000)};

answer(e:string,st:string,c:string) ->

{

answer('Anderson','Main','Armonk'),

answer('Norton','James','Redwood'),

answer('Sanders','High','Redmond'),

answer('Steel','Oak','Redmond'),

answer('Sullivan','Oak','Redmond')

}

Info: 5 tuples computed.

Note that a comma-separated sequence of domain variables is allowed in a quantifier, as in the quantification exists Co,S above. Also, a domain variable occurring at different places of a formula removes the need for introducing new variables and equalities. Without this sugaring, the statement above should be verbosely rewritten as:

{E,St,C | lives(E,St,C) and exists Co (exists E1,S (works(E1,Co,S) and S>1000 and E=E1))};

The following query specifies a division relational operation for the database in jobs.drc, looking for the names of employees working at least for the same companies as the employee Arlington:

{ E | works(E,_,_) and

(forall Co) (works('Arlington',Co,_) -> works(E,Co,_)) }

Relations can be defined with the assignment operator (:=) as in DRC (cf. previous section).

A schema can be either a relation name or an atom. In the first case, each attribute name is the corresponding variable name with its first letter being down cased (in [Diet01] the whole variable identifier is taken in lowercase). Expressions receive a system identifier with the form $ai, where i is an integer starting at 0. In the second case, the functor of the atom is the relation name and its arguments are the names of the attributes.

DES> q2 := {E | works(E,_,_) and not works(E,'IBM',_)};

DES> /dbschema q2

Info: Database '$des'

Info: View:

* q2(e:string)

...

DES> q2(name) := {E | works(E,_,_) and not works(E,'IBM',_)};

DES> /dbschema q2

Info: Database '$des'

Info: View:

* q2(name:string)

...

DES> { 1 | 1=1 }

answer($a0:int) ->

{

answer(1)

}

Info: 1 tuple computed.

Recursive definitions are allowed similarly to the case of TRC. However, formulations can be shortened with the use of shared domain variables. Following the same recursive example as in TRC, it can be expressed in DRC as follows:

DES> :-type(link(who:string, whom:string)) DES> link(X,Z) := { X,Y | knows(X,Y) or exists Z knows(X,Z) and linked(Z,Y) }

In this case, the schema of link must be defined before, because link refers to itself in its definition.

Non-linear recursive definitions are also allowed, as the following equivalent formulation to the previous one, which also retrieves the same tuples:

DES> linked(X,Z) := { X,Y | knows(X,Y) or exists Z linked(X,Z) and linked(Z,Y) }

Duplicates are also allowed in DRC similarly to TRC.

Propositional relations are the same in both DRC and TRC (cf. previous section on TRC).

DES compiles DRC queries to Datalog, which eventually solves them. The equivalent Datalog rules for a given DRC query can be inspected by enabling compilation listings with the command /show_compilations on. The final executable Datalog form can be inspected alternatively by enabling development listings with the command /development on. The next session, which considers the relations defined in examples/jobs.drc, shows this:

DES> {E1 | exists Co,S (works(E1,Co,S) and not exists E2,Co2,S2 (works(E2,Co2,S2) and E1=E2 and Co2='IBM'))};

Info: DRC statement compiled to:

answer(E1) :-

exists([Co,S],(works(E1,Co,S), not exists([E2,Co2,S2],((works(E2,Co2,S2),E1=E2),Co2='IBM')))).

answer(e1:string) ->

{ ... }

Info: 7 tuples computed.

DES> /development on

DES> {E1 | exists Co,S (works(E1,Co,S) and not exists E2,Co2,S2 (works(E2,Co2,S2) and E1=E2 and Co2='IBM'))};

Info: DRC statement compiled to:

answer(E1) :-

works(E1,_Co,_S),

not '$p8'(E1).

'$p8'(E1) :-

works(E1,_Co,_S),

works(E1,'IBM',_S2).

answer(e1:string) ->

{ ... }

Info: 7 tuples computed.

4.5.1 DRC Grammar

% Domain Relational Calculus statement:

DRCstmt ::=

{ VarsCtes | Formula }

Formula ::=

Formula AND Formula

Formula OR Formula

Formula IMPLIES Formula

Formula -> Formula % Synonymous for IMPLIES

(Formula)

Relation (VarsCtes)

VarsCtes [NOT] IN Relation

NOT Formula

Condition

QuantifiedFormula

QuantifiedFormula ::=

Quantifier Formula

Quantifier QuantifiedFormula

Quantifier ::=

EXISTS Vars

FORALL Vars

Condition ::=

VarCte RelationalOp VarCte

VarCte ::=

Variable

Constant

VarsCtes ::=

VarCte

VarCte, VarsCtes

Vars ::=

Variable

Variable, Vars

RelationalOp ::=

| >

| <

| <>

| !=

| >=

| <=

% View definition (assignment statement):

DRCview ::=

[Schema | ViewName] := [DRCstmt | ViewName]

Schema ::=

ViewName

ViewName(ColName,...,ColName)

4.6 Prolog

Syntax of Prolog programs and goals is the same as for Datalog, including all built-in operators (cf. next Section) but metapredicates. Notice that negation is written as not Goal, instead of the usual \+ Goal in Prolog.

When a goal is solved, instead of displaying the variable substitution for the answer, the goal is displayed with the substitution applied, as in:

DES-Prolog> t(X)

t(1)

? (type ; for more solutions, <Intro> to continue) ;

t(2)

? (type ; for more solutions, <Intro> to continue) ;

4.7 Built-ins

Most built-ins are shared by all the languages. For instance, w.r.t. comparison operators, the first difference is the less or equal (=<) operator used in Datalog and Prolog. This operator is different from the used in SQL, TRC, DRC and RA, which is written as <=. The former is written that way since in Prolog and Datalog, it is distinguished from the implication to the left operator (<=). SQL does not provide implications; so, the SQL syntax seems to be more appealing since the order of the two symbols matches the order of words. The second difference is the disequality symbol: In Datalog and Prolog, it is used \=,[15] while in SQL, TRC, DRC and RA the alternative symbols <> and != are used.

Arithmetic expressions are constructed with the same built-ins in the three languages. However, in Datalog and Prolog, you need to use the infix is (cf. Section 4.7.2), and in Datalog, the equality = can also be used.

The built-in predicates is_null/1 and is_not_null/1 belong to the Datalog language.

Also, consult Section 5.3 for limitations regarding safety in the use of built-ins in Datalog.

4.7.1 Comparison Operators

All comparison operators are infix and apply to terms. For the inequality and disequality operators (greater than, less than, etc.), numbers are compared in terms of their arithmetical value; other terms are compared in Prolog standard order.

If a compound term is involved in a comparison operator, it is evaluated as an expression and its result is then compared (for all operators except equality) or unified (for equality). Note that this departs from Prolog in which expressions (terms) are simply data terms and therefore are not evaluated.

All comparison operators, except equality, demand ground arguments since they are not constraints, but test operators, and argument domains are infinite. If a ground argument is demanded and a variable is received, an exception is raised.

Next, we list the available comparison operators, where X and Y are terms (variables, constants or expressions of any of the supported types). Expressions are evaluated before comparison. Order of data depends on the underlying Prolog system on which DES runs.

· X = Y (Equality)

Tests equality between X and Y. It also performs unification when variables are involved. This is the only comparison operator that does not demand ground arguments.

· X \= Y (Disequality)

Tests disequality between the evaluation of expressions X and Y.

· X \== Y (Disequality)

Tests syntactic disequality between X and Y, without evaluating them.

· X > Y (Greater than)

Tests whether X is greater than Y.

· X >= Y (Greater than or equal to)

Tests whether X is greater than or equal to than Y.

· X < Y (Less than)

Tests whether X is less than Y.

· X =< Y (Less than or equal to)

Tests whether X is less than or equal to Y.

4.7.2 Datalog and Prolog Arithmetic

Borrowed from most Prolog implementations, arithmetic is allowed by using the infix operator is, which is used to construct a query with two arguments, as follows:

X is Expression

where X is a variable or a number, and Expression is an arithmetic expression built from numbers, variables, built-in arithmetic operators, constants and functions, mainly following ISO for Prolog (they are labelled, if so, in the listings below). Availability of arithmetic built-ins mainly depends on the underlying Prolog system (binary distributions cope with all the listed built-ins).

At evaluation time, the expression must be ground (i.e., its variables must be bound to numbers or constants); otherwise, problems as stated in the previous section may arise. Evaluating the above query amounts to evaluate the arithmetic expression according to the usual arithmetic rules, which yields a number (integer or float), and X is bound to this number if it is a variable, or tested its equivalence if it is a number. Precision depends on the underlying Prolog system.

Arithmetic built-ins have meaning only in the second argument of is or as any operand of equality. They cannot be used elsewhere. For example:

DES> X is sqrt(2)

{

1.4142135623730951 is sqrt(2)

}

Info: 1 tuple computed.

Here, sqrt(2) is an arithmetic expression that uses the built-in function sqrt (square root). But:

DES> sqrt(2) is sqrt(2)

raises an input error because an arithmetic expression can only occur as the right argument of is. Another example is:

DES> X is e

{

2.718281828459045 is exp(1)

}

Info: 1 tuple computed.

Note that arithmetic expressions are compound terms which are translated into an internal equivalent representation. The last example shows this since the constant e is translated to exp(1).

Concluding, the infix (infinite) relation is is understood as the set of pairs <V, E> such that V is the equivalent value to the evaluation of the arithmetical expression E. Note that, since this relation is infinite, we may reach non-termination: Let’s consider the following program (loop.dl in the distribution directory) with the query loop(X):

loop(0).

loop(X) :-

loop(Y),

X is Y + 1.

Evaluating that query results in a non-terminating cycle because unlimited tuples is(N,N+1) become computed. To show it, try the query, press Ctrl-C, and type listing(et) at the Prolog prompt (only when DES has been started from a Prolog interpreter). Should you want a limited answer for loop, you can use the Top-N built-in top/2 (see forthcoming Section 4.7.13).

This infix operator is can be replaced by the equality comparison with the same results (but not the other way round). For instance:

DES> X=sqrt(2)

{

1.4142135623730951=sqrt(2)

}

Info: 1 tuple computed.

DES> X is sqrt(2)

{

1.4142135623730951 is sqrt(2)

}

Info: 1 tuple computed.

DES> sqrt(2) is X

Error: (DL) Invalid number after 'sqrt(2'

4.7.3 SQL, TRC and DRC Arithmetic

Arithmetic expressions are constructed with the arithmetic operators listed in the next section. They are used in projection lists and conditions.

4.7.4 Arithmetic Built-ins

This section contains the listings for the supported arithmetic operators, constants, and functions.

4.7.4.1 Arithmetic Operators

The following operators are the only ones allowed in arithmetic expressions, where X and Y stand also for arithmetic expressions.

· X (Bitwise negation) ISO
Bitwise negation of the integer X.

· -X (Negative value) ISO

Negative value of its single argument X.

· X ** Y (Power) ISO

X raised to the power of Y.

· X ^ Y (Power)

Synonym for X ** Y.

· X * Y (Multiplication) ISO

X multiplied by Y.

· X / Y (Real division) ISO

Float quotient of X and Y.

· X + Y (Addition) ISO

Sum of X and Y.

· X - Y (Subtraction) ISO

Difference of X and Y.

· X // Y (Integer quotient) ISO

Integer quotient of X and Y. The result is always truncated towards zero.

· X rem Y (Integer remainder) ISO

The value is the integer remainder after dividing X by Y, i.e., integer(X)-

integer(Y)*(X//Y). The sign of a nonzero remainder will thus be the same as that of the dividend.

· X \/ Y (Bitwise disjunction) ISO

Bitwise disjunction of the integers X and Y.

· X /\ Y (Bitwise conjunction) ISO

Bitwise disjunction of the integers X and Y.

· X xor Y (Bitwise exclusive or) ISO

Bitwise exclusive or of the integers X and Y.

· X << Y (Shift left) ISO

X shifted left Y places.

· X >> Y (Shift right) ISO

X shifted right Y places.

4.7.4.2 Arithmetic Constants

· pi (π)

Archimedes' constant.

· e (Neperian number)

Neperian number.

4.7.4.3 Arithmetic Functions

· sqrt(X) (Square root) ISO

Square root of X.

· log(X) (Natural logarithm) ISO

Logarithm of X in the base of the Neperian number (e).

· ln(X) (Natural logarithm)

Synonym for log(X).

· log(X,Y) (Logarithm)

Logarithm of Y in the base of X.

· sin(X) (Sine) ISO

Sine of X.

· cos(X) (Cosine) ISO

Cosine of X.

· tan(X) (Tangent) ISO

Tangent of X.

· cot(X) (Cotangent)

Cotangent of X.

· asin(X) (Arc sine)

Arc sine of X.

· acos(X) (Arc cosine)

Arc cosine of X.

· atan(X) (Arc tangent) ISO

Arc tangent of X.

· acot(X) (Arc cotangent)

Arc cotangent of X.

· abs(X) (Absolute value) ISO

Absolute value of X.

· power(B,E) (Power)

B raised to the power of E.

· exp(E) (Power)

Euler number raised to the power of E.

· float(X) (Float value) ISO

Float equivalent of X, if X is an integer; otherwise, X itself.

· integer(X) (Integer value)

Closest integer between X and 0, if X is a float; otherwise, X itself.

· sign(X) (Sign) ISO

Sign of X, i.e., -1, if X is negative, 0, if X is zero, and 1, if X is positive, coerced into the same type as X (i.e., the result is an integer, iff X is an integer).

· gcd(X,Y) (Greatest common divisor)

Greatest common divisor of the two integers X and Y.

· min(X,Y) (Minimum)

Least value of X and Y.

· max(X,Y) (Maximum)

Greatest value of X and Y.

· trunc(X) (Truncate)

Closest integer between X and 0.

· truncate(X) (Truncate) ISO

Closest integer between X and 0.

· trunc(X,D) (Truncate)

Return X truncated to D decimals.

· truncate(X,D) (Truncate) ISO

Return X truncated to D decimals.

· float_integer_part(X) (Integer part as a float) ISO

The same as float(integer(X)).

· float_fractional_part(X) (Fractional part as a float) ISO

Fractional part of X, i.e., X - float_integer_part(X).

· round(X) (Closest integer) ISO

Closest integer to X. X has to be a float. If X is exactly half-way between two integers, it is rounded up (i.e., the value is the least integer greater than X).

· round(X,Y) (Closest integer)

Round X to the number of places Y w.r.t. the decimal point. Y can be negative.

· floor(X) (Floor) ISO

Greatest integer less than or equal to X. X has to be a float.

· ceiling(X) (Ceiling) ISO

Least integer greater than or equal to X. X has to be a float.

· rand (Random number)

Random float number between 0 and 1. A Datalog predicate '$rand'/1 is available (with a single argument as its output).

· rand(X) (Random number)

Random float number between 0 and 1 with a 64 bit integer seed X. A Datalog predicate '$rand'/3 is available available (the input in the first argument and the output in the last one).

4.7.5 String Functions and Operators

All the functions listed below find a counterpart Datalog predicate with an additional argument at the end representing the result. The name of the predicate is prepended with $ and enclosed between quotes as, for instance, '$length'(X,Y) , which returns in Y the length of X. So, in Datalog, one can use both a function in expressions and its counterpart predicate in goals.

Functions:

· length(X) (Length of string)

· concat(X,Y) (Concatenation of strings)

· left(X,Y) (Return the first Y characters of X)

· lower(X) (Lowercase conversion)

· ltrim(X) (Remove leading spaces)

· repeat(X,Y) (Repeat the string X as many times as Y)

· right(X,Y) (Return the last Y characters of X)

· rtrim(X) (Remove trailing spaces)

· space(X) (Return a string with X spaces)

· substr(X,Y,Z) (Substring starting at offset Y with length Z)

· upper(X) (Uppercase conversion)

Operators:

· X like Y [escape Z] (Comparison of strings) ISO

The escape part is optional. Not available as an operator in Datalog, but as the predicates $like/3 and $like/4.

· X + Y (Concatenation of strings) ISO

· X || Y (Concatenation of strings)

4.7.6 Date and Time: Data Structures, Functions and Operators

Date and time representation in computers has been a cumbersome task since computer science inception. Recall, for instance, the Y2K issue (only the last two digits for storing a year). Calendars [US12] are not unique around the world. For example, the Gregorian calendar, which replaced the Julian calendar, was adopted at different years in different countries. The SQL standard defines dates for years in the range 0-9999, omitting BC dates (before year 1), and uses a proleptic Gregorian (Gregorian calendar extrapolated to dates before its inception, omitting the original Julian). While DB2 is the DBMS most closer to this standard, others, as Oracle, follow a more "real" approach (including both Julian and Gregorian calendars and BC dates). Here, we follow this approach, but not limiting the upper bound to dates, in the following way.

Dates start at -4712 (BC 4713), where the year 0 corresponds to BC 1. The Julian calendar is used up to 1582-10-4 (year-month-date as of ISO 8601), while the Gregorian calendar is used from 1582-10-15 on. Note that there are 11 days (from 1582-10-5 to 1582-10-14) which are not accepted as valid dates (they were removed from the calendar to adjust the accumulated imprecisions of the Julian calendar). For internal calculations, the Julian Date, as used by astronomers, is applied.

In the rest of this subsection, format, date/time data structures, functions and operators for both Datalog and SQL are described.

Date and Time Format:

By default, dates are displayed in answers and user listings following ISO 8601: YYYY-MM-DD (4 digits for the year, 2 for the month, and 2 for the day of the month). Date and time formatting can be disabled with the command /format_datetime off, and can be changed with the command /date_format Format and /time_format Format (cf. Section 5.17.12).

Datalog Data Structures:

The following data structures can be used in the different languages:

· date(Year,Month,Day)
Dates start at date(-4712,1,1) (begin of the current astronomical Julian Date) and has no upper limit. Note that year -4712 is read as BC 4713, and year 0 in this structure is read as BC 1.

· time(Hour,Minute,Second)
Times are also stored normalized, even for negative numbers. For example, time(1,-1,0) is normalized as time(0,59,0).

· datetime(Year,Month,Day,Hour,Minute,Second) (Timestamp)
A timestamp is stored normalized.

SQL, RA, TRC and DRC Data Structures:

· date 'Year-Month-Day' ISO
As an extension to ISO, Year can be negative or can be prepended by BC (for years before 1). As in Datalog, non-valid dates are converted to valid dates before storing or using them.

· time 'Hour:Minute:Second' ISO
As an extension to ISO, negative parts of the time are allowed.

· timestamp 'Year-Month-Day Hour:Minute:Second ' ISO

· datetime 'Year-Month-Day Hour:Minute:Second '
This data structure is a synonymous for timestamp.

Notes:

· Seconds can have a fractional part.

· Though discouraged, you can write dates and times with outbound values as, e.g., 32 for the day (or even negative), which is converted into (i.e., normalized to) a valid date before storing or using it. So, an input as date(2018,12,32) would be internally represented as date(2019,1,1), and date(2018,12,-1) as date(2018,11,31).

Crossing the bounds between Gregorian and Julian calendars for non-valid dates may develop unexpected results. For example, date(1582,11,-31) would be (incorrectly) stored as date(1582,9,20) .

· Neither time zones nor leap seconds are implemented yet.

· When type casting in enabled (with /type_casting on), strings can be directly used to specify dates.

· Use cast(StringDate as date) to convert a string value to a date value, following the current date format (see /date_format)

· Use cast(StringTime as time) to convert a string value to a date value, following the current time format (see /time_format)

· Use cast(StringDatetime as datetime) to convert a string value to a datetime value, following the current time and date formats (see /date_format and /time_format)

· Use to_char(DatetimeType, StringFormat) for a more flexible formatting than cast(StringDatetime as DatetimeType)

Functions:

Almost all the functions listed below find a counterpart Datalog predicate with an additional argument at the end representing the result (exceptions are noticed). The name of the predicate is prepended with $ and enclosed between quotes as, for instance, '$year'(X,Y) , which returns in Y the year of X.

· year(X) ISO

Extract the year of a date/time value as a number.

· month(X)
Extract the month of a date/time value as a number.

· day(X)
Extract the day of a date/time value as a number.

· hour(X)
Extract the hour of a date/time value as a number.

· minute(X)
Extract the minute of a date/time value as a number.

· second(X)
Extract the second of a date/time value as a number.

· extract(X from Y) ISO
Extract the field X from the date/time value Y, where X can be year, month, day, hour, minute, or second .
This function is not available for Datalog.

· to_char(X)
Convert a datetime to a string.

· to_char(X,Y)
Convert a datetime to a string for a given format (see /time_format).

· to_date(X)
Convert a string to a date.

· to_date(X,Y)
Convert a string to a date for a given format (see /date_format).

· current_date ISO
Return the current date.

· current_time ISO
Return the current time.

· current_timestamp ISO
Return the current timestamp.

· sysdate
Synomym for current_date (Oracle syntax).

· add_months(X,Y)

Add to the datetime X the number of months Y

· datetime_add(X,Y)

Return the datetime X increased by the number Y. If X is a date, Y represents days, and seconds otherwise. This function is equivalent to the overloaded X + Y

· datetime_sub(X,Y)

If Y is a number, return the datetime X decreased by the days Y. If X and Y are dates, return the number of days between them. If X and Y are either times or timestamps, return the number of seconds between them. This function is equivalent to the overloaded X - Y

· last_day(X)

Return the last day of the month for the given datetime X

Operators:

· X + Y (Addition) ISO

Sum of X and Y. Arguments can be a date/time and an integer value, but two date/times cannot be added. Adding a number to a date means adding days, whereas adding a number to a time or datetime means adding seconds.

· X - Y (Subtraction) ISO

Difference of X and Y. Arguments can be either a date/time or an integer value. Subtracting two dates computes the number of days between them. Subtracting two times or datetimes computes the seconds between them.

Comparison operators apply to values with the same date/time types. Comparing different date/time values in Datalog does not raise any exception but may yield an unexpected behaviour. For example (with date formatting disabled) :

DES> datetime(2010,1,1,0,0,0)>date(2010,1,1)

{

datetime(2010,1,1,0,0,0)>date(2010,1,1)

}

Info: 1 tuple computed.

That is, one might interpret to be asking whether the start time of the day 1/1/2010 is after the day 1/1/2010, which intuitively would not succeed. However, date and time comparisons in Datalog are syntactic comparison, and the term datetime(2010,1,1,0,0,0) is actually after the term date(2010,1,1), and so the comparison in this example does succeed.

4.7.7 Selection Functions

· coalesce(ExpList) SQL ISO

Return the first non-null value in the list of evaluated expressions ExpList.

· greatest(ExpList)

Return the greatest value in the list of evaluated expressions ExpList.

· iif(Cond,Exp1,Exp2)

Return Exp1 if Cond evaluates to true; otherwise return Exp2.

· least(ExpList)

Return the least value in the list of evaluated expressions ExpList.

· nullif(Exp1,Exp2)

Return null if Exp1 and Exp2 are equal; otherwise return Exp1.

· nvl(Exp1,Exp2)

Return Exp2 if Exp1 evaluates to null; otherwise return Exp1. Equivalent to

· case(CVList,Exp) SQL ISO

Given the list CVList of pairs (Condition,Value), return the first value for which its condition holds; otherwise, return Exp.

· case(Value,MVList,Exp) SQL ISO

Return the first ReturnValue in the list MVList of pairs (MatchValue,ReturnValue) for which its value MatchValue matches Value; otherwise, return Exp.

4.7.8 Negation

· not Query (Stratified negation)

It stands for the complement of the relation Query w.r.t. the meaning of the program (i.e., closed world assumption). See sections 4.1.8 and 5.22.3. If Query is not an atom, a new predicate defined by a head Head with relevant variables in Query is built, and defined by the single rule Head :- Query. Then, not Head is replaced by not Query.

4.7.9 Datalog Outer Joins

· lj(LeftRelation,RightRelation,JoinCondition) (Left join)

It stands for the left outer join of the relations LeftRelation and relations RightRelation, under the condition JoinCondition (expressed as literals, cf. Section 4.1.1), as understood in extended relational algebra (LeftRelation_{JoinCondition} RightRelation).

· rj(LeftRelation,RightRelation,JoinCondition) (Right join)

It stands for the right outer join of the relations LeftRelation and relations RightRelation, under the condition JoinCondition (expressed as literals, cf. Section 4.1.1), as understood in extended relational algebra (LeftRelation _{JoinCondition} RightRelation).

· fj(LeftRelation,RightRelation,JoinCondition) (Full join)

It stands for the full outer join of the relations LeftRelation and relations RightRelation, under the condition JoinCondition (expressed as literals, cf. Section 4.1.1), as understood in extended relational algebra (LeftRelation _{JoinCondition} RightRelation).

4.7.10 Datalog Aggregates

This section lists both aggregate functions (to be used in expressions) and aggregate predicates (including grouping).

4.7.10.1 Aggregate Functions

Aggregate functions can only occur in the context of a group_by aggregate predicate (see next section) and apply to the result set for its input relation.

· count(Variable)

Return the number of tuples in the group so that the value for Variable is not null.

· count

Return the number of tuples in the group, disregarding tuples may contain null values.

· sum(Variable)

Return the sum of values for Variable in the group, ignoring nulls.

· times(Variable)

Return the product of values for Variable in the group, ignoring nulls.

· avg(Variable)

Return the average of values for Variable in the group, ignoring nulls.

· min(Variable)

Return the minimum value for Variable in the group, ignoring nulls.

· max(Variable)

Return the maximum value for Variable in the group, ignoring nulls.

4.7.10.2 Predicate group_by

· group_by(Query,Variables,GroupConditions)

Solve GroupConditions in the context of Query, building groups w.r.t. the possible values the variables in the list Variables. This list is specified as a Prolog list, i.e., a sequence of comma-separated values enclosed between square brackets. If this list is empty, there is only one group: the answer set for Query. The (possibly compound) goal GroupConditions can contain aggregate functions ranging over set variables.

4.7.10.3 Aggregate Predicates

· count(Query,Variable,Result)

Count in Result the number of tuples in the group for the query Query so that Variable is a variable of Query (an attribute of the result relation set) and this attribute is not null. It returns 0 if no tuples are found in the result set.

· count(Query,Result)

Count in Result the total number of tuples in the group for the query Query, disregarding whether they contain nulls or not. It returns 0 if no tuples are found in the result set.

· sum(Query,Variable,Result)

Sum in Result the numbers in the group for the query Query and the attribute Variable, which should occur in Query. Nulls are simply ignored.

· times(Query,Variable,Result)

Compute in Result the product of all the numbers in the group for the query Query and the attribute Variable, which should occur in Query. Nulls are simply ignored.

· avg(Query,Variable,Result)

Compute in Result the average of the numbers in the group for the query Query and the attribute Variable, which should occur in Query. Nulls are simply ignored.

· min(Query,Variable,Result)

Compute in Result the minimum of the numbers in the group for the query Query and the attribute Variable, which should occur in Query. Nulls are simply ignored. If there are no such numbers, it returns null.

· max(Query,Variable,Result)

Compute in Result the maximum of the numbers in the group for the query Query and the attribute Variable, which should occur in Query. Nulls are simply ignored. If there are no such numbers, it returns null.

4.7.11 Null-related Predicates

· is_null(Term)

Succeed if Term is bound to a null value. It raises an exception if Term is a variable.

· is_not_null(Term)

Succeed if Term is not bound to a null value. It raises an exception if Term is a variable.

4.7.12 Duplicates

The following built-ins take effect when duplicates are enabled via the command /duplicates on.

· distinct(Query)

Succeed as many times as different ground answers are computed for Query.

· distinct([Variables], Query)

Succeed as many times as different ground tuples (built with Variables) are computed for Query.

4.7.13 Top-N Queries

· top(N,Query)

Succeed at most N times for Query. This metapredicate can occur at the top-level and in any rule body.

As tuples are usually (but not always) retrieved in the chronological order in which they were asserted, this metapredicate has not a declarative reading. So, the answer to a top-N query depends on either when tuples were asserted, or they become ordered, or even on how they were solved by the deductive engine. In addition, for intensional predicates, their EDB rules are firstly fetched, followed by their IDB rules. Let's consider the following system session:

DES> /assert t(1)

DES> /assert t(2)

DES> top(1,t(X))

Info: Processing:

answer(X) :-

top(1,t(X)).

{

answer(1)

}

Info: 1 tuple computed.

DES> /abolish

DES> /assert t(2)

DES> /assert t(1)

DES> top(1,t(X))

Info: Processing:

answer(X) :-

top(1,t(X)).

{

answer(2)

}

Info: 1 tuple computed.

DES> /assert p(X):-X=0;p(Y),X=Y+1

DES> /assert p(1)

DES> top(1,p(X))

Info: Processing:

answer(X) :-

top(1,p(X)).

{

answer(1)

}

Info: 1 tuple computed.

Depending on current and previous queries, results of top-N queries may not follow the order in which tuples were asserted in the database, because their processing depends on the tabled deductive engine, which keeps results from former computations.

4.7.14 Pagination Queries

Pagination queries are useful to retrieve pages of tuples starting at a given position (offset) with an optional given size (limit). There are two predicates to achieve this:

· offset(Query,Offset)

· offset(Query,Offset,Limit)

The first one retrieves all tuples resulting from solving Query starting at position Offset. The first query starts at position 0. The second predicate behaves as the first one but retrieving only a Limit number of tuples. For example:

DES> /abolish

DES> /assert t(1)

DES> /assert t(2)

DES> /assert t(3)

DES> t(X),t(Y)

Info: Processing:

answer(X,Y) :- t(X),t(Y).

{

answer(1,1),

answer(1,2),

answer(1,3),

answer(2,1),

answer(2,2),

answer(2,3),

answer(3,1),

answer(3,2),

answer(3,3)

}

Info: 9 tuples computed.

DES> offset((t(X),t(Y)),3,3)

Info: Processing:

answer(X,Y)

in the program context of the exploded query:

answer(X,Y) :- offset((t(X),t(Y)),3,3).

{

answer(2,1),

answer(2,2),

answer(2,3)

}

Info: 3 tuples computed.

As with the top predicate, the order in which tuples are returned affects semantics:

DES> % t(1) was asserted first

DES> /retract t(1)

DES> % Asserting t(1) again makes it the last tuple

DES> /assert t(1)

DES> % By default, answers are ordered; so, we disable this

DES> /order_answer off

DES> t(X),t(Y)

Info: Processing:

answer(X,Y) :- t(X), t(Y).

{

answer(2,2),

answer(2,3),

answer(2,1),

answer(3,2),

answer(3,3),

answer(3,1),

answer(1,2),

answer(1,3),

answer(1,1)

}

Info: 9 tuples computed.

DES> offset((t(X),t(Y)),3,3)

Info: Processing:

answer(X,Y)

in the program context of the exploded query:

answer(X,Y) :- offset((t(X),t(Y)),3,3).

{

answer(3,2),

answer(3,3),

answer(3,1)

}

Info: 3 tuples computed.

Note that the command /order_answer only affects to how the final result of the query is displayed. It is not needed to disable answer ordering for obtaining the same results with offset.

Solving this predicate implies to solve Query in a deeper stratum. Thus, offset cannot be used in a recursive cycle.

4.7.15 Order-By Predicate

· order_by(Query, [Expr1, …, ExprN])

· order_by(Query, [Expr1, …, ExprN], [Ord1, …, OrdN])

Order the result tuples for Query following Expr1, …, ExprN, where Expri is an expression and Ordi is the (optional) ordering criterion which can be either a (for ascending order) or d (for descending order). The order depends on the standard order of terms provided by the underlying Prolog system. For instance, the following is extracted from the SICStus Prolog manual, which specifies its particular order:

Variables, by age (oldest first—the order is not related to the names of variables).
Floats, in numeric order (e.g. -1.0 is put before 1.0).
Integers, in numeric order (e.g. -1 is put before 1).
Atoms, in alphabetical (i.e. character code) order.
Compound terms, ordered first by arity, then by the name of the principal functor, then by age for mutables and by the arguments in left-to-right order for other terms. Recall that lists are equivalent to compound terms with principal functor ./2.

So, variables come before floats, floats before integers, and son on. In particular, this means that [p(1.0), p(0)] is actually sorted because any integer is before than any float, even when the number it represents is not less. In contrast, the default configuration of SWI-Prolog considers both as numbers and the ordered list in this example would be [p(0), p(1.0)] .

The default answer ordering (set with /order_answer) is overridden if a top-level query includes this predicate in any place of its computation paths. If the list of ordering criterion is omitted, an ascending ordering is applied. Solving an order_by predicate requires to have its query argument completely evaluated, analogously to the requirement for a negated query. So, it cannot be used in any recursive computation path.

The following system session shows some uses of this predicate:

DES> /assert t(3,1)

DES> /assert t(2,2)

DES> /assert t(1,3)

DES> /assert t(2,1)

DES> /order_answer off

DES> t(X,Y)

{

t(3,1),

t(2,2),

t(1,3),

t(2,1)

}

Info: 4 tuples computed.

DES> /order_answer off

DES> t(X,Y)

{

t(1,3),

t(2,1),

t(2,2),

t(3,1)

}

Info: 4 tuples computed.

DES> order_by(t(X,Y),[Y])

Info: Processing:

answer(X,Y) :-

order_by(t(X,Y),[Y],[a]).

{

answer(3,1),

answer(2,1),

answer(2,2),

answer(1,3)

}

Info: 4 tuples computed.

DES> order_by(t(X,Y),[X],[d])

Info: Processing:

answer(X,Y) :-

order_by(t(X,Y),[X],[d]).

{

answer(3,1),

answer(2,2),

answer(2,1),

answer(1,3)

}

Info: 4 tuples computed.

DES> order_by(t(X,Y),[X,Y],[d,a])

Info: Processing:

answer(X,Y) :-

order_by(t(X,Y),[X,Y],[d,a]).

{

answer(3,1),

answer(2,1),

answer(2,2),

answer(1,3)

}

Info: 4 tuples computed.

Note, however, that ordering affects the result of a computation. The next example shows how, depending on the order criterion and coupled with a top-N query, the answer can be different:

DES> top(1,order_by(t(X,Y),[X],[a]))

Info: Processing:

answer(X,Y)

in the program context of the exploded query:

answer(X,Y) :-

top(1,'$p0'(Y,X)).

'$p0'(Y,X) :-

order_by(t(X,Y),[X],[a]).

{

answer(1,3)

}

Info: 1 tuple computed.

DES> top(1,order_by(t(X,Y),[X],[d]))

Info: Processing:

answer(X,Y)

in the program context of the exploded query:

answer(X,Y) :-

top(1,'$p0'(Y,X)).

'$p0'(Y,X) :-

order_by(t(X,Y),[X],[d]).

{

answer(3,1)

}

Info: 1 tuple computed.

5. System Description

This section includes descriptions about the connection to relational database systems via ODBC connections, persistence, safety and computability issues, modes, syntax checking, source-to-source transformations, the multiline and development modes, the declarative debuggers and tracers, the SQL test case generator, batch processing, the configuration file, the system variables and messages, the lists of all the available commands, the Textual API, the ISO escape character syntax, a database instances generator, and finally some notes on the implementation of DES.

5.1 RDBMS connections via ODBC

DES provides support for connections to (relational) database management systems (RDBMS's) in order to provide data sources for relations. This means that a relation defined in a RDBMS as either a view or a table is allowed as any other relation defined via a predicate in the deductive database. Then, computing a query can involve computations both in the deductive inference engine and in the external RDBMS SQL engine. Such relations become first-class citizens in the deductive database and, therefore, can be queried in Datalog, RA, TRC and DRC. If the relation is a view, it will be processed by the SQL engine. When an ODBC connection is opened, all SQL statements are redirected to such connection, so DES does not longer process such statements. This means that all the SQL features of the connected RDBMS are available. However, in this case it is possible to submit DES SQL queries to test novel features as hypothetical queries. The command /des Query drives the query to DES instead of to the external database, nonetheless being possible to using the external tables and views. The local, in-memory Datalog database can also be accessed in this case, merging in-memory data with external data for relations with the same name.

Almost any relational database (RDB) can be accessed from DES using an ODBC connection. Relational database management system (RDBMS) manufacturers provide ODBC implementations which run on many operating systems (Microsoft Windows, Linux, Mac OS X, ...) RDBMS's include enterprise RDBMS (as Oracle, MySQL, DB2, ...) and desktop RDBMS (as MS Access and FileMaker).

ODBC drivers are usually bundled with OS platforms, as Windows OS's (ODBC implementation), Linux OS distributions as Ubuntu, Red Hat and Mandriva (UnixODBC implementation), and Mac OS's 10x (iODBC implementation). However, additional drivers for specific databases are needed to be installed.

Since each RDBMS provides an ODBC driver and each OS an ODBC implementation, details on how to configure such connections are out of the scope of this manual. However, to configure such a connection, typically, the ODBC driver is looked for and installed in the OS, if not yet available. Then, following the manufacturer recommendations, it is configured. You can find many web pages with advice on this. Here, we assume that there are ODBC connections already available.

5.1.1 Opening an ODBC Connection

To access an RDB in DES, first open the connection with the following command, where test is the name of a previously created ODBC connection to a database:

DES> /open_db test

You can also provide a user name and password (if needed) as in:

DES> /open_db test user('smith') password('my_pwd')

Notice that these values are enclosed between apostrophes (').

Additional ODBC configuration values can be stated as well, which must be also enclosed between apostrophes, as in:

DES> /open_db sqlserver 'MultipleActiveResultSets=true'

Incidentally, note that DES requires the support of multiple active result sets for SQL Server connections, which is what this configuration value is intended for.

If you have previously created some database objects (tables, views, ...) in DES without an ODBC connection, they are still available and can be queried too (for more information see Section 5.1.7).

5.1.2 Using a Connection

Assuming that the connection links to an empty database, let's start creating some database objects:

(Note that, depending on the installed MySQL ODBC driver version, annoying messages might be displayed.)

DES> create table t(a varchar(20) primary key)

DES> create table s(a varchar(20) primary key)

DES> create view v(a,b) as select * from t,s

DES> insert into t values(1)

Info: 1 tuple inserted.

DES> insert into s select * from t

Info: 1 tuple inserted.

DES> insert into s values(2)

Info: 1 tuple inserted.

Next, one can ask for the database schema (metadata) with the command:

DES> /dbschema

Info: Database 'mysql'

Info: Table(s):

* father(father:varchar(60),child:varchar(60))

* s(a:varchar(60))

* t(a:varchar(60))

Info: View(s):

* v(a:varchar(60),b:varchar(60))

- Defining SQL statement:

SELECT ALL t.a AS a, s.a AS b

FROM (

(

INNER JOIN

));

Info: No integrity constraints.

The SQL text for external views is displayed if the DBMS is supported (DB2, MySQL, Oracle and PostgreSQL have been tested on Windows) and the SQL statement is recognized by the DES SQL dialect. In addition, the dependency graph (PDG, cf. Section 4.1.8) is also built for the external relations. Note that the SQL text will not coincide in general with the one in the user-submitted statement as external databases keep their own internal representations for view statements and output rendered queries.

All of these tables and views can be accessed from DES, as if they were local:

DES> select * from s;

answer(a:varchar) ->

{

answer('1'),

answer('2')

}

Info: 2 tuples computed.

DES> select * from t;

answer(a:varchar) ->

{

answer('1')

}

Info: 1 tuple computed.

DES> select * from v;

answer(a:varchar,b:varchar) ->

{

answer('1','1'),

answer('1','2')

}

Info: 2 tuples computed.

DES> insert into t values('1')

Exception: error(odbc(23000,1062,[MySQL][ODBC 3.51 Driver][mysqld-5.0.41-community-nt]Duplicate entry '1' for key 1),_G3)

In this example, as table t has its single column defined as its primary key, trying to insert a duplicate entry results in an exception from the ODBC driver. Integrity constraints are handled by the RDBMS connected, instead of DES (notice that the exception message is different from the one generated by DES).

Moreover, you can submit SQL statements that are not supported by DES but otherwise by the connected RDBMS, as:

DES> alter table t drop primary key;

Then, you can insert again and see the result (including duplicates):

DES> insert into t values('1')

Info: 1 tuple inserted.

DES> select * from v;

answer(a:varchar,b:varchar) ->

{

answer('1','1'),

answer('1','2'),

answer('1','2')

}

Info: 4 tuples computed.

Also, duplicate removing is also possible by the external RDBMS:

DES> select distinct * from v;

answer(a:varchar,b:varchar) ->

{

answer('1','1'),

answer('1','2')

}

Info: 2 tuples computed.

Nonetheless, these external objects can be accessed from Datalog as well (to this end, remember to enable duplicates to get the expected result):

DES> /duplicates on

Info: Duplicates are on.

DES> s(X),t(X)

Info: Processing:

answer(X) :-

s(X),

t(X).

{

answer('1'),

answer('1')

}

Info: 2 tuples computed.

This is equivalent to the following SQL statement:

DES> select s.a from s,t where s.a=t.a

answer(a:varchar) ->

{

answer('1'),

answer('1')

}

Info: 2 tuples computed.

However, whilst the former has been processed by the Datalog engine, the latter has been processed by the external RDBMS. Some SQL statements might be more efficiently processed by the external RDBMS and vice versa.

Duplicates are relevant in a number of situations. For instance, consider the following, where duplicates are initially disabled:

DES> group_by(v(X,Y),[X,Y],C=count)

Info: Processing:

answer(X,Y,C) :-

group_by(v(X,Y),[X,Y],C = count).

{

answer('1','1',1),

answer('1','2',1)

}

Info: 2 tuples computed.

Although there are a couple of tuples for each group (see the table contents above), only one is returned in the count because they are indistinguishable in a set. Now, if duplicates are allowed, we get the expected result in an SQL scenario:

DES> /duplicates on

Info: Duplicates are on.

DES> group_by(v(X,Y),[X,Y],C=count)

Info: Processing:

answer(X,Y,C) :-

group_by(v(X,Y),[X,Y],C = count).

{

answer('1','1',2),

answer('1','2',2)

}

Info: 2 tuples computed.

Note that, even when you can access external SQL objects from Datalog, the contrary is not allowed because there is neither Datalog metadata information for the external SQL engine, nor access to Datalog data. The data bridge is only opened from DES to the external DBMS, but not the other way round. This is in contrast to the SQL database internally provided by DES, which allows a bidirectional communication with the in-memory database because type information is supported for Datalog predicates. The only way to access a predicate from a DBMS is to make it persistent in the same DBMS (cf. Section 5.2), though this has some limitations if not all the rules of the predicate have been made persistent.

5.1.3 Opening Several Connections

From release 3.0 on, several ODBC connections can be opened simultaneously. Each time a new connection is opened, it becomes the new current connection, and all query processing is related to it by default. For instance, to inspect (a rather limited set of) metadata, one can submit the following command:

DES> /open_db mysql

DES> /dbschema

Info: Database 'mysql'

Info: Table(s):

* s(a:varchar(20))

* t(a:integer(4))

* w(a:varchar(20))

Info: View(s):

* v(a:varbinary(20))

Info: No integrity constraints.

To list all the opened connections, use the command:

DES> /show_dbs

$des

access

csv

db2

excel

mysql

oracle

postgresql

sqlserver

where you can see the list of opened connections, starting with $des, which is the default database (DES deductive engine). You can close all connections but the default one. As the names suggest, you can open a wide range of data sources, not only from database management systems as DB2, Oracle, SQL Server but also from other sources as datasheets (Excel) and text files (CSV (comma-separated values) files). For defining a "table" in MS Excel, you should use Insert -> Name -> Define, where you specify the name of the table and the cell range it covers (where the first row can be used as field names, optionally). Types are inferred by the Excel system. Similarly, when defining a connection to a text file, field names can be those in the first line of explicitly given. Again, types are inferred. In both cases, you can inspect the "database" schema and query them with either SQL, or Datalog, or RA, or TRC, or DRC queries.

Note that some data sources do neither creating views nor constraints, such as datasheets and text files.

A warning for newbies: You have to define connection names following ODBC installation. Do not expect the ones listed above are provided by default, you need both the ODBC connection and the data provider (database server or whatever) already installed and configured.

5.1.4 Current Connection

To find out the current opened ODBC database, use the command:

DES> /current_db

5.1.5 Making a Connection the Current One

Making a given connection the current one is simply done with:

DES> /use_db access

where access is an example of an already opened connection name.

5.1.6 Closing a Connection

Closing the current connection is simply done with:

DES> /close_db

You can also specify to close a given connection, as in:

DES> /close_db access

5.1.7 Schema and Data Visibility

Any submitted query or command refer to the current connection if not otherwise specified as an argument of a command. When opening a connection (and automatically making it the current one), their data and schema are visible, but not the data and schema of other already opened connections. In contrast, data from the default deductive database are visible for Datalog, RA, TRC and DRC queries, although their schema are not. Recall that you can create tables and views in the default database, which will be handled by DES but not delegated to any external database (unless you make a predicate persistent; see Section 5.2). Anyway, data from the default deductive database ($des) are not visible for SQL statements for a current connection other than $des, as they are submitted for processing to the external database.

In the following system session, one creates a table in the default database of DES (DDB), inserts a value, opens a connection, and realize that the table schema is not visible, but its data do. This comes from the fact that, first, SQL data is translated by DES to Datalog data and, second, Datalog data can be seamlessly combined with external databases (EDB).

DES> create table t(a int)	% Create table t in DDB
DES> insert into t values(1) Info: 1 tuple inserted.	% Insert t(1) in DDB
DES> select * from t answer(t.a:int) -> { answer(1) } Info: 1 tuple computed.	% Select data from DDB
DES> /open_db mysql	% Open an EDB
DES> select * from t Error: ODBC Code (1146): [MySQL][ODBC 5.1 Driver][mysqld-5.5.9]Table 'test.t' doesn't exist	% Select data from EDB % As t is not defined in % EDB, then, error
DES> t(X) { t(1) } Info: 1 tuple computed.	% Predicate t is known to % DDB and so it can be % queried from Datalog

In this way, you can also combine data from DES and the external data source. Next system session example shows this by creating a new table in the external database and combining above predicate t/1, defined in DDB, with a new table s created in EDB:

DES> create table s(a int)	% Create table s in EDB
DES> insert into s values(2) Info: 1 tuple inserted.	% Insert s(2) in EDB
DES> select * from s answer(a:integer(4)) -> { answer(2) } Info: 1 tuple computed.	% Select data from EDB % Note the different type % w.r.t. DDB
DES> t(X),s(Y) Info: Processing: answer(X,Y) :- t(X), s(Y). { answer(1,2) } Info: 1 tuple computed.	% Join t/1 (DDB) with % s/1 (EDB)

5.1.8 Solving Engine and ODBC Connections

When the current database is an open ODBC connection, any statement is submitted to the external database for its solving by default. However, this behaviour can be changed by forcing DES to solve SQL DQL queries submitted to an external database. This allows to experiment with more expressive forms of SQL queries as allowed by the local deductive engine, as hypothetical queries, non-linear and mutually recursive queries.

To force a single SQL DQL query to be processed by DES, simply use the command /des followed by the query. Note however that DML and DDL queries are still sent to the external DBMS. Let's consider MySQL, which does not support recursive queries up to its current version 5.6. If we had available the table edge(a int, b int), we can compute its transitive closure as follows:

DES> /open_db mysql

DES> select * from edge

answer(a:integer(4),b:integer(4)) ->

{

answer(1,2),

answer(2,3),

answer(3,4)

}

Info: 3 tuples computed.

DES> /des assume select e1.a,e2.b from edge e1, edge e2 where e1.b=e2.a in edge(a,b) select * from edge

answer(edge.a:int,edge.b:int) ->

{

answer(1,2),

answer(1,3),

answer(1,4),

answer(2,3),

answer(2,4),

answer(3,4)

}

Info: 6 tuples computed.

Note, however, that local data is not known by the external database. If we assume on an external table and use a view on that table, the assumption will not be available to the external database because the assumption is locally added (to the deductive database, not to the external relational database), as in:

DES> /open_db mysql

DES> create table t(a int)

DES> insert into t values (1)

DES> create view v as select * from t

DES> select * from v

answer(A:INTEGER(4)) ->

{

answer(1)

}

Info: 1 tuple computed.

DES> /des assume select 2 in t select * from v

answer(v.A:int) ->

{

answer(1)

}

Info: 1 tuple computed.

However, by querying the table for which we assume data, we get also the assumption as DES computes the union of the local data and the external data:

DES> /des assume select 2 in t select * from t

answer(t.a:string) ->

{

answer(1),

answer(2)

}

Info: 2 tuples computed.

This merging of local and external data is also possible for relations with the same name in both databases. If you have a table t already defined in the local database, the current database is an external one, and force DES to solve the SQL query, you will get data from both sources, as in:

DES> % Current DB is the local, deductive one

DES> create table t(a int)

DES> insert into t values(1) % Data in DES

Info: 1 tuple inserted.

DES> /open_db mysql

DES> create table t(a int)

DES> insert into t values(2) % Data in MySQL

Info: 1 tuple inserted.

DES> /des select * from t % Solved by DES

answer(t.a:int) ->

{

answer(1),

answer(2)

}

Info: 2 tuples computed.

DES> select * from t % Solved by MySQL

answer(a:integer(4)) ->

{

answer(2)

}

Info: 1 tuple computed.

5.1.9 Integrity Constraints, ODBC Connections, and Persistence

Integrity constraints as described in Section 4.1.18 are monitored by DES for the local deductive database. This means that inserting values directly into external tables (either by submitting an INSERT INTO statement from the opened connection or by inserting values out of DES) is not monitored for constraint consistency. However, as constraint consistency checking considers all visible data, when asserting into the local database, data from the current opened connection is also taken into account. The following system session shows a possible scenario illustrating these situations:

DES> /use_db $des

DES> create or replace table t(a int primary key)

DES> /dbschema

Info: Database '$des'

Info: Table(s):

* t(a:int)

- PK: [a]

Info: No views.

Info: No integrity constraints.

DES> /open_db mysql

The table t is also an external table in the connection mysql:

DES> /dbschema t

Info: Database 'mysql'

Info: Table:

* t(a:integer(4))

Retrieve tuples from the external table t:

DES> select * from t

answer(a:integer(4)) ->

{

}

Info: 0 tuples computed.

The following is inserted in the external table t. Recall that SQL statements under an opened connection are submitted directly to the external RDBMS:

DES> insert into t values (1)

Info: 1 tuple inserted.

DES> insert into t values (1) % Not rejected as it is not monitored by DES

Info: 1 tuple inserted.

DES does monitor the following assertion as it is directed to the local database:

DES> /assert t(1)

Error: Primary key violation t.[a]

when trying to insert: t(1)

Error: Asserting rules due to integrity constraint violation.

DES> /use_db $des

When the current database is the local database ($des), the external table t is not visible. So, the following fact is asserted in the local database:

DES> insert into t values (1)

Info: 1 tuple inserted.

Any other attempt to assert the same fact t(1) is rejected:

DES> /assert t(1)

Error: Primary key violation t.[a]

when trying to insert: t(1)

Error: Asserting rules due to integrity constraint violation.

The following would also go to the local database:

DES> insert into t values (1)

Error: Primary key violation t.[a]

when trying to insert: t(1)

Error: Asserting rules due to integrity constraint violation.

Info: 0 tuples inserted.

Finally, any persistent predicate (see forthcoming Section 5.2) which has attached constraints is checked for its consistency, irrespective of the external database it is stored. Also, any of the supported constraints can be attached to persistent predicates, therefore providing a high expressivity and declarative consistency level.

5.1.10 Caveats and Limitations

This section lists some caveats and limitations of the current implementation of ODBC connections to external data sources.

5.1.10.1 Caching

Data in relational tables are cached in the extension (answer) table during Datalog computations, and it is not requested anymore until this cache is cleared (either explicitly with the command /clear_et or because a command or statement invalidating its contents, as an SQL update query). Therefore, it could be possible to access outdated data from a Datalog query. Let's consider:

DES> t(X)

{

t('1')

}

Info: 1 tuple computed.

Then, from the MySQL client:

mysql> insert into t values('2');

Query OK, 1 row affected (0.06 sec)

And, after, in DES, the new tuple is not listed via a Datalog query:

DES> t(X)

{

t('1')

}

Info: 1 tuple computed.

However, an SQL statement returns the correct answer because it clears the extension table (SQL is compiled to Datalog rules, which are added to the database and the cache is cleared):

DES> select * from t;

answer(a:varchar) ->

{

answer('1'),

answer('2')

}

Info: 2 tuples computed.

In addition, it is not recommended to mix Datalog and SQL data unless one is aware of what’s going on. It is possible to assert tuples with the same name and arity as existing RDBMS's tables and/or views. Let's consider the same table t as above with the same data (two tuples t('1') and t('2')) and assert a tuple t('3') as follows:

DES> /assert t('3')

DES> t(X)

{

t('1'),

t('2'),

t('3')

}

Info: 3 tuples computed.

DES> select * from t

answer(a:varchar) ->

{

answer('1'),

answer('2')

}

Info: 2 tuples computed.

This reveals that, although on the DES side, Datalog data are known, they are not on the RDBMS side. This is in contrast to the DES management of data: if no ODBC connection is opened, the DES engine is aware of any changes to data, both from Datalog and SQL sides.

Concluding, those updates that are external to DES might not be noticed by the DES engine. And, also, an ODBC connection should be seen as a source of external data that should not be mixed with Datalog data. However, you can safely use the more powerful Datalog language to query external data (and to be sure the current data is retrieved, clear the cache with /clear_et).

5.1.10.2 ODBC Metadata

When computing the predicate dependency graph and stratification, metadata from the external DBMS is retrieved, which can be a costly operation if the number of tables and views is large. This is the default case when opening connections to DBMS's as SQL Server or Oracle, where many views are defined for an empty database. Also, ODBC connections to Oracle seem to be slow on some platforms.

It is however possible to restrict the number of retrieved objects from the external database with the settings in the ODBC connection. For instance, returned schemas in DB2 can be limited to user schemas with the property SchemaList by providing the user name.

Listing the database schema can suffer this situation as well, by issuing the command /dbschema. Instead, it is better to focus on the required object to display, as either /dbschema relname or /dbschema connection:relname.

Another issue is the un-syncing of the part of the predicate dependency graph related to the external metadata. Each time an external database is opened or the current database is set to it, the PDG is computed. Any changes to the external data from an external source are not available until one of these operations are performed (with the commands /open_db and /use_db, respectively) or a DDL statement is locally issued. It is also possible to refresh the PDG with the command /refresh_db.

5.1.10.3 Platform-specific Issues

ODBC connections are only supported by the provided binaries, and the source distributions for SWI-Prolog and SICStus Prolog.

If you use a 64 bit Windows OS, notice that you can select to run either a 64 bit version of DES or a 32 bit one. In the first case (64 bit), you must use the Database Connectivity (ODBC) Data Source Administrator tool (Odbcad32.exe):

· The 32-bit version of the Odbcad32.exe file is located in the folder %systemdrive%Windows%SysWoW64. Note that the number 64 in this folder name is correct even when it is intended for the 32-bit version.

· The 64-bit version of the Odbcad32.exe file is located in the folder %systemdrive%Windows%System32. Note that this number 32 in this folder name is correct even when it is intended for the 64-bit version.

Also notice that a 64 bit driver requires also a 64 bit database installation. For instance, you can define a 32 bit ODBC connection to 32 bit MS Access installation and a 64 bit ODBC connection to a 64 bit Oracle installation. In this scenario, both connections cannot be opened from the same DES instance (which is either a 32 bit or 64 bit release).

Some data types are not yet supported by the ODBC library in the SICStus releases, while in SWI-Prolog they do. So, if you find an exception including something as unsupported_datatype in the first system, try to use the second system instead (the DES download page specifies the Prolog system for each download). However, in this second system you may get an answer of string type for unknown data types (which might be numeric in the database), as follows:

DES> /prolog_system

Info: Prolog engine: SWI-Prolog 7.2.0.

DES> /open_db db2

Info: Computing predicate dependency graph...

Info: - Reading external metadata...

Info: - Building graph...

Info: Computing strata...

DES> select 1.0/2.0 from dual

answer ->

{

answer('0,50000000000000000000000000000')

}

Info: 1 tuple computed.

Notice also that the answer does not include neither the column name nor its data type. In SICStus:

DES> /prolog_system

Info: Prolog engine: SICStus 4.3.1 (x86-win32-nt-4): Thu Nov 27 18:31:25 WEST 2014.

DES> /open_db db2

Info: Computing predicate dependency graph...

Info: - Reading external metadata...

Info: - Building graph...

Info: Computing strata...

DES> select 1.0/2.0 from dual

Exception: error(odbc_error(unsupported_datatype,describeandbindcolumn(statement_handle(1),1,_367,_369,_371)),odbc_error(unsupported_datatype,describeandbindcolumn(statement_handle(1),1,_367,_369,_371)))

5.1.11 Tested ODBC Drivers

Several data sources have been successfully tested on Windows XP/Vista/7 32 bit with both SICStus Prolog and SWI-Prolog executables and sources:

§ IBM DB2 v9.7.200.358

§ Oracle Database Express Edition 11g Release 2 (also tested with Windows 7 64 bit and SWI-Prolog 6.0.0 64 bit)

§ SQL Server Express 2008 (including spatial components)

§ MySQL 5.5.9

§ PostgreSQL 9.1.3

§ Access 2003

§ Excel 2003

§ CSV text files

5.2 Persistence

Since DES 3.0, it is possible to use persistent predicates on an external database via an ODBC connection. This section describes how to declare a persistent predicate, use it, examine its schema, and remove its persistence assertion. Finally, a couple of caveats are included.

5.2.1 Declaring a Persistent Predicate

An assertion is used to declare a persistent predicate, as in:

DES> :-persistent(p(a:int),mysql)

where its first argument is the predicate and its schema (where types include all the supported types by DES, cf. Section 4.1.18.1), and the second one is the ODBC connection name. This name can be omitted if the current connection is the one you want to use for declaring predicate persistence, as in:

DES> /current_db

Info: Current database is 'mysql'. DBMS: mysql

DES> :-persistent(p(a:int))

You can confirm that the predicate p has been declared as persistent with:

DES> /list_persistent

mysql:p(a:int)

where the connection name is shown, followed by a semicolon and the predicate schema.

Also, if you have type information declared already, you can simply refer to the predicate with its name and arity in the persistence assertion:

DES> /use_db $des

DES> create table p(a int)

DES> /use_db mysql

DES> :-persistent(p/1)

DES> /list_persistent

mysql:p(a:int)

The general form of a persistence assertion is as follows:

:-persistent(PredSpec[,Connection]))

This assertion makes a predicate to persist on an external RDBMS via an ODBC connection. PredSpec can be either the pattern PredName/Arity or PredName(Schema), where Schema can be either ArgName1, …, ArgNameN or ArgName1:Type1, …, ArgNameN:TypeN. If a connection name is not provided, the current open database is used. The local, default database $des cannot be used to persist, but an ODBC connection.

5.2.2 Using Persistent Predicates

You can assert facts as usual and query the persistent predicate p/1 as the following example shows:

DES> /assert p(1)

DES> p(X)

{

p(1)

}

Info: 1 tuple computed.

And, as expected, it can be seamlessly combined with other non-persistent predicates, as in:

DES> /assert q(2)

DES> p(X),q(Y),X<Y

Info: Processing:

answer(X,Y) :-

p(X),

q(Y),

X < Y.

{

answer(1,2)

}

Info: 1 tuple computed.

where q(2) is in the meaning of q/1.

Also, you can use SQL, RA, TRC or DRC languages to query such persistent predicates, as in:

DES> :-type(q(a:int))

DES> select * from p,q where p.a<q.a

answer(p.a:int,q.a:int) ->

{

answer(1,2)

}

Info: 1 tuple computed.

DES> p zjoin p.a<q.a q

answer(p.a:int,q.a:int) ->

{

answer(1,2)

}

Info: 1 tuple computed.

DES> {P,Q | P in p and Q in q and P.a<Q.a}

answer(p_a:int,q_a:int) ->

{

answer(1,2)

}

Info: 1 tuple computed.

DES> {P,Q | p(P) and q(Q) and P<Q}

answer(p:int,q:int) ->

{

answer(1,2)

}

Info: 1 tuple computed.

Submitting the same query to the SQL ODBC bridge and to the deductive engine returns the same result:

DES> /show_compilations on

DES> /show_sql on

DES> /prompt des_db

DES:access> select * from p

answer(a:INTEGER(4)) ->

{

answer(1)

}

Info: 1 tuple computed.

DES:access> /des select * from p

Info: SELECT * FROM [p]

Info: SQL statement compiled to:

answer(A) :-

p(A).

answer(p.a:int) ->

{

answer(1)

}

Info: 1 tuple computed.

DES:access> /des select * from p

Info: SELECT * FROM [p]

Info: SQL statement compiled to:

answer(A) :-

p(A).

answer(p.a:int) ->

{

answer(1)

}

Info: 1 tuple computed.

DES:access> {P | P in p}

Info: SELECT * FROM [p]

Info: TRC statement compiled to:

answer(A) :-

p(A).

answer(a:int) ->

{

answer(1)

}

Info: 1 tuple computed.

The first query is completely processed by the external database. The second and third ones are submitted to the deductive engine, which translates the SQL query to a Datalog goal and program under which the result is computed. This amounts to query the external database with the SQL statement built for the persistent predicate (SELECT * FROM [p]). When such a query is directed to the deductive engine, note that if a condition is included, it would be computed by this engine (as opposed to directing the query to the external database), as in:

DES:access> /des select * from p where a>0

Info: SELECT * FROM [p]

Info: SQL statement compiled to:

answer(A) :-

p(A),

A>0.

answer(p.a:int) ->

{

answer(1)

}

Info: 1 tuple computed.

Persistent predicates can be combined even with external data coming from other ODBC connections, as in:

DES> /open_db access

DES> /dbschema t

Info: Database 'access'

Info: Table:

* t(a:INTEGER(4))

DES> select * from t

answer(a:INTEGER(4)) ->

{

answer(1),

answer(2)

}

Info: 2 tuples computed.

DES> p(X),t(X)

Info: Processing:

answer(X) :-

p(X),

t(X).

{

answer(1)

}

Info: 1 tuple computed.

Here, the current database is access and all its data is available (as already introduced in Section 5.1.2); in particular, the table t, which contains the tuple t(1).

Moreover, a persistent predicate can refer to external relations (tables and views) as well. Assuming the external table u in MySQL:

DES:mysql> select * from u

answer(a:integer(4)) ->

{

answer(2),

answer(3)

}

Info: 2 tuples computed.

DES:mysql> /assert p(X):-u(X)

DES:mysql> p(X)

{

p(1),

p(2),

p(3)

}

Info: 3 tuples computed.

However, if you add a new tuple to the relation u in the local deductive database, the external database will not be aware of this when computing a query on the persistent predicate p, as in:

DES:mysql> /assert u(4)

DES:mysql> p(X)

{

p(1),

p(2),

p(3)

}

Info: 3 tuples computed.

If you want to mix data from both databases in this case, it is needed to use the metapredicate st/1, as the following session illustrates:

DES:mysql> /retract p(X):-u(X)

DES:mysql> /assert p(X):-st(u(X))

DES:mysql> p(X)

{

p(1),

p(2),

p(3),

p(4)

}

Info: 4 tuples computed.

Though this could be automatically provided without resorting to using the metapredicate st/1, this option is left up to the user because mixing both the deductive and the external databases in this way will lead to read all the contents of the external relation. Without using st/1, only the needed contents are read (for instance, selecting only some tuples by a call with ground arguments, as posing the query p(2)). The metapredicate st/1 enforces that its predicate argument is to be located at a lower strata than the predicate in whose body the metapredicate occurs. This forces to solve its argument by using both the external database engine and the deductive engine. Thus, in the above example u/1 is located at a lower strata than p/1:

DES:mysql> /strata

[(u/1,1),(p/1,2)]

Recall also that to be able to mix both databases, the external database must be the current one. Otherwise, only the tuples computed with the rules in the deductive database are obtained:

DES:mysql> /use_ddb

Info: Computing predicate dependency graph...

Info: Computing strata...

DES:$des> p(X)

{

p(1),

p(4)

}

Info: 2 tuples computed.

Here, as the rule p(X):-st(u(X)) has been kept in the local database, the data source for u/1 is only coming from this database, and the external tuples u(2) and u(3) are not retrieved.

Finally, one can retract the rules previously asserted as well. For instance:

DES> /retract p(1)

DES> /retract p(X):-st(u(X))

5.2.3 Processing a Persistence Assertion

Processing a persistence assertion means to make persistent a predicate and delegate either all or part of its computation. All of its current rules as well as rules added afterwards are stored in a persistent media, as a relational database. A fact is translated into a table row whereas a rule is translated into an SQL view. Each persistent predicate is translated into a view which is the union of the table holding its facts and all the SQL translations for its rules. Translating rules into SQL views includes an adaptation of Draxler's Prolog to SQL compiler [Drax92]. Rules that cannot be delegated to the external media are kept in the local database for its storing and processing, therefore coupling the processing of the external and deductive engines.

Any rule belonging to the definition of a predicate pred which is being made persistent is expected, in general, to involve calls to other predicates. Each callee (such other called predicate) can be:

§ An existing relation in the external database.

§ A persistent predicate restored already in the local database.

§ A persistent predicate not yet restored in the local database.

§ A non-persistent predicate.

For the first two cases, besides making pred persistent, nothing else is performed when processing its persistence assertion. For the third case, a persistent predicate is automatically restored in the local database, i.e., it is made available to the deductive engine. For the fourth case, each non-persistent predicate is automatically made persistent if types match; otherwise, an error is raised. This is needed in order for the external database to be aware of a predicate only known by the deductive engine so far, as this database will be eventually involved in computing the meaning of pred..

However, not all rules can be externally processed for a number of reasons including: the external database does not support some features, and the translations of some built-ins are not supported yet. In the current state of the implementation, the following conditions must hold for a rule to be externally processed:

§ Only the following built-ins are supported: comparison operators and the infix arithmetic is.

§ The rule does not form a recursive cycle.

§ The rule is not a restricting rule (with a minus before its head; cf. Section 4.1.19).

Nonetheless, they are kept in the in-memory database for computing the meaning of the predicate when needed. This is performed by the deductive engine, which couples the processing of the external database with its own processing to derive the meaning of the predicate. Therefore, all the deductive computing power is preserved although the external persistent media lacks some features as, for instance, recursion (think of MySQL and MS Access). Anyway, such rules which are not translated into the external database are stored on it as metadata information. This is needed to restore the complete definition of a persistent predicate upon restoring (c.f. next section). Further releases might contain relaxed conditions. The following system session shows an example of this.

DES> /open_db access

DES> :-persistent(q(a:int))

DES> /assert q(X):-X=1;q(Y),X=Y+1

DES> select top 3 * from q

answer(a:INTEGER(4)) ->

{

answer(1)

}

Info: 1 tuple computed.

DES> /des select top 3 * from q

answer(q.a:int) ->

{

answer(1),

answer(2),

answer(3)

}

Info: 3 tuples computed.

Here, the first select statement is processed by Access, which is only able to retrieve the extensional part from the definition of q (the recursive, intensional part is kept in the local, deductive database). In the second select statement, DES processed the whole meaning because it is able to process recursive definitions in contrast to Access, which cannot.

Any time a predicate is made persistent, its associated connection is opened if it not was opened already (the current connection is not changed, anyway). The connection is not closed even when you drop the assertion (see Section 5.2.6).

5.2.4 Restoring Predicates

As expected, if you make a predicate persistent and quit DES, in a next session you can recover the state of this predicate. It is simply done by submitting again the same assertion as used to make the predicate persist for the first time.

However, note that any rule in the in-memory database for such a predicate will be persisted, too. This is to say that, for instance, if you have persisted a predicate which is not restored already, and you have a rule asserted in the in-memory database for this predicate, then the result of restoring it is the union of the asserted rule and the rules in the external database. For instance, let's consider the following system session:

DES> :-persistent(p(a:int),mysql)

DES> /assert p(1)

Now, let's assume another system session (quit and restart DES):

DES> /assert p(2)

DES> :-persistent(p(a:int),mysql)

Info: Recovering existing data from external database for 'p'...

DES> /listing

p(1).

p(2).

Info: 2 rules listed.

As it can be seen, the resulting database is composed of the union of the external rules and the local rules. The fact p(2) is automatically made persistent during restoring.

Finally, restoring compiled rules in a different system session does not recover source rules as they were originally asserted. They are recovered in its compiled form and without textual variable names as they were originally typed. Let's consider the following:

DES> :-persistent(p(a:int),mysql)

DES> /assert p(X):-X=1;X=2

DES> /listing

p(X) :-

X = 1

;

X = 2.

Info: 1 rule listed.

DES> /drop_assertion :-persistent(p(a:int),mysql)

DES> /listing

p(X) :-

X = 1

;

X = 2.

Info: 1 rule listed.

DES> :-persistent(p(a:int),mysql)

DES> /listing

p(X) :-

X = 1

;

X = 2.

Info: 1 rule listed.

DES> /quit

Then, we open a new system session and type:

DES> :-persistent(p(a:int),mysql)

Info: Recovering existing data from external database...

DES> /listing

p(A) :-

A = 2.

p(A) :-

A = 1.

Info: 2 rules listed.

As it can be seen, two rules are the result of the compilation of the originally asserted single rule with a disjunctive body. Also original variable names (only X in this case) are missing. However, a next release of DES might deal with this, allowing to restore the very same rules as the original ones.

5.2.5 Schema of Persistent Predicates

You can request the current database schema with:

DES> /dbschema

Info: Database '$des'

Info: No tables.

Info: View(s):

* p(a:int)

- Defining SQL statement:

CREATE VIEW p(a) AS

SELECT ALL *

FROM

p_des_table;

- Datalog equivalent rules:

Info: No integrity constraints.

where the persistent predicate is listed in the database schema of the default database $des and, therefore, it can be combined in a query with any predicate visible in this database.

Note that the predicate p has been declared as a view depending on a table (with the same name as the predicate and view, but ending with "_des_table"). Since predicates are defined in general with intensional rules, the view p will contain those intensional rules whereas the table will contain the extensional rules (facts). For instance, assuming that the predicate r has been made persisted already in the same connection, we assert an intensional rule for p, and examine its schema:

DES> /assert p(X):-r(X)

DES> /dbschema p

Info: Database '$des'

Info: View:

* p(a:int)

- Defining SQL statement:

CREATE VIEW p(a) AS

(

SELECT ALL *

FROM

p_des_table

)

UNION ALL

(

SELECT ALL rel1.a

FROM

r AS rel1

);

- Datalog equivalent rules:

p(1).

p(2).

p(X) :-

r(X).

If you change the current database to the external one and request the schema for p, you get:

DES> /use_db mysql

DES> /dbschema p

Info: Database 'mysql'

Info: View:

* p(a:integer(4))

which is the schema of theview p as provided by the external database system. Now, the detailed metadata information supplied by $des is not available in the external database.

Also note that the above couple of commands can be simply written as a single one without resorting to change the current database, with:

DES> /dbschema mysql:p

5.2.6 Removing Predicate Persistence

One can make a given predicate non-persistent by simply dropping its assertion, as in:

DES> /drop_assertion :-persistent(p(a:int),mysql)

This retrieves all the data stored in the external database and stores it back in the in-memory database of DES. In addition to the view p and table p_des_table created in the external database for p, there is also a table p_des_metadata holding the Datalog intensional rules that have been made persistent. This is needed to recover the original rules as they were asserted (in its compiled Datalog form).

If you have made persistent a predicate which depends on other for which no type constraints has been given before, a type constraint is derived, if possible, and both predicates are made persistent. This type constraint remains even when the persistence assertion is removed. If you want to remove this too, then submit a /drop_ic command. The following session illustrates this:

DES> /dbschema

Info: Database '$des'

Info: No tables.

Info: No views.

Info: No integrity constraints.

DES> :-persistent(p(a:int),access)

DES> /assert p(X):-q(X)

Warning: Undefined predicate: [q/1]

DES> /dbschema

Info: Database '$des'

Info: No tables.

Info: View(s):

* p(a:int)

- Defining SQL statement:

CREATE VIEW p AS

(

SELECT ALL *

FROM

p_des_table

)

UNION ALL

(

SELECT ALL rel1.col1

FROM

q AS rel1

);

* q(col1:int)

- Defining SQL statement:

CREATE VIEW q AS

SELECT ALL *

FROM

q_des_table;

Info: No integrity constraints.

DES> /drop_assertion :-persistent(p(a:int),access)

DES> /dbschema

Info: Database '$des'

Info: Table(s):

* p(a:int)

Info: View(s):

* q(col1:int)

- Defining SQL statement:

CREATE VIEW q AS

SELECT ALL *

FROM

q_des_table;

Info: No integrity constraints.

DES> /drop_ic :-type(p(a:int))

DES> /drop_assertion :-persistent(q(col1:int),access)

DES> /drop_ic :-type(q(col1:int))

DES> /dbschema

Info: Database '$des'

Info: No tables.

Info: No views.

Info: No integrity constraints.

If you want to completely remove a predicate, even its persistent representation, you can use the command /abolish, as in:

DES> /abolish p

DES> /dbschema

Info: Database '$des'

Info: No tables.

Info: No views.

Info: No integrity constraints.

DES> /listing p

Info: 0 rules listed.

DES> /use_db access

DES> /dbschema access:p

Info: Database 'access'

Error: No table or view found with name 'p'.

5.2.7 Closing a Persistent Predicate Connection

It is also possible to close the connection to a persistent predicate with the command /close_persistent Name, where Name is the name of the predicate. This means that the predicate will be no longer visible for the local database (though its type information metadata are kept). However, and by contrast to the command /drop_assertion, the external relations supporting persistence for the predicate are not dropped and, therefore, a subsequent persistent assertion can be issued (either in the same or in a different session) and the predicate is again restored. Only the connection to the predicate given as argument is closed. If it depends on other persistent predicates, they will be still persistent after closing the connection. The following system session illustrates all this:

DES> :-persistent(p(a:int),access)

DES> /assert p(X):-r(X)

DES> /list_persistent

access:p(a:int)

access:r(col1:int)

DES> /close_persistent p

DES> /list_persistent

access:r(col1:int)

DES> /dbschema $des

Info: Database '$des'

Info: Table(s):

* p(a:int)

* t(a:int)

Info: View(s):

* r(col1:int)

- Defining SQL statement:

CREATE VIEW r AS

SELECT ALL *

FROM

r_des_table;

Info: No integrity constraints.

DES> /dbschema access

Info: Database 'access'

Info: Table(s):

* dual(void:INTEGER(4))

* p_des_metadata(txtrule:LONGCHAR(2147483646))

* p_des_table(a:INTEGER(4))

* r_des_metadata(txtrule:LONGCHAR(2147483646))

* r_des_table(col1:INTEGER(4))

Info: View(s):

* p(a:INTEGER(4))

* r(col1:INTEGER(4))

Info: No integrity constraints.

5.2.8 Schema and Data Visibility

The default database (DDB) is called $des, and it contains metadata of each predicate for which either a type assertion or an SQL table creation statement has been issued. If one makes a predicate persistent in an external database (EDB), its metadata as well as its data is visible both to DDB and EDB. The following session illustrates this:

DES> /use_db $des

DES> :-persistent(p(a:int),mysql)

DES> /assert p(1)

DES> /show_compilations on

DES> select * from p

Info: SQL statement compiled to:

answer(A) :-

p(A).

answer(p.a:int) ->

{

answer(1)

}

Info: 1 tuple computed.

DES> /use_db mysql

DES> select * from p

answer(a:integer(4)) ->

{

answer(1)

}

Info: 1 tuple computed.

Note that in the first case (first SELECT above) when the current database is $des, DES solves the query (in this case retrieving tuples from DDB), and in the second case (second SELECT above), the query is directly submitted to the EDB, which solves it. In the first, case, the SQL statement is compiled to Datalog and solved by the deductive engine, and in the second one, data and metadata are collected from EDB and shown as a result. Retrieved types from an external database differ in general to those managed by DES, as it can be seen in this example. This is not an issue as long as equivalent types are found (in this case, number(integer) is considered as equivalent to integer(4), as numeric size constraints are not handled by DES, up to now).

As already introduced in Section 5.1.7, even when a connection is opened, their data and metadata are not known unless it becomes the current database, as illustrated next:

DES> /use_db mysql

DES> create table q(a int)

DES> insert into q values (2)

Info: 1 tuple inserted.

DES> select * from q

answer(a:integer(4)) ->

{

answer(2)

}

Info: 1 tuple computed.

DES> /use_db $des

DES> select * from q

Error: Unknown table or view "q"

DES> q(X)

Warning: Undeclared predicate(s): [q/1]

{

}

Info: 0 tuples computed.

However, a persistent predicate does have access to data and metadata in the EDB it was made persistent. To show this, and following the above system session, let's assert the following rule:

DES> /assert p(X):-q(X)

Warning: Undefined predicate(s): [q/1]

DES> p(X)

{

}

Info: 0 tuples computed.

DES> :-persistent(p(a:int),mysql)

DES> p(X)

{

p(2)

}

Info: 1 tuple computed.

Here, the external database is assumed to hold a relation q/1 with a tuple q(2) in its meaning.

5.2.9 Applications

Persisting predicates opens a brand new scenario for Datalog applications because several reasons: First, predicates are no longer limited by available memory; instead, persistent predicates are using as much secondary storage as needed and provided by the underlying external database. Predicate size limit is therefore moved to the external database. Second, processing is directed to the external database for rules that can be delegated, and to the deductive engine for rules that can not. This way, one can take advantage of the external database performance and scalability. Third, queries which are not possible in an external database can be solved by the deductive engine. So, one can extend external database expressiveness with the added features in DES. Finally, as several ODBC connections are allowed at a time, different predicates can be made persistent in different DBMS's, which allows for interoperability among external relational engines and the local deductive engine, therefore enabling business intelligence applications.

For instance, let's consider MySQL, which does not support recursive queries up to its current version 5.6. The following predicate can be made persistent in this DBMS even when it is recursive:

DES> :-persistent(path(a:int,b:int),mysql)

DES> /assert path(1,2)

DES> /assert path(2,3)

DES> /assert path(X,Y):-path(X,Z),path(Z,Y)

Warning: Recursive rule cannot be transferred to external database (kept in local database for its processing):

path(X,Y) :-

path(X,Z),

path(Z,Y).

DES> path(X,Y)

{

path(1,2),

path(1,3),

path(2,3)

}

Info: 3 tuples computed.

Here, non-recursive rules are stored in the external database whereas the recursive one is kept in the local database. External rules are processed by MySQL and local rules by the local deductive engine.

In addition, recall that you can use SQL on the current database schema (for which the persistent predicate schema is known). Then, even special SQL features included in DES, such as hypothetical queries, can be used. For example, and following the above system session:

DES> assume select 3,1 in path(a,b) select * from path

answer(path.a:int,path.b:int) ->

{

answer(1,1),

answer(1,2),

answer(1,3),

answer(2,1),

answer(2,2),

answer(2,3),

answer(3,1),

answer(3,2),

answer(3,3)

}

Info: 9 tuples computed.

This example also shows that DES is able to compute more queries than an DBMS. For instance, neither MS SQL Server nor DB2 allow cycles in the above path definition. This is not the most important limitation of recursion in current DBMS's, note that stratified recursion is not supported for more than one stratum. This means that recursive SQL queries involving EXCEPT, NOT IN, aggregates, ... are not allowed in current DBMS's such as SQL Server and DB2. Another limitation is linear recursion: the above rules cannot be expressed in DBMS's as there are several recursive calls. To name another, UNION ALL is enforced in those SQL's, so that just UNION is not allowed. For instance, the following query is rejected in any current commercial DBMS, but accepted by DES:

DES> /duplicates on

DES> /multiline on

DES> CREATE TABLE edge(a int, b int);

DES> INSERT INTO edge VALUES(1,2);

Info: 1 tuple inserted.

DES> INSERT INTO edge VALUES(2,3);

Info: 1 tuple inserted.

DES> INSERT INTO edge VALUES(1,3);

Info: 1 tuple inserted.

DES> :-persistent(edge(a:int,b:int),mysql).

DES> :-persistent(path(a:int,b:int),mysql).

DES> WITH RECURSIVE path(a, b) AS

SELECT * FROM edge

UNION -- Discarding duplicates (ALL is not required)

SELECT p1.a,p2.b

FROM path p1, path p2

WHERE p1.b=p2.a

SELECT * FROM path;

Warning: Recursive rule cannot be transferred to external database (kept in local database for its processing):

path_2_1(A,B) :-

path(A,C),

path(C,B).

answer(path.a:int,path.b:int) ->

{

answer(1,2),

answer(1,3),

answer(2,3)

}

Info: 3 tuples computed.

Note the difference against the next query, which does not discard duplicates:

DES> WITH RECURSIVE path(a, b) AS

SELECT * FROM edge

UNION ALL -- Keeping duplicates

SELECT p1.a,p2.b

FROM path p1, path p2

WHERE p1.b=p2.a

SELECT * FROM path;

Warning: Recursive rule cannot be transferred to external database (kept in local database for its processing):

path(A,B) :-

path(A,C),

path(C,B).

answer(path.a:int,path.b:int) ->

{

answer(1,2),

answer(1,3),

answer(2,3)

}

Info: 4 tuples computed.

5.2.10 Caveats

This section includes some caveats which deserve to be highlighted.

5.2.10.1 Supported Built-ins

The current version supports comparison operators (<, >, =, ...) and the built-in infix operator is for arithmetical expressions. Note that the equality is treated as a comparison in the translation.

5.2.10.2 Incomplete Meanings

If a predicate p which depends on an external relation r is made persistent, then it may be the case that the default database engine cannot get the meaning of r but via p unless this meaning is requested from the current database in which the relation is defined, as illustrated in the following example:

DES> /current_db

Info: The current database is '$des'. DBMS: $des

DES> /assert p(1)

DES> /assert p(X):-r(X)

Warning: Undefined predicate(s): [r/1]

DES> :-persistent(p(a:int),access)

DES> p(X)

{

p(1),

p(2),

p(3)

}

Info: 3 tuples computed.

DES> % For the local database, 'r' is not visible:

DES> r(X)

{

}

Info: 0 tuples computed.

DES> % If 'access' is the current database, then 'r' is visible:

DES> /use_db access

DES> /current_db

Info: The current database is 'access'. DBMS: access

DES> r(X)

{

r(2),

r(3)

}

Info: 2 tuples computed.

As well, you can have a local relation with the same name of an external relation (as r in the example above) on which a persistent predicate depends on (as p). In such a case, local data is not visible for the persistent predicate as its meaning is externally computed.

To avoid this issue, simply make persistent the relation.

Finally, in general there are missing tuples for a persistent predicate p that depend on others for which some rule cannot be externally processed. In the following example, as p is completely processed by the external DBMS, the meaning of q is not joined with the results from the deductive engine unless q(X) was issued at the top-level:

DES> /assert r(1)

DES> /assert q(X):-distinct(r(X))

DES> /assert p(X):-q(X)

DES> p(X)

{

p(1)

}

Info: 1 tuple computed.

DES> :-persistent(p(a:int),access)

DES> p(X)

{

}

Info: 0 tuples computed.

DES> q(X)

{

q(1)

}

Info: 1 tuple computed.

Note that the metapredicate distinct is responsible of this issue, as it precludes the single rule for q to be delegated to the external database. This incomplete behaviour is expected to be fixed in a forthcoming release. In addition, more built-ins (as distinct and top) are expected to be supported for the translation from Datalog rules to SQL statements.

5.2.10.3 Opening and Closing Connections

Each time a persistent assertion is issued over a given connection, this connection is opened, although the current database is not changed to it. In addition, it is not closed although a /drop_assertion command was issued.

A connection cannot be closed (with the command /close_db) if any persistent predicate remains on it.

5.2.10.4 Abolishing Predicates

The command /abolish not only abolishes rules in the deductive database but also those predicates that have been persistent in the external database, dropping their table and view definitions.

5.2.10.5 Null Values

Processing of null values involving the local and external database is not still supported as they have different representations. So, outer joins are not supported up to now.

5.2.10.6 External Database Processing

Only the transferred rules of persistent predicates can be processed by the EDB. In particular, neither Datalog queries nor SQL queries submitted from $des are translated into external SQL and therefore processed by such EDB. Only SQL queries in the same connection as the persistent predicate are processed by the EDB. However, future releases might translate queries submitted from $des.

5.2.10.7 Supported Platforms

A limited number of systems have been tested, including MySQL, MS Access, IBM DB2, Oracle, PostgreSQL and others. However, test suites are rather small up to now. Please report any fault for your application in order to be fixed.

5.3 Safety and Computability

This section explains notions related to safety and computability of Datalog queries. Both classical safety as explained in [Ullm95], safety for metapredicates and limited domain predicates are discussed. Computability includes dealing with solving unsafe rules from the classical point-of-view, but that are safe in certain scenarios, such as null providers and checking predicates.

5.3.1 Classical Safety

Built-in predicates are appealing, but they come at a cost, which was already noticed in Section 4.7. The domain of their arguments is infinite, in contrast to the finite domain of each argument of any user-defined predicate. Since it is neither reasonable nor possible to (extensionally) give an infinite answer, when a subgoal involving a built-in is going to be computed, its arguments need to be range-restricted, i.e., the arguments have to take values provided by other subgoals. To illustrate this point, consider submitting the following view to the program file relop.dl:

less(X,Y) :- X < Y, c(X,Y).

Since the goal is less(X,Y), and the computation is left to right, both X and Y are not range-restricted when computing the goal X < Y and, therefore, this goal ranges over two infinite domains: the one for X and the one for Y. We do not allow the computation of such rules. However, if we reorder the two goals as follows:

less(X,Y) :- c(X,Y), X < Y.

we get the expected result:

{

less(a1, b2),

less(a2, b2)

}

An analogous situation occurs when any variable in the head of a rule is not range-restricted. For example, we can consider the fact (not the Prolog built-in) atomic(X) stating that any value for X is atomic. But the system is unable to compute the complete (infinite) meaning of this predicate. Then, the following goal returns an open tuple, which is not what is expected from a Datalog system:

FDES> /assert atomic(X)

Warning: This rule is unsafe because of variable: [X]

Warning: This rule has a singleton variable: [X]

FDES> atomic(X)

{

answer(A)

}

Asserting the fact raises a warning about unsafety, a notion together the way it is detected will be explained a bit later in this section. If the call had been closed, the answer would be correct. Note that some unsafe predicates would be interesting to be included in a program. For example: positive(Number) :- Number>=0, which is expected to be a checking predicate (of course, the intention of a checking predicate could be more elaborated, such as testing if the argument is a prime number). Section 5.4 elaborates on modes for predicates, which specify the correct call modes for their arguments.

Note, then, that built-in predicates affect declarative semantics, i.e., the intended meaning of the two former views should be the same, although actually it is not. Declarative semantics is therefore affected by the underlying operational mechanism. Notice, however, that Datalog is less sensitive to operational issues than Prolog and it could be said to be more declarative (pure Datalog[16] is a truly declarative language). First, because of terminating issues as already introduced, and second, because the problematic first view can be automatically transformed into the second, computation-safe, one, as we explain next.

We can check whether a rule is safe in the sense that all its variables are range-restricted and, if needed, reorder the goals for allowing a safe computation (recall the predicate example less at the beginning). First, we need a notion of safety, which intuitively seems clear but that actually is undecidable [ZCF+97]. Some simple sufficient conditions for the safety of Datalog programs can be imposed, which means that rules obeying these conditions can be safely computed, although there are rules that, even violating some conditions, can be actually computed. We impose the following (weak) conditions [Ullm95, ZCF+97] for safe rules adapted to our context:

1) Any variable X in a rule r is safe if:

a) X occurs in some positive goal referring to a user-defined predicate.

b) r contains some equality goal X=Y, where Y is safe (Y can be a constant, which, obviously, makes X safe).

c) A variable X in the goal X is Expression is safe whenever all variables in Expression are safe.

2) A rule is safe if all its variables are safe.

Notice that these conditions, currently supported by the system, are weak since they assume that user-defined predicates are safe, which is not always the case (but only require analysing locally each rule for deciding weak safety). To make these conditions stronger, 1.a. has to be changed to: “X occurs in some positive goal referring to a safe user-defined predicate”, and add “3. A predicate is safe if all of its variables are safe”. The changed conditions would require a global analysis of the program, which is not supported by DES up to now.

The variables in a negated call to a limited domain predicates are always restricted (see sections 4.1.18.5 and 4.1.20) and therefore safe.

The built-in predicate is has the same problem as comparison operators as well, but it only demands ground its second argument (cf. condition 1.c above). Negation requires its argument to have no unsafe variables. In addition, to be correctly computed, the restrictions in the domains of the safe variables it may contain should be computed before. The reader is referred to Section 3.6 in [Ullm95] to discovering the problems when interpreting rules with negation.

DES provides a check that decides if a rule is safe and, if so, it may apply a program transformation for reordering its goals in order to make it computable in a left-to-right order. This transformation does not come by default, and it can be enabled with the command /safe Switch, where Switch can take two values: on, for enabling program transformation, and off, for disabling this transformation. If Switch is not included, then the command informs whether program transformation is enabled or disabled.

The analysis performed by the system at compile-time warns about safety and computability as follows:

1) Raise an error if:

a) A goal involving a comparison operator will be non-ground at run-time.

b) The expression E in a goal X is E will be non-ground at run-time.

c) The goal not G contains unsafe variables or its safe variables are not restricted so far.

1) Raise a warning if:

a) A goal involving a comparison operator may be non-ground at run-time.

b) The expression E in a goal X is E may be non-ground at run-time.

This analysis is performed in several cases:

· Whenever a rule is asserted (either manually with the command /assert or automatically when consulting programs). A rule is always asserted, even when it is detected as unsafe or it may raise an exception at run-time. Recall that safety is undecidable and there are rules detected as unsafe that can be actually and correctly computed.

· When a query, conjunctive query (autoview) or view is submitted. They are rejected and not computed if unsafety or uncomputability is detected and cannot be repaired (because program transformation is disabled or no way is found out). Notice that there can be unsafe or uncomputable rules already consulted than can result either in an incorrect result or raise a run-time exception.

Concluding, one can expect a correct answer whenever no unsafe, uncomputable rule has been asserted to an empty database. Recall that the local analysis relies on the weak condition that assumes that the consulted rules are safe.

Next, an example of unsafe rule including negation is provided. As introduced, such a rule, when asserted, raises an error, but it is asserted in any case in order to show its misbehaviour.

DES> /assert q(0)

DES> /assert p(X):-not q(X)

Error: not q(X) might not be correctly computed because of the unrestricted variable(s):

[X]

Warning: This rule is unsafe because of variable(s):

[X]

DES> p(X)

{

}

Info: 0 tuples computed.

As the domain of X in p(X) is not range-restricted, no tuples are found in the left-to-right top-down search. If we submit a query as p(1), the negation not q(1) should be proven:

DES> p(1)

{

}

Info: 0 tuples computed.

However, as illustrated, there is no tuples in the answer for such a query. The misbehaviour of the rule for p/1 emerges here due to the way answers are computed via an extension table. As far as the query p(1) is subsumed by a previous call (p(X)), results in the extension table are reused. But if the extension table is cleared, then p(1) can be proven:

DES> /clear_et

DES> p(1)

{

p(1)

}

Info: 1 tuple computed.

Notice that both calls can occur during a computation, disabling the opportunity to clear the extension table, as in:

DES> p(X),p(1)

Info: Processing:

answer(X) :-

p(X),

p(1).

{

}

Info: 0 tuples computed.

A similar situation happens with equality:

DES> p(X),X=1

Info: Processing:

answer(X) :-

p(X),

X = 1.

{

}

Info: 0 tuples computed.

Also notice that, if simplification mode is enabled with the command /simplification on, then this conjunctive query is simplified and computed as follows:

DES> p(X),X=1

Info: Processing:

answer(1) :-

p(1).

{

answer(1)

}

Info: 1 tuple computed.

5.3.2 Safety and Variables

Depending on the syntactical name of variables and the safety check for a given query, view, autoview or rule those variables occur may develop different conclusions.

There are certain negated, unsafe calls that can be rewritten to end up with safe calls [Ullm95]. For instance, let's consider the unsafe rule p :- not t(X). Since X is not range-restricted, the negated call is unsafe, dealing to the floundering problem. This rule can be translated into the safe rules p :- not t1 and t1 :- t(_X).

DES includes a couple of ways to deal with this. First, by using underscored variables, where the transformation is automatically applied (even if the safety transformations are not enabled). In this example, p :- not t(_X) is considered a safe rule because it can be transformed into safe rules because _X is considered as a non-relevant variable for the outcome. And, second, by using an explicit existential quantifier on the non-underscored variable: p :- exists([X],not t(X)).

Note that, for queries, non-underscored variables are free variables (universally quantified in the clausal form of the logic rule) that are required to occur in the answer. So, even if safety transformations are enabled (via /safe on), the query not t(X) is not transformed.

However, a rule with such variables not occurring in the head can be transformed, as the rule v :- not t(X), which will be accepted as a safe rule if safe transformations are enabled and unsafe otherwise. But if the variable is underscored, then it is removed even from the head:

DES> v(_X):-not t(_X)

Info: Processing:

in the program context of the exploded query:

v :-

not '$p0'.

'$p0' :-

t(_X).

Warning: Undefined predicate: [t/1]

{

}

Info: 1 tuple computed.

5.3.3 Safety for Aggregates and Duplicate Elimination

Another source of unsafety, departing from the classical notion, resides in metapredicates as distinct/2 and aggregates. A set variable is any variable occurring in a metapredicate such that it is not bound by the metapredicate. For instance, Y in the goal distinct([X],t(X,Y)) is a set variable, as well as in group_by(t(X,Y), [X],C=count).

Because computing a goal follows SLD order, if a set variable is used after the metapredicate, as in distinct([X],t(X,Y)), p(Y), then this is an unsafe goal as in the call to distinct, the variable Y is not bound, and all tuples in t/2 are considered for computing its outcome. Swapping both subgoals yields a safe goal. So, data providers for set variables are only allowed before their use in such metapredicates.

Another source of unsafety is placing a set variable in the head of a rule. Unless such variable comes bound, open tuples might be delivered as a result, as in:

DES> /assert t(1,2)

DES> /assert v(X,Y,C):-group_by(t(X,Y),[X],C=count(X))

Warning: This rule is unsafe if called with nonground variable: [Y]

DES> v(X,Y)

{

v(1,A)

}

Info: 1 tuple computed.

5.3.4 Unsafe Rules from Compilations

Along compilations, unsafe rules can be automatically generated, as in the translations from outer joins. However, they are considered safe because a couple of reasons:

· Unsafe arguments of such rules are always given as input in goals.

· Goal arguments are null providers. A null provider has the open form '$NULL'(V), is generated by the system, and it is not supposed to be called explicitly by the user. An argument of this form is specifically handled by the system for outer join computations [Saen12].

Mode information for predicates is handled throughout program compilations to detect truly unsafe rules, avoiding to raise warnings about (non-classical safe) system generated rules. Notice, however, that you can still manually write an unsafe call to these system-generated predicates, yielding to incorrect results, as the following examples illustrates (which needs to enable development listings to inspect those unsafe rules):

DES> /assert t(1)

DES> /assert s(2)

DES> /assert l(X):-lj(t(X),s(Y),X=Y)

DES> /development on

DES> /listing

'$p0'(X,Y) :-

'$p1'(X,Y).

'$p0'(X,'$NULL'(A)) :-

t(X),

not '$p1'(X,Y).

'$p1'(X,Y) :-

X = Y,

t(X),

s(Y).

l(X) :-

lj('$p0'(X,Y)).

s(2).

t(1).

Info: 6 rules listed.

DES> '$p0'(X,Y)

{

'$p0'(1,'$NULL'(0))

}

Info: 1 tuple computed.

DES> /list_et

Answers:

{

not '$p1'(1,A),

t(1),

'$p0'(1,'$NULL'(0))

}

Info: 3 tuples in the answer table.

Calls:

{

'$p0'(A,B)

}

Info: 1 tuple in the call table.

The extension (answer) table contains the non-ground entry not '$p1'(1,A), which is not safe.

5.3.5 Safety for Limited Domain Predicates

The inference engine of DES is able to process non-ground negated calls for limited domain predicates as already introduced in Section 4.1.20. This kind of predicates are range-restricted because their domains are known. Thus, a negated call always grounds its goal (if it succeeds) because the values that are not in the meaning of a predicate must belong to its domain. In the next example, the predicate p is allowed to take values only in the meaning of q because of the foreign key declaration (if fact, the values that the referenced arguments can take, which in this case are all the arguments of q):

DES> :-type(p(a:int)),type(q(a:int)),pk(q,[a]),fk(p,[a],q,[a])

DES> /assert q(1)

DES> /assert q(2)

DES> /assert q(3)

DES> /assert p(2)

DES> p(X)

{

p(2)

}

Info: 1 tuple computed.

DES> not p(X)

Info: Processing:

answer(X) :-

not p(X).

{

answer(1),

answer(3)

}

Info: 2 tuples computed.

The goal p(X) is instantiated with as many values as there are in its domain (the tuples (1), (2) and (3)) and its negation succeeds for all that are not in its positive meaning (the tuple (2)), i.e., for the tuples (1) and (3).

For referenced extensional predicates, a negated call always terminates because the domain is finite, but intensional predicates may lead to non-termination in presence of infinite built-ins, as in:

DES> :-type(p(a:int)),type(q(a:int)),pk(q,[a]),fk(p,[a],q,[a])

DES> /assert q(X):-X=0;q(Y),X=Y+1

DES> % q has no upper bound, so let's take the first 10 just to check that it delivers integers from 0

DES> top(10,q(X))

Info: Processing:

answer(X) :-

top(10,q(X)).

{

answer(0),

answer(1),

...,

answer(9)

}

Info: 10 tuples computed.

DES> not p(X)

Info: Processing:

answer(X) :-

not p(X).

% .... non-termination

5.4 Modes for Unsafe Predicates

Modes in Prolog are typically used to declare properties of predicates at call and/or exit times. Here, we borrow the notion of modes to specify expected properties for a predicate in order to be correctly computed. We use mode i (for an input argument) and o (for an output argument) in a different way as in Prolog so that i means that the argument is expected to be ground at call time, and o means that it is not, though it might be. Whereas in safe Datalog, all modes should be o, in DES we can find i modes as well because unsafe predicates are allowed. For instance, because there are infinite built-ins as comparison operators (<, >, ...), it is interesting to allow i modes as well, as in the next example, that is intended to compute the first T natural numbers:

nat(T,1).

nat(T,X) :- nat(T,Y),X=Y+1,X<T.

Expected goals must have a ground first argument, as:

nat(100,X)

which returns the first 100 naturals. Otherwise, a run-time exception is raised:

DES> nat(X,Y)

Exception: Non ground argument(s) found in goal 1<T in the instanced rule:

nat(T,X) :-

nat(T,1),

1<T,

X=1+1.

Asserted at 10:23:37 on 1-18-2025.

So, each time a rule is asserted, it is checked for classical safety and, if not safe, a mode assertion is stored, indicating the input requirement of offending arguments. The assertion has the following syntax:

:-mode(ModeSchema)

ModeSchema ::= PredName(Mode,...,Mode)

Mode ::= i % The argument must be ground at call time

Mode ::= o % The argument can be a free variable at call time

In the example above, the automatically-stored assertion is:

:-mode(nat(i,o)).

This can listed with the command /list_modes, which lists all asserted modes, and /list_modes N/A for a give predicate of name N and arity A.

The mode assertion is created only for predicates including a mode i in an argument. If no mode is asserted for a given predicate, it is classical safe. If the predicate becomes classical safe (e.g., because one of its defining rules is removed), the mode assertion is removed.

Although the user can only examine predicate modes, the system keeps track of modes at rule-level. Each time a rule is asserted or retracted, the modes for its predicate are updated with the already stored modes for the rest of the predicate rules, if any.

Therefore, such declarations are understood more from a documentation point-of-view than from constraints (as types, referential integrity constraints, ...), because mode assertions recall users about expected properties for the queries (in addition to the first message they got when compiling an unsafe rule).

5.5 Datalog Syntax Checking

A number of syntax checks are conducted when asserting rules, consulting programs, processing commands and submitting queries. These checks include basic syntax errors, arguments of built-ins and metapredicates errors, safety warnings and errors, undefined predicate warnings, singleton variable warnings, and set variable errors.

5.5.1 Basic Syntax

Basic syntax error checking tries to devise the incorrect part of the parsed element by consuming it as much as an unexpected fragment is found. For instance, parsing in the following example succeeds before the closing parenthesis is found, because the number is not ended properly (maybe because during typing the parenthesis and the dot were interchanged):

DES> p(1.)

Error: (DL) Invalid fractional number after 'p(1.'

Note that the language for which the error is detected is shown between parentheses (DL, SQL, RA, TRC, or DRC standing respectively for Datalog, SQL (cf. Section 4.2.12 for a description of both syntax and semantic checking), Relational Algebra, Tuple Relational Calculus and Domain Relational Calculus) before the error message. Since there are several languages available in the same prompt, there may be several errors for the same input as well. Let's consider the following:

DES> select ,

Error: (DL) Invalid atom or (SQL) Invalid SELECT list or (SQL) Expected valid SQL expression or (RA) Expected valid SQL expression near 'select '

From the point of view of Datalog, 'select ,' is not a valid atom (to be used as a query); from SQL, after the keyword 'select' it is expected a list of expressions (the SELECT list); and from RA, the operator select requires a valid expression. Whereas in this second example the error can come from considering the input as either a Datalog, SQL or RA input, in the first example the input cannot be considered as part of SQL and hence only one error message is displayed. Next subsection shows another example for which two different errors are raised for the same language.

Only when some part of the input is recognized as a valid fragment of the language, a language-specific error can be displayed. In the following erroneous input, it is not recognized as starting any valid input:

DES> X

Error: Unrecognized start of input.

If you want to parse your input in a given language, either write your input after the language selection command or switch to the required language (/sql, ...) as follows:

DES> % First option:

DES> /datalog select ,

Error: (DL) Invalid atom after '/datalog select '

DES> /sql select ,

Error: (SQL) Invalid SELECT list after '/sql select '

DES> % Second option:

DES> /sql

DES-SQL> select ,

Error: (SQL) Invalid SELECT list after 'select '

There is no an isolated Datalog system mode yet, so that if you want parsing only for Datalog, you should use the first option (a Datalog mode can be expected in a future version). As well, this basic syntax error system can be expected also for Relational Algebra and Prolog.

5.5.2 Arguments of Built-ins and Metapredicates

Most built-ins and metapredicates include syntax checks to discard rules and queries with incorrect arguments. An example of incorrect argument of a built-in is:

DES> X is a+1

Error: (DL) Arithmetic expression expected after 'X is '

where a is not a valid reference in the arithmetic expression.

Another example for a metapredicate is:

DES> lj(X,Y,Z)

Error: (DL) First argument of lj/3 must be a relation or (DL) Expected sequence of non-compound terms after 'lj('

The system determines that this input may correspond either to the left-join built-in, which demands a relation in its first argument, or a call to a user predicate lj but with an incorrect sequence of non-compound terms (a user predicate which should have an arity different from 3 to avoid a name clash).

5.5.3 Safety

By default, safety warnings are issued when inserting rules which are not classical safe, set variable safe, and duplicate elimination safe (see Section 5.3). If a query is not safe, an error is displayed, and the query is not executed.

This warning is enabled by default. To remove undefined predicate warnings, use the command /safety_warnings off. However, an unsafe query will still raise an error.

5.5.4 Undefined Predicates

An undefined predicate is a predicate for which there are no rules defining it and has no type declaration. Undefined predicates are signals of possible program errors. So, each time the database is changed by asserting or retracting rules, undefined predicates are listed as a warning (offending rules are anyway accepted). As well, when submitting a query containing calls to undefined predicates, such a warning is also issued.

This warning is enabled by default. To remove undefined predicate warnings, use the command /undef_pred_warnings off.

5.5.5 Singleton Variables

A singleton variable is a variable occurring once in a rule. Such variables are usually warned in Prolog systems as they can be signalling a program error. Following the same criterion as in SWI-Prolog, both syntactic and semantic singletons are detected in DES when consulting a file and asserting rules. While a syntactic singleton denotes a single occurrence of a variable in a rule, as in p :- q(X), a semantic singleton denotes a single occurrence of a variable in a branch of a rule, as in p :- q(X) ; r(X). As this last rule is translated into p :- q(X) and p :- r(X), the semantic singleton check simply resorts to the syntactic singleton check on the translated rules.

This warning is enabled by default. To avoid singleton warnings there are two options: Either simply disable this check with the command /singleton_warnings off, or use underscored variables (see Section 4.1.1):

DES> /assert p :- q(X)

Warning: This rule has singleton variable: [X]

DES> /assert p :- q(_X)

DES> /assert p :- q(X) ; r(X)

Warning: This rule has singleton variable: [X]

DES> /singleton_warnings off

DES> /assert p :- q(X) ; r(X)

5.5.6 Set Variables

Set variables (Section 5.3.3) occurring in more than one metapredicate (aggregate or distinct) in the context of a query or a rule raise an error and the rule is rejected. When submitting a query with such an error, the query is not processed. When asserting or consulting a rule with this error, the rule is neither asserted nor consulted. For instance:

DES> /assert v(C,D):-count(t(X),C),count(t(X),D)

Error: Set variable [X] is not allowed to occur in different metapredicates.

In addition, a set variable cannot occur in expressions but as an argument of an aggregate. For example:

DES> group_by(t(X,Y),[X],C=count(X)+Y)

Error: Ungrouped variables [Y] cannot occur in C=count(X)+Y out of aggregate functions.

5.5.7 Stratification

When changing the database by asserting or retracting rules, a stratification is computed, if it exists (see Section 5.22.3). If the current database is not stratifiable, a warning is submitted. Also, if a query involving a cycle with negation for its sub-PDG is submitted, a warning is issued.

DES> /assert t:-not t

Warning: Non stratifiable program.

DES> t

Warning: Unable to ensure correctness/completeness for this query.

{

}

Info: 0 tuples computed.

Undefined:

{

}

Info: 1 tuple undefined.

5.6 Source-to-Source Transformations

Currently, two source-to-source transformations are possible under demand: First, as explained in the previous section, when safety transformations are enabled via the command /safe on, rule bodies are reordered to try to produce a safe rule. Second, when simplification is enabled via the command /simplification on, rule bodies containing equalities, true, and not BooleanValue are simplified.

In addition, there is also place for several automatic transformations (cf. Section 5.8 to know how to display such transformations):

· A clause containing a disjunctive body is transformed into a sets of clauses with conjunctive bodies.

· A clause containing an outer join predicate is transformed into its executable form.

· A clause containing an aggregate predicate is transformed into its executable form including grouping criterion.

· A clause containing the goal not is_null(+Term) is transformed into a clause with this goal replaced by is_not_null(+Term).

5.7 Multi-line Mode

By default, DES command prompt reads single-line inputs and, therefore, ending termination character is optional (as the dot (.) in Datalog and the semicolon (;) in SQL and RA). But, when writing a long query, as usual in SQL, breaking down the sentence along several lines enhances readability. This is also possible in DES by enabling multi-line mode with the command /multiline on. However, in this scenario, the terminating character must be issued in order to know when to finish parsing the input query. Returning to single-line mode is just by issuing /multiline off.

With multi-line input, multi-line remarks (enclosed between /* and */) are also allowed. Note that nested remarks are supported, too, as:

First remark

Second, nested remark

5.8 Development Mode

This section is focused at those interested in modifying and extending the system. So, from a system implementor viewpoint, it is handy to show several implementation-specific issues such as source-to-source transformations and internal representation of null values. To this end, the command /development [on|off] has been made available. Let’s consider the following system session:

DES> /development off

DES> /assert p(X):-X=1;X=2

DES> /assert c(C):-count(p(X),X,C)

DES> /assert q(1)

DES> /assert l(X,Y):-lj(p(X),q(Y),X=Y)

DES> /listing

c(C) :-

count(p(X),X,C).

l(X,Y) :-

lj(p(X),q(Y),X = Y).

p(X) :-

X = 1

;

X = 2.

q(1).

Info: 4 rules listed.

DES> l(X,Y)

{

l(1,1),

l(2,null)

}

Info: 2 tuples computed.

Next, we enable the development mode for listings:

DES> /development on

DES> l(X,Y)

{

l(1,1),

l(2,'$NULL'(59))

}

Info: 2 tuples computed.

Here, the internal representation of nulls is available. If we request the listing of the stored rules in development mode:

DES> /listing

'$p0'(A,'$NULL'(B)) :-

p(A),

not '$p1'(A,C).

'$p0'(A,B) :-

'$p1'(A,B).

'$p1'(A,B) :-

p(A),

q(B),

A = B.

c(C) :-

count(p(X),X,'[]',C).

l(X,Y) :-

'$p0'(X,Y).

p(X) :-

X = 2.

p(X) :-

X = 1.

q(1).

Info: 8 rules listed.

Here, we see several source-to-source transformations: First, the left join, then the aggregate count, and finally the disjunctive rule.

Development listings also allows to inspect the extension table looking at (repeated) facts involving nulls, as follows:

DES> /assert q(null)

DES> q(X)

{

q(1),

q(3),

q('$NULL'(64)),

q('$NULL'(67))

}

Info: 4 tuples computed.

Compare this to the non-development mode:

DES> /development off

DES> q(X)

{

q(1),

q(3),

q(null)

}

Info: 3 tuples computed.

Also, one can be aware from where nulls come because of their IDs, as in:

DES> /assert p(null)

DES> /listing p

p('$NULL'(70)).

p(X) :-

X = 1.

p(X) :-

X = 2.

Info: 3 rules listed.

DES> l(X,Y)

{

l(1,1),

l(2,'$NULL'(72)),

l('$NULL'(70),'$NULL'(74))

}

Info: 3 tuples computed.

Observe above ID 70. There, the data source rule providing such an entry in the answer is the first rule of p.

As SQL statements and RA expressions are compiled to Datalog programs, the command /show_compilations on enables the display of compilations each time an SQL statement is submitted, as the following example illustrates:

DES> /show_compilations on

DES> create table t(a int, b int)

DES> create table s(a int, b int)

DES> select * from t where a>1 union select * from s where b<2

Info: SQL statement compiled to:

answer(A,B) :-

distinct(answer_2_1(A,B)).

answer_2_1(A,B) :-

t(A,B),

A > 1.

answer_2_1(A,B) :-

s(A,B),

B < 2.

answer(t.a, t.b) ->

{

}

Info: 0 tuples computed.

5.9 Datalog and SQL Tracers

In contrast to imperative programming languages, deductive and relational database query languages feature solving procedures which are far from the query languages itself. Whilst one can trace an imperative program by following each statement as it is executed, along with the program state, this is not feasible in declarative (high abstraction) languages as Datalog and SQL. However, this does not apply to Prolog, also acknowledged as a declarative language, because one can follow the execution of a goal via the SLD resolution tree and use the four-port debugging approach.

Datalog stems from logic programming and Prolog in particular, and it can be also understood as a subset of Prolog from a syntactic point-of-view. However, its operational behaviour is quite different, since the outcome of a query represents all the possible resolutions, instead of a single one as in Prolog. In addition, tabling (cf. Section 5.6) and program transformations (due to outer joins, aggregates, simplifications, disjunctions, ...) make tracing cumbersome.

Similarly, SQL represents a truly declarative language which is even farthest from its computation procedure than Prolog. Indeed, the execution plan for a query include transformations considering data statistics to enhance performance. These query plans are composed of primitive relational operations (such as Cartesian product and set operators) and specialized operations (such as theta joins) for which efficient algorithms have been developed, containing in general references to index usage.

Therefore, instead of following a more imperative approach to tracing, here we focus on a declarative approach which only takes into account the outcomes at some program points. This way, the user can inspect each point and decide whether its outcome is correct or not. This approach will allow users to examine the syntactical graph of a query, which possibly depends on other views or predicates (SQL or Datalog, resp.) This graph may be cyclic when recursive views or predicates are involved. A given node in the graph will be traversed only once during tracing, either because there is a cycle in the graph or the node is repeated (used in several views or relations). In the case of Datalog queries, this graph contains the nodes and edges in the dependency graph restricted to the query, ignoring other nodes which do not take part in its computation. In the case of SQL, the graph shows the dependencies between a view and its data sources (in FROM clauses).

Next, tracing for both Datalog queries and SQL views are explained and illustrated with examples.

5.9.1 Tracing Datalog Queries

The command /trace_datalog Goal [Order] allows to trace a Datalog goal in the given order (either postorder or the default preorder). Goals should be basic, i.e., no conjunctive or disjunctive goals are allowed. For instance, let's consider the program in the file examples/negation.dl and its dependency graph, shown in Figure 1 (page 60). A tracing session could be as follows:

DES> /c negation

Warning: Undefined predicate(s): [d/0]

DES> /trace_datalog a

Info: Tracing predicate 'a'.

{

}

Info: 1 tuple in the answer table.

Info: Remaining predicates: [b/0,c/0,d/0]

Input: Continue? (y/n) [y]:

Info: Tracing predicate 'b'.

{

not b

}

Info: 1 tuple in the answer table.

Info: Remaining predicates: [c/0,d/0]

Input: Continue? (y/n) [y]:

Info: Tracing predicate 'c'.

{

}

Info: 1 tuple in the answer table.

Info: Remaining predicates: [d/0]

Input: Continue? (y/n) [y]:

Info: Tracing predicate 'd'.

{

}

Info: No more predicates to trace.

5.9.2 Tracing SQL Views

Tracing SQL views is similar to tracing Datalog queries, but, instead of posing a goal (involving in general variables and constants) to trace, only the name of a view should be given. For example, let's consider the file examples/family.sql, which contains view definitions for ancestor and parent, where tables father and mother are involved in the latter view. Note that this view is recursive since it depends on itself:

create view parent(parent,child) as

select * from father

union

select * from mother;

create or replace view ancestor(ancestor,descendant) as

select parent,child

from parent

union

select parent,descendant

from parent,ancestor

where parent.child=ancestor.ancestor;

Then, tracing the view ancestor is as follows:

DES> /trace_sql ancestor

Info: Tracing view 'ancestor'.

{

ancestor(amy,carolIII),

...

ancestor(tony,carolIII)

}

Info: 16 tuples in the answer table.

Info: Remaining views: [parent/2,father/2,mother/2]

Input: Continue? (y/n) [y]:

Info: Tracing view 'parent'.

{

parent(amy,fred),

...

parent(tony,carolII)

}

Info: 8 tuples in the answer table.

Info: Remaining views: [father/2,mother/2]

Input: Continue? (y/n) [y]:

Info: Tracing view 'father'.

{

father(fred,carolIII),

...

father(tony,carolII)

}

Info: 4 tuples in the answer table.

Info: Remaining views: [mother/2]

Input: Continue? (y/n) [y]:

Info: Tracing view 'mother'.

{

mother(amy,fred),

...

mother(grace,amy)

}

Info: 4 tuples in the answer table.

Info: No more views to trace.

5.10 Datalog Declarative Debugger

Debugging a Datalog program may be cumbersome as there are few and rather simple tools. Here, we propose a novel way to applying declarative debugging, also called algorithmic debugging (a term first coined in the logic programming field by E.H. Shapiro [Shap83]) to Datalog programs. Instead of considering a procedural way following how programs are solved (which turns out to be impractical due to the high gap between the program specification and program solving), we focus at the semantic level. That is, we no longer consider Prolog approaches to debugging as the procedure box control flow model for port tracers [Byrd80,CM87] and rather we automatically inspect the computation graph asking the user for what the actual semantics meets the intended semantics for selected nodes.

We have developed along time a couple of tools following this approach. In the first one [CGS07], the tools asks the user about the validity of certain nodes (goals) and can infer the erroneous predicate or even the clause, informing about the missing or wrong tuples. In the second tool [CGS15a], the user can answer not only whether the node is valid or not, but also inform the debugger about either a missing or wrong tuple. This makes the debugger to focus in this more detailed information when posing new questions, which now can be more elaborated but simpler to answer as it includes fewer tuples for the user to inspect. Next, we describe these two tools:

5.10.1 Basic Debugging of Datalog Programs

With this approach, it is possible to debug queries and diagnose missing answers (an expected tuple is not computed) as well as wrong answers (a given computed tuple should not be computed). Our system uses a question-answering procedure which starts when the user detects an unexpected answer for some query. Then, if possible, it points to the program fragment responsible of the incorrectness.

The debugging process consists of two phases. During the first phase the debugger builds a computation graph (CG) for the initial query Q w.r.t. the program P. This graph represents how the meaning of the initial query is constructed from all the calls made along its computation. These calls correspond to the literals in the rule bodies used in such computation, which in general belong to many predicates. Each node in the graph is composed of a literal and its meaning (i.e., a set of facts). See more details in [CGS07]. The second phase consists of traversing the CG to find either a buggy vertex or a set of related incorrect vertices. The vertex associated to the initial query Q is marked automatically as non-valid by the debugger. The rest of the vertices are marked initially as unknown. In order to minimize the number of questions asked by a declarative debugger, several traversing strategies have been studied [Caba05,Silv07]. However, these strategies are only adequate for declarative debuggers based on trees and not on graphs. The currently implemented strategy already contains some ideas of how to minimize the number of questions in a CG:

· First, the debugger asks about the validity of vertices that are not part of cycles in order to find a buggy vertex, if it exists. Only when this is no longer possible, the vertices that are part of cycles are visited.

· Each time the user indicates that a vertex (Query = FactSet) is valid, i.e., the validity of the answer for the subquery Query is ensured, the tool changes to valid all the vertices with queries subsumed by Query.

· Each time the user indicates that a vertex (Query = FactSet) is non-valid, the tool changes to non-valid all the vertices with queries subsumed by Query.

The last two items help to reduce the number of questions, deducing automatically the validity of some vertices from the validity of others.

As an example, we show a debugger session for the query br_is_even in the program examples/DLDebugger/parity.dl, which has been changed to contain an error in the following rule:

has_preceding(X) :− br(X), br(Y), Y>X. % Error: Y>X should be Y<X

In this case, the user expects the answer for the query br_is_even to be {br_is_even}, because the relation br contains two elements: a and b. However, the answer returned by the system is {}, which means that the corresponding query was unsuccessful.

The available command for starting a debugging session is /debug_datalog Goal, where Goal is a basic goal, i.e., neither conjunctive nor disjunctive goals are allowed. Therefore, the user can start a typical debugging session as follows:

DES> /debug_datalog br_is_even

Is br(a) = {br(a)} valid(v)/nonvalid(n)/abort(a) [v]?

Is br(E) = {br(a),br(b)} valid(v)/nonvalid(n)/abort(a) [v]?

Is next(nil,D) = {next(nil,b)} valid(v)/nonvalid(n)/abort(a) [v]? n

Is has_preceding(a) = {has_preceding(a)} valid(v)/nonvalid(n)/abort(a) [v]? n

Error in relation: has_preceding/1

Witness query : has_preceding(a) -> {has_preceding(a)}

Info: Debug Statistics:

Info: Number of questions : 3

Info: Number of inspected tuples: 4

Info: Number of root tuples : 3

Info: Number of non-root tuples : 1

More information? (yes(y)/no(n)/abort(a)) [n]? y

Is the witness query a wrong answer(w)/missing answer(m)/abort(a) [w]? w

Error in relation: has_preceding/1

Error in rule :

has_preceding(X) :-

br(X),

br(Y),

Y>X.

File : c:/des/desdevel/examples/dldebugger/parity.dl

Lines: 21-22

Info: Debug Statistics:

Info: Number of questions : 4

Info: Number of inspected tuples: 4

Info: Number of root tuples : 0

Info: Number of non-root tuples : 4

In this particular case, only four questions are necessary to find out that the relation has_preceding is incorrectly defined. In addition, by requesting for more information, we can even find out the particular offending rule in the predicate.

In order to minimize the number of questions asked to the user, the tool relies on a navigation strategy similar to the divide & query presented in [Shap82] for deciding which vertex is selected at each step. In other paradigms it has been shown that this strategy requires an average of log₂n questions to find the bug [Caba05], with n the number of nodes in a (non-recursive) computation tree.

Another example is a view of the cosmos for orbiting objects as the following simple program illustrates:

star(sun).

orbits(earth, sun).

orbits(moon, earth).

orbits(X,Y) :-

orbits(X,Z),

orbits(Z,Y).

planet(X) :-

orbits(X,Y),

star(Y),

not(intermediate(X,Y)).

intermediate(X,Y) :-

orbits(X,Y), % This is an error. It should be orbits(X,Z)

orbits(Z,Y).

When you consult the program:

DES> /c examples/DLDebugger/orbits1

Warning: Next rule has a singleton variable: [Z]

intermediate(X,Y) :-

orbits(X,Y),

orbits(Z,Y).

Info: 6 rules consulted.

you can notice a warning. Indeed, this is the cause of the error the debugger will catch should you did not notice this warning (the variable Z is not used in the rule, so that most likely, something is going wrong). Let us try it:

DES> /debug_datalog planet(X) p

Is orbits(sun,sun) = {} valid(v)/nonvalid(n)/abort(a) [v]? v

Is orbits(earth,F) = {orbits(earth,sun)} valid(v)/nonvalid(n)/abort(a) [v]? v

Is intermediate(earth,sun) = {intermediate(earth,sun)} valid(v)/nonvalid(n)/abort(a) [v]? n

Is orbits(sun,F) = {} valid(v)/nonvalid(n)/abort(a) [v]? v

Is orbits(L,sun) = {orbits(earth,sun),orbits(moon,sun)} valid(v)/nonvalid(n)/abort(a) [v]? v

Error in relation: intermediate/2

Witness query : intermediate(earth,sun) -> {intermediate(earth,sun)}

Info: Debug Statistics:

Info: Number of questions : 5

Info: Number of inspected tuples: 4

Info: Number of root tuples : 0

Info: Number of non-root tuples : 4

More information? (yes(y)/no(n)/abort(a)) [n]? y

Is the witness query a wrong answer(w)/missing answer(m)/abort(a) [w]? w

Error in relation: intermediate/2

Error in rule :

intermediate(X,Y) :-

orbits(X,Y),

orbits(Z,Y).

File : c:/des/desdevel/examples/dldebugger/orbits1.dl

Lines: 23-26

Info: Debug Statistics:

Info: Number of questions : 6

Info: Number of inspected tuples: 4

Info: Number of root tuples : 0

Info: Number of non-root tuples : 4

So, by answering a total of 5 questions and inspecting 4 tuples, the debugger catches the erroneous relation. But also as before it can point to the responsible rule if we request for more information and answer a simple one more question. In this case, the relation intermediate is composed of only one rule, but it might contain more.

The complete syntax of the command is:

/debug_datalog Goal [Level]

which starts the debugger for the basic goal Goal at predicate or clause level. Level is indicated with the options p and c for Level, respectively. The default is p.

If you specify a clause level debugging, the debugger automatically look for incorrect clauses, as in the following example, which ends with no further questions:

DES> /debug_datalog planet(X) c

Is orbits(sun,sun) = {} valid(v)/nonvalid(n)/abort(a) [v]? v

Is orbits(earth,F) = {orbits(earth,sun)} valid(v)/nonvalid(n)/abort(a) [v]? v

Is intermediate(earth,sun) = {intermediate(earth,sun)} valid(v)/nonvalid(n)/abort(a) [v]? n

Why is nonvalid, is a wrong answer(w)/missing answer(m)/abort(a) [w]? w

Is orbits(sun,F) = {} valid(v)/nonvalid(n)/abort(a) [v]? v

Is orbits(L,sun) = {orbits(earth,sun),orbits(moon,sun)} valid(v)/nonvalid(n)/abort(a) [v]? v

Error in relation: intermediate/2

Error in rule :

intermediate(X,Y) :-

orbits(X,Y),

orbits(Z,Y).

File : c:/des/desdevel/examples/dldebugger/orbits1.dl

Lines: 23-26

Info: Debug Statistics:

Info: Number of questions : 6

Info: Number of inspected tuples: 4

Info: Number of root tuples : 0

Info: Number of non-root tuples : 4

5.10.2 Debugging Datalog Programs with Wrong and Missing Answers

With this second tool, the main goal is to overcome or at least to reduce the number of inspected tuples when debugging by using a modification[17] of the former tool. This is done by asking for more specific information from the user. Now, the user can indicate not only that a result (set of answers) is non-valid, but also which tuple is unexpected in the set (wrong answer) or was expected but is not in the set (missing answer). This information is not compulsory, but it is usually easy to provide and leads to a reduction both in the number of questions and in the size of the considered result sets. The reduction is achieved by using three optimizations which use the information about wrong and missing answers to concentrate only on the parts of the program which are related to the particular errors. Thus, this approach combines ideas of algorithmic debugging [Shap82], slicing [Tip95] and database provenance [GKT07].

In contrast to the first tool, instead of a goal, a predicate is requested. A file name can be provided with the option file(File), containing the program to be debugged. If this file is not provided, a default file ('./debug/_debug_dl_default_file.dl') will be produced with the contents of the database. The original program suffers a (semantics-preserving) program transformation for debugging purposes [CGS15a], which is saved in ('./debug/_debug_dl_default_file.t.dl'), together with a CHR module ('./debug/_debug_dl_default_file.t.dl'). Also, the state of the system is saved before starting debugging in './debug/_debug_dl.sds'.

It is assumed that a predicate name only occurs in the program with the same arity; otherwise, debugging cannot proceed. Also, extensional predicates can be skipped by assuming they are valid with the option trust_extension(yes) (the default option is do not trust extensional predicates).

The syntax of the debugger command is:

/debug_dl Name/Arity Options

where:

Options = [Answer]

[trust_extension([yes|no])]

[file(File)]

where the file name will be typically enclosed between single quotes (following syntax of Prolog atoms), and:

Answer = abort |

valid |

nonvalid |

missing(PartialTuple) |

wrong(TotalTuple)

Defaults are no answer and trust extension (trust_extension(yes). An answer can be optionally provided to the first implied question. If present, this answer must be the first option, and the implied question will be omited. A total tuple is of the form rel(arg₁, ..., arg_n), where rel is the relation name and each argument arg_i is a Datalog constant. A partial tuple, in turn, may include the special symbol _ (underscore) in any of its arguments (but not in all of them). This symbol is intended to match any actual constant. For example, missing(t(_,a)) means that a tuple with a as its second argument is missing with respect to the expected result (no matter the value of the first argument).

Let us consider the following program (example1 in the folder examples/
DLDebugger):

% Intensional database (program rules)

p(X) :- s(X).

p(X) :- q(X,B), not r(B).

s(f).

s(X) :- t(B,X), r(B).

t(b,X) :- q(c,X), r(X).

t(X,g) :- r(X).

% Extensional database (facts)

q(a,c).

q(e,e).

q(c,d).

r(a).

r(b).

r(c).

Where its intended interpretation (what the user expects to be in the extension of each predicate) is:

I(p) = { p(a), p(c), p(f), p(g)}

I(q) = { q(a,c), q(c,d) }

I(r) = { r(a), r(b), r(c) }

I(s) = { s(a), s(f), s(g) }

I(t) = { t(a,g), t(b,g), t(c,g), t(c,a) }

When the user submits the query t(c,X) he gets:

DES> t(c,X)

{

t(c,g)

}

Info: 1 tuple computed.

But the user would have expected t(c,a) as well (as depicted in the intended interpretation above). Then, he starts a debugging session as follows:

DES> /debug_dl t/2 file(example1.dl)

Info: 12 rules consulted.

Info: Loading and transforming file...

{

1 - t(a,g),

2 - t(b,g),

3 - t(c,g)

}

Input: Is this the expected answer for t/2?

(y/n/mT/wN/a/h) [n]: ma,c

Info: Bug source: [buggy(t,unmatched atom,[(a,c)])]

Info: Debug Statistics:

Info: Number of questions : 1

Info: Number of inspected tuples: 3

Info: Number of root tuples : 3

Info: Number of non-root tuples : 0

The single question the user needs to answer is about the validity of the relation t (of course, the answer is unexpected because the user started the debugger pointing at t/2, but he is allowed to answer a more detailed information). In this case, the user answers ma,c, where m stands for missing, and a,c stands for the missing tuple (a,c). Observe that the user can also indicate a wrong tuple using w or simply choose to answer yes (y) (respectively no (n)) indicating that the result set is valid (respectively non-valid). In the case of y and n the debugger behaves as a traditional algorithmic debugger and no optimization is applied.

This very same debugging can be started by including the detailed source of the error as an explicit answer:

DES> /debug_dl t/2 missing(t(a,c)) file(example1.dl)

Info: 12 rules consulted.

Info: Loading and transforming file...

Info: Bug source: [buggy(t,unmatched atom,[(a,c)])]

Info: Debug Statistics:

Info: Number of questions : 1

Info: Number of inspected tuples: 3

Info: Number of root tuples : 3

Info: Number of non-root tuples : 0

Another session for the same program but for a different relation is as follows, where there is an unexpected, wrong answer for the meaning of p.

DES> /debug_dl p/1 file(example1.dl)

Info: 12 rules consulted.

Info: Loading and transforming file...

{

1-p(c),

2-p(e),

3-p(f),

4-p(g)

}

Input: Is this the expected answer for p/1? (y/n/mT/wN/a/h) [n]: w2

{

1-q(e,e)

}

Input: Do you expect that ALL these tuples be in q/2? (y/n/mT/wN/a/h) [n]:

Info: Buggy relation found: q

Info: Debug Statistics:

Info: Number of questions : 2

Info: Number of inspected tuples: 5

Info: Number of root tuples : 4

Info: Number of non-root tuples : 1

The user indicates that the tuple (e) in p is wrong. Here, we use the user answer w2, stating that the second tuple is wrong with respect to the intended interpretation of the program (notice that all tuples are numbered so that they can be easily pointed out). Then, the debugger chooses questions (and some of them are automatically answered) for the user to answer. The user answer is yes for the second question indicating that (e) is not expected in the result of the query r(X), while the user answer is no for the last question, indicating that the tuple (e,e) is not expected in the result of the query q(X,Y). With this information the debugger determines that the relation q is a buggy relation.

Next, we include the debugging session using the debugger of the last subsection. Notice that the debugger needs to formulate four questions to the user before finding the error, one of which requires the examination of all the tuples in t. In this case, the debugger points out the relation t as a buggy relation, however it is not the cause of the wrong answer e in p. This happens by chance since we are considering a program with two errors.

DES> /debug_datalog p(F)

Is r(a) = {r(a)} valid(v)/nonvalid(n)/abort(a) [v]? v

Is r(F) = {r(a),r(b),r(c)} valid(v)/nonvalid(n)/abort(a) [v]? v

Is t(C,D) = {t(a,g),t(b,g),t(c,g)} valid(v)/nonvalid(n)/abort(a) [v]? n

Is q(c,E) = {q(c,d)} valid(v)/nonvalid(n)/abort(a) [v]? v

Error in relation: t/2

Witness query : t(C,D) -> {t(a,g),t(b,g),t(c,g)}

Info: Debug Statistics:

Info: Number of questions : 4

Info: Number of inspected tuples: 8

Info: Number of root tuples : 4

Info: Number of non-root tuples : 4

More information? (yes(y)/no(n)/abort(a)) [n]? n

It is worth remarking that the difference in the number of tuples will increase in realistic applications. Suppose that the extensional predicate r is defined by thousands of different values instead of just three as in our toy example. Then, the debugger proposed in this paper will still ask the same questions with the same number of tuples to consider (six, where four of them corresponding to the initial symptom), while the debugger in [CGS08] will ask a question about the whole content of r in the second question, therefore displaying thousands of values to the user.

5.10.2.1 TAPI Interface for Datalog Debugging

The full Datalog debugger can be automated and connected to other interfaces via the textual API (TAPI, cf. Section 5.18). This section explains the TAPI interface for Datalog debugger commands. First, some definitions are listed:

· Node states. Each node in the predicate dependency graph can be assigned to a state:

State :=

valid |

nonvalid |

erroneous

· Tuples are defined as:

Tuple :=

Relation(Value,...,Value)

As any other Datalog user identifier, a relation name will be enclosed between single quotes if it contains a blank or starts with a non-lowercase letter. As well, constants follow Datalog notation (cf. Subsection 4.1.1).

· User answers:

Answer :=

abort |

valid |

nonvalid |

missing(Tuple) |

wrong(Tuple)

· Questions to the user:

Question :=

all(Name/Arity) |

subset(Name1/Arity,Name2/Arity) |

nonsubset(Name1/Arity,Name2/Arity) |

empty(Name/Arity) |

nonempty(Name/Arity)

Any question admits the answer abort, which ends the debugging session. The first question (all(Name/Arity)) asks whether the relation Name/Arity is correct. Any answer above is possible for this question. The second question (subset(Name1/Arity,Name2/Arity)) asks whether the tuples in the relation Name1/Arity should be a subset of the tuples in Name2/Arity. Next one, (nonsubset(Name1/Arity,Name2/Arity)) asks whether the tuples in the relation Name1/Arity should not be a subset of the tuples in Name2/Arity. The question empty(Name/Arity) asks whether the relation Name/Arity should be empty, whereas nonempty(Name/Arity) should be non-empty. These four last questions admit valid (affirmative answer) and nonvalid (negative answer) as possible answers.

5.10.2.1.1 Start Debugging

The following command starts a debugging session for the relation Name/Arity, which has been identified by the user as non valid.

/tapi /debug_dl Name/Arity Options

where Name/Arity is the name and arity of the relation to debug, and Options is a list of debugging options (as described in Subsection 5.10.2) and delimited by blanks. Possible TAPI answers are:

· Success step:

NodeName

State

...

NodeName

State

$eot

· Error step:

Standard error answer (cf. Subsection 5.18.1.2).

5.10.2.1.2 Set Node Status

It is possible to tag any node with its status at any time. If the user knows the state of a node (or any number of them), he can tag it to improve the automatic debugging, hopefully pruning the search space, with the command:

/tapi /debug_dl_set_node Name/Arity State

State can be any answer but abort. Possible TAPI answers are the same as in Subsection 5.10.2.1.

5.10.2.1.3 Current Question to the User

The following command returns the current question to the user:

/tapi /debug_dl_current_question

Possible TAPI answers are:

· The question, any of those explained in the beginning of Subsection 5.10.2.1:

Question

· Error step:

Standard error answer (cf. Subsection 5.18.1.2).

5.10.2.1.4 Current Solutions

The question subset comes accompanied by a set of solutions that can be consulted with the command /debug_dl_solutions.

· Success step:

relation_name

arity

value

...

value

...

value

...

value

$eot

Where relation_name is the name of the predicate for which the question is posed, arity is the number of its arguments, value is each argument value, $ is the record delimiter and $eot is the end of the transmission.

Remarks:

This command returns in the first line the name of the predicate, then its arity, and finally, each tuple (one value per line) in the predicate preceded by the record delimiter ($). Last line is the end of transmission.

Examples:

Input:

/tapi /debug_dl_solutions

Output:

mother

'grace'

'amy'

$eot

Input, considering an empty set of solutions:

/tapi /debug_dl_solutions

Output:

$eot

5.10.2.1.5 User Answer

With the following command, the user answer can be sent as the answer to the current question:

/tapi /debug_dl_answer Question Answer

Possible TAPI answers are the same as in Subsection 5.10.2.1.1.

5.10.2.1.6 Debug Statistics

The following command returns different statistics for the last debug session:

/tapi /debug_dl_statistics

Possible TAPI answers are:

· Success: pairs of item-value for the different measures:

Item1

Value1

...

ItemN

ValueN

$eot

· Error:

Standard error answer (cf. Subsection 5.18.1.2).

5.10.2.1.7 Debug Cleanup

The following command returns different statistics for the last debug session:

/tapi /debug_dl_cleanup

Possible TAPI answers are:

· Success: pairs of item-value for the different measures:

Standard successful answer with no return data (cf. Subsection 5.18.1.2).

· Error:

Standard error answer (cf. Subsection 5.18.1.2).

5.11 SQL Declarative Debugger

As in the previous section, here we focus on a declarative approach to debugging, following [CGS12a] (former version of the debugger is based on [CGS11b] and subsumed by the current one, which is a brand new implementation). There, possible erroneous objects correspond to views, and the debugger looks for erroneous views asking the user whether the result of a given view is as expected. In addition to the local database, note that external databases can also be debugged when connected via ODBC (we have tested some DBMSs such as MySQL, PostgreSQL, DB2.[18] However, the current version cannot deal with recursive definitions and WITH statements.

When the user starts the debugger for a view with the command /debug_sql View, the debugger builds internally its computation tree and starts the debugging session. The root of the tree is the view under debugging, its nodes can be either views or tables, and children of a view are all of the views and tables occurring in that view (table nodes do not have children). This tree is traversed and the validity (whether the view outcome matches its intended meaning) of each node is asked to the user. If a given node is checked as valid, its subtree is assumed to be valid and it is no longer traversed. Otherwise, the node itself or one of its descendants is assumed to be non-valid. In this case, the subtree is traversed to find the erroneous node.

Starting the debugging is done with the command:

/debug_sql View [Options]

where:

Options = [Answer]

[trust_tables([yes|no])]

[trust_file(FileName)]

[oracle_file(FileName)]

[debug([full|plain])]

[order([cardinality|topdown])]

where file names will be typically enclosed between single quotes (following syntax of Prolog atoms), and:

Answer = abort |

valid |

nonvalid |

missing(PartialTuple) |

wrong(TotalTuple)

Defaults are no answer, trust tables (trust_tables(yes)), no trust file, no oracle file, full debugging (debug(full)), and navigation order based on relation cardinality (order(cardinality)). An answer can be optionally provided to the first implied question on View. If present, this answer must be the first option, and the implied question will be omited. A total tuple is an SQL tuple of the form rel(cte₁, ..., cte_n), where rel is the relation name and each argument cte_i is an SQL constant. A partial tuple, in turn, may include the special symbol _ (underscore) in any of its arguments (but not in all of them). This symbol is intended to match any actual constant. For example, missing(Guest(_, 'John Smith')) means that a tuple with 'John Smith' as its second argument is missing with respect to the expected result (no matter the value of the first argument).

Trusting tables means that they are considered correct and no question about their contents are posed to the user. Trust files, oracle files, debugging type and navigation order are explained later. Let's consider the file pets1.sql in the directory examples/SQLDebugger (the problem is explained in the same file). Here, we find that the view Guest returns an unexpected answer:

DES> /process examples/SQLDebugger/pets1.sql

...

DES> select * from Guest;

answer(Guest.id:int,Guest.name:varchar(50)) ->

{

answer(1,'Mark Costas'),

answer(2,'Helen Kaye'),

answer(3,'Robin Scott')

}

Info: 3 tuples computed.

In fact, only Robin Scott is expected in the result set. Then, we can debug that view as follows:

DES> /debug_sql Guest

Info: Debugging view 'Guest'.

{

1 - 'Guest'(1,'Mark Costas'),

2 - 'Guest'(2,'Helen Kaye'),

3 - 'Guest'(3,'Robin Scott')

}

Input: Is this the expected answer for view 'Guest'? (y/n/m/mT/w/wN/a/h) [n]: n

Info: Debugging view 'CatsAndDogsOwner'.

{

1 - 'CatsAndDogsOwner'(1,'Wilma'),

2 - 'CatsAndDogsOwner'(2,'Lucky'),

3 - 'CatsAndDogsOwner'(3,'Rocky')

}

Input: Is this the expected answer for view 'CatsAndDogsOwner'? (y/n/m/mT/w/wN/a/h) [y]: n

Info: Debugging view 'NoCommonName'.

{

1 - 'NoCommonName'(1),

2 - 'NoCommonName'(2),

3 - 'NoCommonName'(3)

}

Input: Is this the expected answer for view 'NoCommonName'? (y/n/m/mT/w/wN/a/h) [y]: n

Info: Debugging view 'LessThan6'.

{

1 - 'LessThan6'(1),

2 - 'LessThan6'(2),

3 - 'LessThan6'(3),

4 - 'LessThan6'(4)

}

Input: Is this the expected answer for view 'LessThan6'? (y/n/m/mT/w/wN/a/h) [y]: y

Info: Debugging view 'AnimalOwner'.

{

1 - 'AnimalOwner'(1,'Kitty',cat),

2 - 'AnimalOwner'(1,'Wilma',dog),

3 - 'AnimalOwner'(2,'Lucky',dog),

4 - 'AnimalOwner'(2,'Wilma',cat),

5 - 'AnimalOwner'(3,'Oreo',cat),

6 - 'AnimalOwner'(3,'Rocky',dog),

7 - 'AnimalOwner'(4,'Cecile',turtle),

8 - 'AnimalOwner'(4,'Chelsea',dog)

}

Input: Is this the expected answer for view 'AnimalOwner'? (y/n/m/mT/w/wN/a/h) [y]: y

Info: Buggy view found: CatsAndDogsOwner

Info: Debug Statistics:

Info: Number of nodes : 8

Info: Max. number of questions : 8

Info: Number of questions : 5

Info: Number of inspected tuples: 21

Info: Number of root tuples : 3

Info: Number of non-root tuples : 18

In this example, tables have been trusted, but it is also possible to ask the user for the validity of the involved tables in the debugging process via the command /debug_sql Guest trust_tables(no). In this example session, the validity of the table Owner would be asked to the user.

By providing the first answer as a command option, the first question is skipped:

DES> /debug_sql Guest nonvalid

Info: Debugging view 'CatsAndDogsOwner'.

{

1-'CatsAndDogsOwner'(1,'Wilma'),

2-'CatsAndDogsOwner'(2,'Lucky'),

3-'CatsAndDogsOwner'(3,'Rocky')

}

Input: Is this the expected answer for view 'CatsAndDogsOwner'? (y/n/m/mT/w/wN/a/h) [y]:

5.11.1 Trusted Specifications

In SQL, the following scenario is very usual: A set of correct views is updated to improve its efficiency. The new set of views includes both new views and improved versions of some old views, keeping their names and intended answers. Sometimes, the new, usually more involved system, no longer produces the expected results. We use the first, reliable version, which we call a trusted specification during the subsequent debugging session as a valid reference.

For instance, let's consider that the user has corrected the former example, which is now working properly. Now, suppose that, in order to improve readability, the set of views is changed by removing AnimalOwner, adding instead a new view CatsOrDogsOwner, and modifying LessThan6 and CatsAndDogsOwner, which now make use of CatsOrDogsOwner.

Next, the modified and new views (Guest and NoCommonName remain the same; this new version is located in the file examples/SQLDebugger/pets2.sql) are listed.

create or replace view CatsOrDogsOwner(id,aname,specie) as

select O.id, P.name, P.specie

from Owner O, Pet P, PetOwner PO

where O.id = PO.id and P.code=PO.code

and (specie='cat' or specie='dog');

create or replace view CatsAndDogsOwner(id,aname) as

select A.id, A.aname

from CatsOrDogsOwner A, CatsOrDogsOwner B

where A.id=B.id and A.specie=B.specie;

create or replace view LessThan6(id) as

select id from CatsOrDogsOwner

group by id having count(*)<6;

The intended answer of the views with the same name is kept. In the case of CatsOrDogsOwner, its intended answer is the multiset of owners with their pet names and species, but limited to cats and dogs.

The very same computation tree as for pets1.sql results after replacing literals AnimalOwner by CatsOrDogsOwner. However, the new set of views is erroneous, since the where condition A.specie=B.specie of CatsAndDogsOwner should be A.specie<>B.specie, in order to ensure that the owner has at least one dog and one cat.

Now, the user again detects an unexpected result from the view Guest since its outcome incorrectly includes the owner with identifier 4: Tom Cohen. A new debugging session starts, but now the old version of the views (in the file pets_trust) can be used as a trusted specification as follows:

DES> /process examples/SQLDebugger/pets2.sql

...

DES> /debug_sql Guest
trust_file('examples/SQLDebugger/pets_trust')

Info: Debugging view 'Guest'.

{

1 - 'Guest'(3,'Robin Scott'),

2 - 'Guest'(4,'Tom Cohen')

}

Input: Is this the expected answer for view 'Guest'? (y/n/m/mT/w/wN/a/h) [n]: n

Info: view 'NoCommonName' is nonvalid w.r.t. the trusted file.

Info: view 'LessThan6' is valid w.r.t. the trusted file.

Info: view 'CatsAndDogsOwner' is nonvalid w.r.t. the trusted file.

Info: Debugging view 'CatsOrDogsOwner'.

{

1 - 'CatsOrDogsOwner'(1,'Kitty',cat),

2 - 'CatsOrDogsOwner'(1,'Wilma',dog),

3 - 'CatsOrDogsOwner'(2,'Lucky',dog),

4 - 'CatsOrDogsOwner'(2,'Wilma',cat),

5 - 'CatsOrDogsOwner'(3,'Oreo',cat),

6 - 'CatsOrDogsOwner'(3,'Rocky',dog),

7 - 'CatsOrDogsOwner'(4,'Chelsea',dog)

}

Input: Is this the expected answer for view 'CatsOrDogsOwner'? (y/n/m/mT/w/wN/a/h) [y]: y

Info: Buggy view found: CatsAndDogsOwner

Info: Debug Statistics:

Info: Number of nodes : 8

Info: Max. number of questions : 8

Info: Number of questions : 2

Info: Number of inspected tuples: 9

Info: Number of root tuples : 2

Info: Number of non-root tuples : 7

Here, the debugger traverses the computation tree as before, but the user is not asked for views in the set of trusted views, and the erroneous view is caught with only one final check (compared to the four checks that would be needed otherwise). The debugger detects that the new version of CatsAndDogsOwner is erroneous.

5.11.2 Missing and Wrong Tuples

The debugger also allows the user to specify the error type, indicating if there is either a missing answer (a tuple was expected but it is not in the result) or a wrong answer (the result contains an unexpected tuple). This information is used for slicing the associated queries, keeping only those parts that might be the cause of the error. The validity of the results produced by sliced queries is easier to determine, thus facilitating the location of the error.

5.11.2.1 Missing Tuples

Let's consider another example (located at examples/SQLDebugger/
awards1.sql): The loyalty program of an academy awards an intensive course for students that satisfy the following constraints:

· The student has completed the basic level course (level = 0).

· The student has not completed an intensive course.

· To complete an intensive course, a student must either pass the all in one course, or the three initial level courses (levels 1, 2 and 3).

The database schema includes three tables:

· courses(id,level) contains information about the standard courses, including their identifier and the course level

· registration(student,course,pass) indicates that the student is in the course, with pass taking the value true if the course has been successfully completed

· allInOneCourse(student,pass) contains information about students registered in a special intensive course, with pass playing the same role as in registration.

File awards1.sql contains the SQL views selecting the award candidates. The first view is standard, which completes the information included in the table registration with the course level. The view basic selects those standard students that have passed a basic level course (level 0). The view intensive defines as intensive students those in the table allInOneCourse, together with the students that have completed the three initial levels. However, this view definition is erroneous: We have forgotten to check that the courses have been completed (flag pass). Finally, the main view awards selects the students in the basic but not in the intensive courses. Suppose that we try the query select * from awards, and that in the result we notice that the student Anna is missing. We know that Anna completed the basic course, and that although she registered in the three initial levels, she did not complete one of them, and hence she is not an intensive student. Thus, the result obtained by this query is non-valid.

So, the user starts the debugger as Anna is not among the (possibly large) list of student names produced by the view awards. The debugging session proceeds as follows:

DES> /process examples/SQLDebugger/awards1

...

DES> /debug_sql awards

Info: Debugging view 'awards'.

{

1 - awards('Carla')

}

Input: Is this the expected answer for view 'awards'? (y/n/m/mT/w/wN/a/h) [n]: m'Anna'

Info: Debugging view 'intensive'.

Input: Should 'intensive' include the tuple 'Anna'? (y/n/a) [y]: n

Info: Debugging view 'standard'.

Input: Should 'standard' include the tuple 'Anna,1,1'? (y/n/a) [y]: y

Input: Should 'standard' include the tuple 'Anna,2,1'? (y/n/a) [y]: y

Input: Should 'standard' include the tuple 'Anna,3,0'? (y/n/a) [y]: y

Info: Buggy view found: intensive

Info: Debug Statistics:

Info: Number of nodes : 7

Info: Max. number of questions : 7

Info: Number of questions : 5

Info: Number of inspected tuples: 5

Info: Number of root tuples : 1

Info: Number of non-root tuples : 4

The first answer m'Anna' indicates that ('Anna') is missing in the view awards. Next, the user indicates that view intensive should not include ('Anna'). The debugger then asks three simple questions involving the view standard. After checking the information for Anna, the user indicates that the listed tuples are correct. Then, the tool points out intensive as the buggy view, after only three simple questions. Observe that intermediate views can contain hundreds of thousands of tuples, but the slicing mechanism helps to focus only on the source of the error.

5.11.2.2 Wrong Tuples

Let's consider a modification of the database defined in awards1.sql as found in the file awards2.sql, where the view basicLevelStudents has been incorrectly defined. We process this file, inspect the outcome of awards and notice that Ana should not be in the result set. Then, we proceed with the debugging session as follows:

DES> /process examples/SQLDebugger/awards2

...

DES> /debug_sql awards

Info: Debugging view 'awards'.

{

1 - awards('Ana'),

2 - awards('Mica')

}

Input: Is this the expected answer for view 'awards'? (y/n/m/mT/w/wN/a/h) [n]: w1

Info: Debugging view 'intensiveStudents'.

{

1 - intensiveStudents('Juan')

}

Input: Is this the expected answer for view 'intensiveStudents'? (y/n/m/mT/w/wN/a/h) [y]: y

Info: Debugging view 'candidates'.

Input: Should 'candidates' include the tuple 'Ana'? (y/n/a) [y]: n

Info: Debugging view 'basicLevelStudents'.

Input: Should 'basicLevelStudents' include the tuple 'Ana'? (y/n/a) [y]: n

Info: Debugging view 'salsaStudents'.

Input: Should 'salsaStudents' include the tuple 'Ana,1,teach1'? (y/n/a) [y]: y

Info: Debugging view 'salsaStudents'.

Input: Should 'salsaStudents' include the tuple 'Ana,2,teach2'? (y/n/a) [y]: y

Info: Debugging view 'salsaStudents'.

Input: Should 'salsaStudents' include the tuple 'Ana,3,teach1'? (y/n/a) [y]: y

Info: Buggy view found: basicLevelStudents

Info: Debug Statistics:

Info: Number of nodes : 10

Info: Max. number of questions : 10

Info: Number of questions : 7

Info: Number of inspected tuples: 8

Info: Number of root tuples : 2

Info: Number of non-root tuples : 6

5.11.2.3 Displaying Extended Information

Enabling verbose output allows to extend the display with further information as, e.g., view definitions when they are asked for its validity. As well, enabling development output allows to check how the logic program that represents the computation tree is built (c.f. [CGS12a]). For that, use the following commands, resp.:

DES> /verbose on

Info: Verbose output is on.

DES> /development on

Info: Development listings are on.

5.11.2.4 Automated Benchmarking for Debugging

Assessing the applicability of our approach to declarative debugging of SQL databases can be hard for a large number of database instances. To this end, in order to provide a wide spectrum of benchmarks, we have developed a tool that randomly generates a database instance and a mutated version of this instance, making the root view to deliver different results for both. This way, both an erroneous instance (the mutated one) along with a correct instance (the originally generated one) are available to be compared, where the correct instance plays the role of the intended semantics for the database. The tool then debugs the mutated instance by employing the original instance as a trusted specification, which is used to replace the user by an automated oracle.

The correct instance is generated as described in Section 5.21. The mutation consists of changing the query definition of a view in the computation tree of the root view so that the meaning of the root view changes. We consider the modification of one of the following components of the query: The operator in a set query (involving UNION, INTERSECT or EXCEPT), the comparison operator (<, <>, ...), the logical operator (AND, OR, ...), a column name in the WHERE condition, and a constant in the condition. All these modifications are randomly selected, and only the one that makes the result of the root view to change is preserved in the mutated instance.

The command /debug_sql_bench is similar to /generate_db (c.f. Section 5.21) and generates both the correct and the mutated database. The filename for the first one is added with _trust before its extension. So, as a result of its successful execution for the filename parameter p.sql, we get both p.sql and p_trust.sql.

Having these two files (either automatically generated with the command /debug_sql_bench or manually written) already, it is possible to applying an oracle automaton, which should behave similar to a user with respect to the queries issued by the debugger, this time by using the trusted specification p_trust.sql. The automaton answering a question about the validity of a view can be easily done by comparing the outcomes of the same relation for both instances (as in a plain debugger with no wrong and missing answers). However, when the user has more answer opportunities (as in the debugger explained in this section, including both missing and wrong tuples), then an automaton can consider different possibilities. We have selected among them, the ones that are explained next.

For an unexpected result, it may be the case that only either wrong or missing tuples are observed. In this case, the automaton answers with the first unexpected observation (a wrong or missing tuple). If both kinds of unexpected tuples are present, the automaton selects a missing tuple as an answer to the question.

Other questions include set membership (in) and set containment (subset). While in the first case the answer can be computed as either yes or no, in the second case also a wrong tuple can be signalled (in both cases by simply contrasting with the trusted instance).

Note that the implementation of the automated oracle is similar to the implementation of trusted specifications, but automatically generating detailed answers for the nodes delivering an unexpected result.

To apply the automaton, the command /debug_sql is provided with the parameter oracle_file(FileName). Then, to develop an example to illustrate the whole process, following is a system session showing this:

DES> /set random_seed 44

DES> /debug_sql_bench 3 5 10 3 3 p.sql

Info: Generating the database.

Info: Processing the generated database.

Info: Creating the database.

Info: Processing file 'p_trust.sql' ...

DES> /multiline on

DES> /abolish

DES> /drop_all_relations

Warning: No views found.

Warning: No tables found.

DES> /output on

DES> CREATE TABLE t1(a INTEGER, b INTEGER, c INTEGER, d INTEGER, PRIMARY KEY(a));

DES> CREATE TABLE t2(a INTEGER, b INTEGER, c INTEGER, d INTEGER, PRIMARY KEY(a));

DES> CREATE TABLE t3(a INTEGER, b INTEGER, c INTEGER, d INTEGER, PRIMARY KEY(a));

DES> INSERT INTO t1(a,b,c,d) VALUES (1,5,1,2);

Info: 1 tuple inserted.

DES> INSERT INTO t1(a,b,c,d) VALUES (2,4,2,0);

Info: 1 tuple inserted.

DES> INSERT INTO t1(a,b,c,d) VALUES (3,3,1,1);

Info: 1 tuple inserted.

DES> INSERT INTO t1(a,b,c,d) VALUES (4,2,3,2);

Info: 1 tuple inserted.

DES> INSERT INTO t1(a,b,c,d) VALUES (5,1,2,3);

Info: 1 tuple inserted.

DES> INSERT INTO t2(a,b,c,d) VALUES (1,5,2,4);

Info: 1 tuple inserted.

DES> INSERT INTO t2(a,b,c,d) VALUES (2,4,4,4);

Info: 1 tuple inserted.

DES> INSERT INTO t2(a,b,c,d) VALUES (3,3,3,4);

Info: 1 tuple inserted.

DES> INSERT INTO t2(a,b,c,d) VALUES (4,2,3,4);

Info: 1 tuple inserted.

DES> INSERT INTO t2(a,b,c,d) VALUES (5,1,4,4);

Info: 1 tuple inserted.

DES> INSERT INTO t3(a,b,c,d) VALUES (1,5,0,4);

Info: 1 tuple inserted.

DES> INSERT INTO t3(a,b,c,d) VALUES (2,4,2,1);

Info: 1 tuple inserted.

DES> INSERT INTO t3(a,b,c,d) VALUES (3,3,3,1);

Info: 1 tuple inserted.

DES> INSERT INTO t3(a,b,c,d) VALUES (4,2,1,2);

Info: 1 tuple inserted.

DES> INSERT INTO t3(a,b,c,d) VALUES (5,1,2,2);

Info: 1 tuple inserted.

DES> CREATE VIEW v10(a,b,c,d) AS ( SELECT DISTINCT t3.c,t3.c,t3.d,t3.b FROM t3 WHERE t3.a <= 2 ) UNION ALL ( SELECT ALL t3.c,t3.b,t3.a,t3.b FROM t3 WHERE t3.b = 2 );

DES> CREATE VIEW v5(a,b,c,d) AS ( SELECT DISTINCT t1.d,t1.b,t1.b,t1.c FROM t1 WHERE t1.a = 1 ) INTERSECT ( SELECT DISTINCT t1.d,t1.a,t1.a,t1.c FROM t1 WHERE t1.d > 1 );

DES> CREATE VIEW v6(a,b,c,d) AS SELECT DISTINCT t1.d,t1.d,t1.a,t2.c FROM t1, t2 WHERE (t1.a = t2.b AND (t1.b < 1 OR t2.c >= 0));

DES> CREATE VIEW v7(a,b,c,d) AS ( SELECT ALL t1.d,t1.c,t1.c,t1.a FROM t1 WHERE t1.d < 0 ) UNION ( SELECT ALL t1.a,t1.c,t1.a,t1.a FROM t1 WHERE t1.a < 1 );

DES> CREATE VIEW v8(a,b,c,d) AS ( SELECT DISTINCT t3.d,t3.d,t3.c,t3.b FROM t3 WHERE t3.c = 2 ) EXCEPT ( SELECT DISTINCT t1.b,t1.c,t1.d,t1.c FROM t1 WHERE t1.a > 0 );

DES> CREATE VIEW v9(a,b,c,d) AS ( SELECT DISTINCT t2.c,t2.a,t2.b,t2.d FROM t2 WHERE t2.b < 2 ) INTERSECT ( SELECT DISTINCT t1.c,t1.d,t1.b,t1.b FROM t1 WHERE t1.d = 4 );

DES> CREATE VIEW v2(a,b,c,d) AS ( SELECT ALL v6.d,v6.d,v8.a,v6.a FROM v6, v8 WHERE (v8.a = v6.b AND (v8.c < 0 AND v6.b > 4)) ) INTERSECT ( SELECT ALL v5.d,v5.a,v5.a,v5.c FROM v5 WHERE v5.a < 4 );

DES> CREATE VIEW v3(a,b,c,d) AS ( SELECT ALL v10.a,v10.c,v10.b,v10.d FROM v10 WHERE v10.a = 4 ) INTERSECT ( SELECT DISTINCT v9.c,v9.d,v9.a,v9.c FROM v9 WHERE v9.b <= 3 );

DES> CREATE VIEW v4(a,b,c,d) AS ( SELECT DISTINCT v7.b,v7.d,v7.b,v7.a FROM v7 WHERE v7.a <= 2 ) UNION ALL ( SELECT DISTINCT v7.c,v7.d,v7.b,v7.c FROM v7 WHERE v7.b >= 1 );

DES> CREATE VIEW v1(a,b,c,d) AS SELECT ALL v2.d,v3.b,v2.b,v2.b FROM v2, v3, v4 WHERE ((v4.a = v3.b AND v3.a = v2.b) AND ((v4.d <= 1 AND v3.a <= 0) OR v2.b >= 0));

DES> /output on

DES>

Info: Batch file processed.

Info: Ensuring non-empty views.

Info: Checking cardinality of v10: 3

Info: Checking cardinality of v5: 0..4

Info: Checking cardinality of v6: 5

Info: Checking cardinality of v7: 0..5

Info: Checking cardinality of v8: 2

Info: Checking cardinality of v9: 0..1

Info: Checking cardinality of v2: 0..4

Info: Checking cardinality of v3: 0..0..3

Info: Checking cardinality of v4: 8

Info: Checking cardinality of v1: 3

Info: Mutating the database...

Info: Mutating view v9: 3.

Info: Mutating view v1: 3.

Info: Mutating view v8: 3.

Info: Mutating view v7: 3

Info: Mutating view v10: 3.7 (v1)

DES> /debug_sql v1 oracle_file('p_trust.sql')

Info: Debugging view 'v1'.

{

1-v1(1,1,2,2),

2-v1(1,2,2,2),

3-v1(4,1,2,2),

4-v1(4,2,2,2),

5-v1(5,1,2,2),

6-v1(5,1,3,3),

7-v1(5,2,2,2)

}

Input: Is this the expected answer for view 'v1'? (y/n/m/mT/w/wN/a/h) [n]: w2

Info: Debugging view 'v9'.

{

1-v9(4,5,1,4)

}

Input: Is this the expected answer for view 'v9'? (y/n/m/mT/w/wN/a/h) [y]: y

Info: Debugging view 'v2'.

Input: Should 'v2' include the tuple '1,2,2,1'? (y/n/a) [y]: y

Info: Debugging view 'v3'.

Input: Should 'v3' include the tuple '2,2,2,1'? (y/n/a) [y]: n

Info: Debugging view 'v10'.

Input: Should 'v10' include the tuple '2,2,2,1'? (y/n/a) [y]: n

Info: Buggy view found: 'v10'.

Info: Debug Statistics:

Info: Number of nodes : 13

Info: Max. number of questions : 13

Info: Number of questions : 5

Info: Number of inspected tuples: 11

Info: Number of root tuples : 7

Info: Number of non-root tuples : 4

Notice that mutation did change the meaning of v1 by modifying the view v10 (originally, v1 had 2 tuples and ended with 0, as the Info: Mutating view v10: 2.0 (v1) line above indicates) , so that the automated debugger caught correctly the bug, in this case by answering a couple of questions with detailed information about missing tuples.

It is also possible to compare this evolved debugger to a classical one by specifying in the parameter debug(Type) the type of debugging: either plain (classical) or full (with missing and wrong answers). Also, it can be specified the navigation strategy with the parameter order([cardinality|topdown]), where cardinality seeks for the next dependant node with the smallest cardinality, and topdown selects the next node in the classical top-down order. The next system session illustrates the behaviour of a classical declarative debugger (with the values plain and topdown for the parameters)

DES> /debug_sql v1 oracle_file('p_trust.sql') debug(plain) order(topdown)

Info: Debugging view 'v1'.

{

1-v1(1,1,2,2),

2-v1(1,2,2,2),

3-v1(4,1,2,2),

4-v1(4,2,2,2),

5-v1(5,1,2,2),

6-v1(5,1,3,3),

7-v1(5,2,2,2)

}

Input: Is this the expected answer for view 'v1'? (y/n/m/mT/w/wN/a/h) [n]: n

Info: Debugging view 'v2'.

{

1-v2(1,2,2,1),

2-v2(1,2,2,5),

3-v2(2,3,3,5),

4-v2(3,2,2,4)

}

Input: Is this the expected answer for view 'v2'? (y/n/m/mT/w/wN/a/h) [y]: y

Info: Debugging view 'v3'.

{

1-v3(0,4,0,5),

2-v3(1,2,1,2),

3-v3(1,4,2,2),

4-v3(2,1,2,4),

5-v3(2,2,2,1),

6-v3(3,1,3,3)

}

Input: Is this the expected answer for view 'v3'? (y/n/m/mT/w/wN/a/h) [y]: n

Info: Debugging view 'v10'.

{

1-v10(0,0,4,5),

2-v10(1,1,2,2),

3-v10(1,2,4,2),

4-v10(2,2,1,4),

5-v10(2,2,2,1),

6-v10(3,3,1,3)

}

Input: Is this the expected answer for view 'v10'? (y/n/m/mT/w/wN/a/h) [y]: n

Info: Buggy view found: 'v10'.

Info: Debug Statistics:

Info: Number of nodes : 13

Info: Max. number of questions : 11

Info: Number of questions : 4

Info: Number of inspected tuples: 23

Info: Number of root tuples : 7

Info: Number of non-root tuples : 16

By comparing the statistics at the end of both sessions, we can see that, though the questions in this last case is one less than in the former, they are easier to answer, the number of inspected are roughly a half for the classical one. The benefits of using the more evolved approach has been confirmed for a test suite of 200 database instances.

5.11.2.5 TAPI Interface for SQL Debugging

SQL debugging can be automated and connected to other interfaces via the textual API (TAPI, cf. Section 5.18). Recall that external databases can be connected via ODBC. This section explains the TAPI interface for SQL debugger commands. First, some definitions are listed:

· Node states. Each node (either a table or a view) in the relation dependency graph can be assigned to a state:

State :=

valid |

nonvalid |

erroneous

· Tuples are defined as:

Tuple :=

Relation(Value,...,Value)

As any other SQL user identifier, a relation name will be enclosed between double quotes if it contains a blank. Constants follow SQL notation.

· User answers:

Answer :=

abort |

valid |

nonvalid |

missing(Tuple) |

wrong(Tuple)

· Questions to the user:

Question :=

all(RelationName) |

subset(RelationName1,RelationName2) |

in(Tuple,RelationName)

Any question admits the answer abort, which ends the debugging session. The first question (all(RelationName)) asks whether RelationName is correct. Any answer above is possible for this question. The second question (subset(RelationName1,RelationName2)) asks whether the tuples in RelationName1 should be a subset of the tuples in RelationName2, and admits valid (is is a subset) and nonvalid (it is not a subset) as answers. The last question asks whether Tuple should be in RelationName. and admits the same answers as to subset.

5.11.2.5.1 Start Debugging

The following command starts a debugging session for ViewName, which has been identified by the user as non valid.

/tapi /debug_sql ViewName Options

Where ViewName is the name of the view to debug, and Options is a list of debugging options (as described at the beginning of Section 5.11) and delimited by blanks. Possible TAPI answers are:

· Success step:

NodeName

State

...

NodeName

State

$eot

· Error step:

Standard error answer (cf. Subsection 5.18.1.2).

5.11.2.5.2 Set Node Status

/tapi /debug_sql_set_node NodeName State

State can be valid, nonvalid, missing(Tuple), and wrong(Tuple), where Tuple is of the form rel(cte₁, ..., cte_n), where rel is the relation name and each argument cte_i is an SQL constant. Placeholders (_) are allowed for missing tuples instead of constants (the erroneous state would mean that the offending node has been found, so there would be no need to debug). Possible TAPI answers are the same as in Subsection 5.11.2.5.1.

5.11.2.5.3 Current Question to the User

The following command returns the current question to the user:

/tapi /debug_sql_current_question

Possible TAPI answers are:

· The question, any of the three explained in the beginning of Subsection 5.11.2.5:

Question

· Error step:

Standard error answer (cf. Subsection 5.18.1.2).

5.11.2.5.4 User Answer

With the following command, the user answer can be sent as the answer to the current question:

/tapi /debug_sql_answer Question Answer

Possible TAPI answers are the same as in Subsection 5.11.2.5.1. In addition, if Answer is abort, then, the successful answer is returned if no error has been found:

$success

5.11.2.5.5 Debug Statistics

The following command returns different statistics for the last debug session:

/tapi /debug_sql_statistics

Possible TAPI answers are:

· Success: pairs of item-value for the different measures:

Item1

Value1

...

ItemN

ValueN

$eot

· Error:

Standard error answer (cf. Subsection 5.18.1.2).

5.12 SQL Test Case Generator

Checking that a view produces the same result as its intended interpretation is a daunting task when large databases and both dependent and correlated queries are considered. Test case generation provides tuples that can be matched to the intended interpretation of a view and therefore be used to catch possible design errors in the view.

A test case for a view in the context of a database is a set of tuples for the different tables involved in the computation of the view. Executing a view for a positive test case (PTC)[19] should return, at least, one tuple. This tuple can be used by the user to catch errors in the view, if any. This way, if the user detects that this tuple should not be part of the answer, it is definitely a witness of the error in the design of the view. On the contrary, the execution of the view for a negative test case (NTC) should return at least one tuple which should not be in the result set of the query. Again, if no such a tuple can be found, this tuple is a witness of the error in the design.

A PTC in a basic query means that at least one tuple in the query domain satisfies the where condition. In the case of aggregate queries, a PTC will require finding a valid aggregate verifying the having condition, which in turn implies that all its rows verify the where condition.

In the case of basic query, an NTC will contain at least one tuple in the result set of the view not verifying the where condition. In queries containing aggregate functions, this tuple either does not satisfy the where condition or the having condition. Set operations are also allowed in both PTC and NTC generation.

It is possible to obtain a test case which is both positive and negative at the same time thus achieving predicate coverage with respect to the where and having clauses (in the sense of [AO08]). We will call these tests PNTC's. For instance, let's consider the following system session:

DES> create table t(a int primary key)

DES> create view v(a) as select a from t where a=5

DES> /test_case v

Info: Test case over integers:

[t(5),t(-5)]

The test case {t(5),t(-5)} is a PNTC. However, a PNTC is not always possible to be generated. For instance, it is possible for the following view to generate both PTC's and NTC's but no PNTC:

create view v(a) as select a from t where a=1 and not exists (select a from t where a<>1);

The only PTC for this view is {t(1)} (modulo duplicates). (If you want to check this, ensure that a minimum test case size of 1 has been set with the command /tc_size). There are many NTC's, as, e.g., {t(2)} and {t(1) ,t(2)}.

The command /test_case View [Options] allows two kind of options. First, to specify which test case class is to be generated: all (PNTC, the default option), positive (PTC) or negative (NTC). The second option specifies an action: the results are to be displayed via the option display (default option), added to the corresponding tables (add option) or the contents of the tables replaced by the generated test case tuples (replace option).

For experimenting with the domain of attributes, we provide the command /tc_domain Min Max, which defines the range of values the integer attributes may take. This range is determinant in the search of test cases in a constraint network that can easily become too complex as long as involved views grow. So, keeping this domain small allows to manage bigger problems. This range is set by default to -5..5.

String constants occurring in all the views on which the view for the test case generated depends are mapped to integers in the same domain, starting from 0. So, the size of the domain has to be large enough to hold, at least, the string constants in those views.

Also, we provide the command /tc_size Min Max for specifying the size of the test case generated, in number of tuples. Again, keeping this range small helps in being able to cope with bigger problems. This range is set by default to 1..7.

Currently, we provide support for integer and string attributes. Binary distributions, and both SICStus and SWI-Prolog source distributions allow the functionality described.

5.13 Batch Processing

There are three ways for processing batch files (scripts):

1. If the file des.ini is located at the distribution directory, its contents are interpreted as input prompts and executed before giving control to the user at start-up of the system.

2. If the file des.cnf is located at the distribution directory, its contents are processed as before, but producing no output. It is intended for configuring system settings (though it can be used for other purposes, too).

3. If the file des.out is located at the distribution directory, its contents are interpreted as input prompts and executed upon exiting the system. This file can be used in combination with the file des.ini for restoring the last session state (see commands /save_state and /restore_state in Section 5.17.1).

4. The command /process Filename [Parameters] (or /p as a shorthand) allows to process each line in the script file as it was an input, the same way as above. If no file extension is given and Filename does not exists, then .ini, .sql, .ra, .trc, and .drc are appended in turn to Filename and tried in that order for finding an existing, matching file. The optional argument Parameters is intended to pass parameters to the file to be processed. A parameter is a string delimited by either blanks or double quotes ("), which are needed if the parameter contains a blank. The same is applied to Filename. The value for each parameter is retrieved by the tokens $parv1$, $parv2$, ... for the first, second, ... parameter, respectively. If no value as a parameter is provided for a token occurring in a batch file, a warning is issued. The command /set_default_parameter can be used to set default values for parameters. A different parameter vector exists for each script call to the command /process, so that nested calls with this command are allowed.

5.13.1 Comments in Scripts

When processing batch files, inputs starting with either the symbol % or -- are interpreted as comments. Comments can also be delimited between /* and */ and can be nested (comments spanning for more than a line are only allowed in multi-line mode, c.f. the command /multiline). The user can also interactively input such comments at the command prompt, but again producing no effects.

5.13.2 Logging Script Processing

Batch processing can include logging to register program output. This is useful to feed the system with batch input and get its output in a file, maybe avoiding any interactive input (multiple logs can be opened at a time). For example, consider the following des.ini excerpt:

% Dump output to output.txt

/log output.txt

/pretty_print off

% Process (Datalog, SQL, ... queries and commands)

/c examples/fib

fib(100,F)

% End log

/nolog

The result found in output.txt should be:

DES> /pretty_print off

Info: Pretty print is off.

DES> % Process (Datalog, SQL, ... queries and commands)

DES> /c examples/fib

Warning: N > 1 may raise a computing exception if non-ground at run-time.

Warning: N2 is N - 2 may raise a computing exception if non-ground at run-time.

Warning: N1 is N - 1 may raise a computing exception if non-ground at run-time.

Warning: Next rule is unsafe because of variable: [N]

fib(N,F) :- N > 1,N2 is N - 2,fib(N2,F2),N1 is N - 1,fib(N1,F1),F is F2 + F1.

DES> fib(100,F)

{

fib(100,573147844013817084101)

}

Info: 1 tuple computed.

DES> % End log

DES> /nolog

5.13.3 Script Parameters

Scripts can be invoked with parameters in the expected way:

/process script p₁ p₂ ... p_N

Each parameter p_i can be referenced in script with the name $parvi$.

As an example, let's consider the file numbers.sql (in the examples directory), which contains a query that is intended to display the N first naturals:

WITH nat(n) AS SELECT 1 UNION SELECT n+1 FROM nat SELECT TOP $parv1$ * FROM nat;

For instance, providing the number 3 as a parameter, then $parv1$ is replaced by 3:

DES> /p examples/numbers 3

Info: Processing file 'numbers.sql' ...

DES> WITH nat(n) AS SELECT 1 UNION SELECT n+1 FROM nat SELECT TOP 3 * FROM nat;

answer(nat.n:int) ->

{

answer(1),

answer(2),

answer(3)

}

Info: 3 tuples computed.

Info: Batch file processed.

If we neither provide such a parameter nor specify a default one, most likely an error is returned as in:

DES> /p examples/numbers

Info: Processing file 'numbers.sql' ...

Warning: Parameter $parv1$ has not been passed to this script.

DES> WITH nat(n) AS SELECT 1 UNION SELECT n+1 FROM nat SELECT TOP * FROM nat;

Error: Unknown column 'TOP' in 'select' list

Info: Batch file processed.

Default parameters can be set in the invoked script with the command /set_default_parameter Index Value. , where Index is the integer i denoting the i-th parameter.

For example, adding the line /set_default_parameter 1 5 to the script numbers.sql, we get:

DES> /p examples/numbers

Info: Processing file 'examples/numbers.sql' ...

DES> /set_default_parameter 1 5

DES> WITH nat(n) AS SELECT 1 UNION SELECT n+1 FROM nat SELECT TOP 5 * FROM nat;

answer(nat.n:int) ->

{

answer(1),

answer(2),

answer(3),

answer(4),

answer(5)

}

Info: 5 tuples computed.

Info: Batch file processed.

5.13.4 Script Return Codes

Scripts return a code 0 in the system variable $return_code$ upon completion. However, the command /return Code allows the user to specify any code (which can be of any data type) in Code. Using /return with no argument stops processing of the current script. If you need to stop all parent scripts as well, use the command /stop_batch.

5.13.5 Script Commands

There are several commands for scripting which are listed in Section 5.17.14.

5.14 Configuration File

DES can be configured at start-up by including the file des.cnf at the distribution directory. Its contents are processed as a batch file with no output being displayed. This way, DES can be silently configured each time a new session begins. Typical commands to be included in this file includes those in the command category Settings (cf. Section 5.17.11). This file is processed just before des.ini. For instance, the following contents in that file makes DES to show a plain prompt, no banner, no running information, and compacted output (no extra blank lines):

/display_banner off

/prompt plain

/running_info off

/compact_listings on

5.15 System and User Variables

The following are the system variables which can be used, for instance, when writing strings to either the console or a file with the commands write, writeln, write_to_file, and writeln_to_file:

§ $computation_time$ last query elapsed time due to computing (eliding parsing and display time)

§ $display_time$ last query elapsed time due to display (eliding parsing and computing time)

§ $parsing_time$ last query elapsed time due to parsing (eliding computing and display time)

§ $stopwatch$ current stopwatch time

§ $last_stopwatch$ stopwatch time for its last stop

§ $total_elapsed_time$ last query total elapsed time

§ $command_elapsed_time$ last command elapsed time

In addition, any dynamic predicate of arity 1 implemented in Prolog as included in source files can be accessed as well as system variables. The following is a (most likely non-updated) list of such predicates (the file des.pl contains all declarations of such dynamic predicates):

§ $cf_lookups$ Flag indicating the number of CF lookups

§ $check_ic$ Flag indicating whether integrity constraint checking is enabled (on or off)

§ $compact_listings$ Flag indicating whether compact listings are enabled

§ $computed_tuples$ Flag with the number of computed tuples during fixpoint computation (for running info display)

§ $ct_lookups$ Flag indicating the number of CT lookups

§ $current_db$ Flag indicating the current opened DB

§ $des_sql_solving$ Flag indicating whether DES solving is forced for external DBMSs

§ $development$ Flag indicating a development session. Listings show source and compiled rules

§ $display_answer$ Flag indicating whether answers are to be displayed upon solving (on or off)

§ $display_nbr_of_tuples$ Flag indicating whether the number of tuples are to be displayed upon solving (on or off)

§ $duplicates$ Flag indicating whether duplicates are enabled

§ $edb_retrievals$ Flag indicating the number of EDB retrievals during fixpoint computation

§ $editor$ Flag indicating the current external editor, if defined already

§ $et_flag$ Extension (answer) table flag

§ $et_lookups$ Flag indicating the number of ET lookups

§ $extensional_predicates$ List of extensional predicates

§ $format_timing$ Flag indicating whether formatting of time is enabled or disabled: on or off

§ $fp_iterations$ Flag indicating the number of iterations during fixpoint computation

§ $host_statistics$ Flag for host statistics

§ $hypothetical$ Flag indicating whether hypothetical queries are enabled (on or off)

§ $indexing$ Flag indicating whether indexing on extension table is enabled (on or off)

§ $language$ Flag indicating the current default query language

§ $last_autoview$ Flag indicating the last autoview executed. This autoview should be retracted upon exceptions

§ $multiline$ Flag indicating whether multiline input is enabled (on or off)

§ $my_odbc_query_handle$ Flag indicating the handle to the last ODBC query

§ $my_statistics$ Flag displaying whether statistics are enabled (on or off)

§ $non_recursive_predicates$ List of non-recursive predicates

§ $nr_nd_predicates$ List of non-recursive predicates which do not depend on any recursive predicates

§ $null_id$ Integer identifier for nulls, represented as '$NULL'(i), where 'i' is the null identifier

§ $nulls$ Flag indicating whether nulls are allowed

§ $optimize_cc$ Flag indicating whether complete computation optimization is enabled

§ $optimize_cf$ Flag indicating whether complete flag optimization is enabled

§ $optimize_ep$ Flag indicating whether extensional predicate optimization is enabled

§ $optimize_nrp$ Flag indicating whether non-recursive predicate optimization is enabled

§ $optimize_st$ Flag indicating whether stratum optimization is enabled

§ $order_answer$ Flag indicating whether the answer is to be displayed upon solving (on or off)

§ $output$ Flag indicating whether output is enabled (on or off)

§ $pdg$ Predicate Dependency Graph

§ $pretty_print$ Pretty print for listings (takes more lines to print)

§ $prompt$ Flag indicating the prompt format

§ $recursive_predicates$ List of recursive predicates

§ $return_code$ Flag indicating the last return code from a script invocation with /process

§ $rule_id$ Integer identifier for rules, represented as datalog(Rule, NVs, i, Lines, FileId, Kind), where 'i' is the rule identifier

§ $running_info$ Flag indicating whether running info is to be displayed (number of consulted rules and batch lines)

§ $safe$ Flag indicating whether program transformation for safe rules is allowed

§ $safety_warnings$ Flag indicating whether safety warnings are enabled

§ $shell_exit_code$ Flag indicating the last exit code from a /shell invocation

§ $show_compilations$ Flag indicating whether SQL to DL compilations are displayed

§ $show_sql$ Flag indicating whether SQL compilations are displayed

§ $simplification$ Flag indicating whether program simplification for performance is allowed

§ $start_path$ Path on first initialization

§ $state$ States for various flags to be restored upon exceptions

§ $stopwatch$ Flag indicating stopwatch elapsed time

§ $strata$ Result from a stratification

§ $tapi$ Flag indicating whether a TAPI command is being processed

§ $timing$ Flag indicating elapsed time display: on, off or detailed

§ $trusted_views$ Predicate containing trusted view names

§ $trusting$ Flag indicating whether a trust file is being processed

§ $user_predicates$ List of user predicates

§ $verbose$ Verbose mode flag

Finally, with the command /set_flag Flag Expression it is possible to modify the value of a given system variable (flag). For instance, the following input resets the last exit code returned by a /shell command:

DES> /set_flag shell_exit_code 0

To inspect the value of a flag, use /current_flag Flag:

DES> /current_flag error

Info: error(0)

System flags should not be modified unless you are sure (typically as a system implementor) what you are doing. Otherwise, unexpected results can be obtained.

Setting a new flag is also possible for referring to it as a user variable. For example:

FDES> /timing on

Info: Command elapsed time: 0 ms.

FDES> /c p

Info: 1 rule consulted.

Info: Command elapsed time: 73 ms.

FDES> /set_flag consult_time $last_command_elapsed_time$

Info: Command elapsed time: 3 ms.

FDES> /writeln $consult_time$

A value assigned to a variable is the result of evaluating the expression:

DES> /set_flag i sqrt(2)

DES> /writeln $i$

1.4142135623730951

DES> /set_flag i $i$+1

DES> /writeln $i$

2.4142135623730951

Such an expression can be any expression admitted in Datalog (for integers, strings, dates, ...) If no evaluation is required, delimit the value between single quotes:

DES> /set_flag i 'sqrt(2)'

DES> /writeln $i$

sqrt(2)

Note that an identifier starting with either a capital letter of undescore is considered as a variable:

DES> /set_flag rel TABLE

DES> /writeln $rel$

In this case, TABLE is a variable and, when displayed, it shows A (a variable name) because its original variable name is not kept. Use quotes to surround string values, as in:

DES> /set_flag rel 'TABLE'

DES> /writeln $rel$

TABLE

5.16 Messages

DES system messages are prefixed by:

· Info: An information message which requires no attention from the user. Many information messages are hidden with the command /verbose off, which is the default mode.

· Warning: A warning message which does not necessarily imply an error, but the user is requested to focus on its origin. These messages are always shown.

· Error: An error message handled by DES which requires attention from the user. These messages are always shown.

· Exception: An exception message emerged from the underlying Prolog system and might be the source of a bug. These messages are always shown. Examples of exception messages include instantiation errors and undefined predicates.

Prolog exceptions are caught by DES and shown to the user without any further processing. Depending on the Prolog platform, the system may continue by itself; otherwise the user must type des. (including the ending dot) to continue if DES was started from a Prolog interpreter. Upon exceptions, the extension table is cleared and stratification is recomputed. Note that the latter computation may take a long time if there are multiple tables and views (typically in opened ODBC connections for DBMS’s as Oracle and SQL Server).

5.17 Commands

The input at the prompt (i.e., commands or queries) must be written in a line (i.e., without carriage returns, although it can be broken by the DES console due to space limitations in the terminal window) and can end with an optional dot.

Commands are issued by preceding the command with a slash (/) at the DES system prompt. Command arguments are not a comma-separated list enclosed between brackets as usual, but they simply occur separated by at least one blank. This enables short typing.

Command names and binary flags (as on/off switches) are not case sensitive.

Ending dots are considered as part of the argument wherever they are expected. For instance, /cd .. behaves as /cd ... (this command changes the working directory to the parent directory). In this last case, the final dot is not considered as part of the argument. The command /ls . shows the contents of the working directory, whereas /ls .. shows the contents of the parent directory (which behaves as /ls ...).

Filenames and directories can be specified with relative or absolute names. There is no need of enclosing such names between separators. However, a file or a directory name can be enclosed between double quotes ("), should its name contains blanks.

Since commands are submitted with a preceding slash, they are only recognized as commands in this way. Therefore, you can use command names for your relation names without name clashes. However, there are a few exceptions to this: Some commands can be stated in a Datalog file as a directive (the current list of these commands can be listed with /command_assertions) so that, upon consulting this file, they are executed. A command specified as an assertion has its arguments delimited by brackets and separated by commas. For example:

:- solve(ancestor(X,Y)).

:- fuzzy_relation(near,[reflexive,symmetric]).

Note that such directives are executed in the order in which they occur in the consulted file. In the command descriptions that come next, commands that can be used as directed are noticed. So, for the file p.dl containing:

p(a).

:-solve(p(X)).

:-clear_et.

p(b).

:-solve(p(X)).

Consulting it produces the following output:

DES> /c p

{

p(a)

}

Info: 1 tuple computed.

{

p(a),

p(b)

}

Info: 2 tuples computed.

Info: 2 rules consulted.

Note that the extension table is not updated upon loading each rule. If the directive clear_et was not stated, then the result for both solve directives would be the same because a completed computation is assumed for the goal.

When consulting Datalog files, filename resolution works as follows:

· If the given filename ends with .dl, DES tries to load the file with this (absolute or relative) filename.

· If the given filename does not end with .dl, DES firstly tries to load a file with .dl appended to the end of the filename. If such a file is not found, it tries to load the file with the given filename.

In command arguments, when applicable, you can use relative or absolute pathnames. In general, you can use a slash (/) as a directory delimiter, but depending on the platform, you can also use the backslash (\). Also, it might be needed to enclose path names between either single quotes (') or double quotes (").

Some commands are labelled with TAPI enabled, which means that they can be submitted to the textual application programming interface (TAPI). There is additional information for such commands in Section 5.18.2.

Next, commands are described, where italics indicate a parameter which must be supplied by the user. Square brackets ([ and ]) indicate an optional keyword or parameter (excepting the first two DES Database commands for consulting and reconsulting files, following Prolog syntax). If a parameter is not accepted, please try again enclosing it between single quotes (').

5.17.1 DDB Database

Commands related to the deductive database handling.

· /[FileNames]

Load the Datalog programs found in the comma–separated list [Filenames], discarding both rules already loaded, integrity constraints, and SQL table and view definitions. The extension table is cleared, and the predicate dependency graph and strata are recomputed.

Examples:

Assuming we are on the examples distribution directory, we can write:

DES> /[mutrecursion,family]

TAPI enabled.

See also /consult Filename.

· /[+FileNames]

Load the Datalog programs found in the comma–separated list Filenames, keeping rules already loaded, integrity constraints, and SQL table and view definitions. The extension table is cleared, and the predicate dependency graph and strata are recomputed.

TAPI enabled.

See also /[Filenames].

· /abolish

Delete the Datalog database. This includes all the local rules (including those which are the result of SQL compilations) and external rules (persistent predicates). Integrity constraints and SQL table and view definitions are removed. The extension table is cleared, and the predicate dependency graph and strata are recomputed.

· /abolish Name

Delete the predicates matching Name. This includes all their local rules (including those which are the result of SQL compilations) and external rules (persistent predicates). Their integrity constraints and SQL table and view definitions are removed. The extension table is cleared, and the predicate dependency graph and strata are recomputed.

· /abolish Name/Arity

Delete the predicates matching the pattern Name/Arity. This includes all their local rules (including those which are the result of SQL compilations) and external rules (persistent predicates). Their integrity constraints and SQL table and view definitions are removed. The extension table is cleared, and the predicate dependency graph and strata are recomputed.

· /assert Head[:-Body]

Add a Datalog rule. If Body is not specified, it is simply a fact. Rule order is irrelevant for Datalog computation. The extension table is cleared, and the predicate dependency graph and strata are recomputed.

· /close_persistent

If there is only one connection to a persistent predicate, it is closed. Otherwise, the user is warned with the different predicate alternatives. After closing the connection, the predicate is no longer visible except its metadata. The external DBMS keeps its definition. For restoring its visibility again, simply submit an assertion as :-persistent(PredSpec,DBMS).

· /close_persistent Name

Close the connection to the persistent predicate Name. The predicate is no longer visible except its metadata. The external DBMS keeps its definition. For restoring its visibility again, simply submit an assertion as :-persistent(PredSpec,DBMS).

· /consult FileName

Load the Datalog program found in the file Filename, discarding the rules already loaded, integrity constraints, and SQL table and view definitions. The extension table is cleared, and the predicate dependency graph and strata are recomputed. The default extension .dl for Datalog programs can be omitted.

Examples:

Assuming we are on the distribution directory, we can write:

DES> /consult examples/mutrecursion

which behaves the same as the following:

DES> /consult examples/mutrecursion.dl

DES> /consult ./examples/mutrecursion

DES> /consult c:/des6.8/examples/mutrecursion.dl

This last command assumes that the distribution directory is c:/des6.8.

Synonyms: /c, /restore_ddb.

TAPI enabled.

· /check_db

Check database consistency w.r.t. declared integrity constraints (types, existence, primary key, candidate key, foreign key, functional dependency, and user-defined). Display a report with the outcome.

· /des Input

Force DES to solve Input. If Input is an SQL query, DES solves it instead of relying on external DBMS solving. This allows to try the more expressive queries which are available in DES (as, e.g., hypothetical and non-linear recursive queries).

· /drop_ic Constraint

Drop the specified integrity constraint, which starts with ":-" and can be either one of:

· :- type(Table, [Column:Type])

· :- nn(Table, Columns)

· :- pk(Table, Columns)

· :- ck(Table, Columns)

· :- fk(Table, Columns, RTable, RColumns)

· :- fd(Table, Columns, DColumns)

· :- Goal

where Goal specifies a user-defined integrity constraint). Only one constraint can be dropped at a time. Alternative syntax for constraint is also allowed.

TAPI enabled.

· /drop_assertion Assertion

Drop the specified assertion, which starts with ":-". So far, there is only support for :-persistent(Schema[,Connection]). Where Schema is the ground atom describing the predicate (predicate and argument names, as: pred_name(arg_name1,...,arg_nameN)) that has been made persistent on an external DBMS via ODBC, and Connection is an optional connection name for the external RDB. Only one assertion can be dropped at a time.

· /list_predicate_classes

List classes of predicates: local (local database, either typed or not), deductive database (typed local), mixed database (both in the external and deductive databases), external database (only from an external connection), user (all predicates but built-ins), extensional (only facts or tables), recursive (in a recursive cycle), non-recursive (in no recursive cycle), non-dependent on recursive (not in a recursive cycle and non-dependent on a recursive predicate), restricted (with a restricted rule at least), dependent on restricted, non-completeable (its extension table cannot be closed), non-cacheable (with no entries in the extension table), semi-naïve optimized (amenable for this optimization).

· /list_predicates

List predicates (name and arity). Include intermediate predicates which are a result of compilations if development mode is enabled (cf. the command /development).

TAPI enabled.

· /listing

List the loaded Datalog rules, including restricting rules. Neither integrity constraints nor SQL views and metadata are displayed.

TAPI enabled.

· /listing Name

List the loaded Datalog rules matching Name, including restricting rules. Neither integrity constraints nor SQL views and metadata are displayed.

TAPI enabled.

· /listing Name/Arity

List the loaded Datalog rules matching the pattern Name/Arity, including restricting rules. Neither integrity constraints nor SQL views and metadata are displayed.

TAPI enabled.

· /listing Head

List the Datalog loaded rules whose heads are subsumed by the head Head. Neither integrity constraints nor SQL views and metadata are displayed.

TAPI enabled.

· /listing Head:-Body

List the Datalog loaded rules that are subsumed by Head:-Body. Neither integrity constraints nor SQL views and metadata are displayed.

TAPI enabled.

· /listing_asserted

List the Datalog rules that have been asserted with command. Rules from consulted files are not listed. Neither integrity constraints nor SQL views and metadata are displayed.

TAPI enabled.

· /listing_asserted Name

List the Datalog rules that have been asserted with command matching Name, including restricting rules. Neither integrity constraints nor SQL views and metadata are displayed.

TAPI enabled.

· /listing_asserted Name/Arity

List the Datalog rules that have been asserted with command matching the pattern Name/Arity, including restricting rules. Neither integrity constraints nor SQL views and metadata are displayed.

TAPI enabled.

· /listing_asserted Head

List the Datalog rules that have been asserted with command whose heads are subsumed by the head Head. Neither integrity constraints nor SQL views and metadata are displayed.

TAPI enabled.

· /list_modes

List the expected modes for unsafe predicates in order to be correctly computed. Modes can be 'i' (for an input argument) and 'o' (for an output argument).

· /list_modes Name

List expected modes, if any, for predicates with name Name in order to be correctly computed. Modes can be 'i' (for an input argument) and 'o' (for an output argument).

· /list_modes Name/Arity

List expected modes, if any, for the given predicate Name/Arity in order to be correctly computed. Modes can be 'i' (for an input argument) and 'o' (for an output argument).

· /list_persistent

List persistent predicates along with their ODBC connection names.

· /list_undefined

List undefined predicates, i.e., those which are not built-in, not external (ODBC table/view), and not defined with a Datalog rule.
TAPI enabled.

· /list_sources Name/Arity

List the sources of the Datalog rules matching the pattern Name/Arity .

TAPI enabled.

· /reconsult FileName

Load a Datalog program found in the file Filename, keeping the rules already loaded. The extension table is cleared, and the predicate dependency graph and strata are recomputed.

TAPI enabled.

See also /consult Filename.

Synonyms: /r.

· /restore_ddb

Restore the database from the default file des.ddb . Constraints (type, existence, primary key, candidate key, functional dependency, foreign key, and user-defined) are also restored, if present, from des.ddb.

See also /save_ddb Filename.

· /restore_ddb Filename

Restore the database from the given file (same as consult) . Constraints (type, existence, primary key, candidate key, functional dependency, foreign key, and user-defined) are also restored, if present, from Filename.

See also /save_ddb Filename.

· /restore_state

Restore the database state from the default file des.sds. Equivalent to /restore_state des.sds, where the current path is the start path.
TAPI enabled.

See also /save_state.

· /restore_state Filename

Restore the database state from Filename.

See also /restore_state Filename.

· /retract Head:-Body

Delete the first Datalog rule that unifies with Head:-Body (or simply with Head, if Body is not specified. In this case, only facts are deleted). The extension table is cleared, and the predicate dependency graph and strata are recomputed.

· /retractall Head

Delete all the Datalog rules whose heads unify with Head. The extension table is cleared, and the predicate dependency graph and strata are recomputed.

· /save_ddb

Save the current database to the file des.ddb, rewritting this file if already present. Constraints (type, not nullables, primary key, candidate key, functional dependency, foreign key, and user-defined) are also saved

See also /restore_ddb.

· /save_ddb [force] Filename

Save the current database to the file Filename. If option force is included, no question is asked to the user should the file exists already. Constraints (type, existence, primary key, candidate key, functional dependency, foreign key, and user-defined) are also saved.

See also /restore_ddb Filename.

· /save_state

Save the current database state to the default file des.sds. Equivalent to /save_state force des.sds, where the current path is the start path. The format of the saved stated is typically expected to change among different DES versions.
TAPI enabled.

See also /restore_state.

· /save_state [force] Filename

Save the current database state to the file Filename. Save the current database state to the file FileName. If option force is included, no question is asked to the user should the file exists already. The whole database (including its current state) can be saved to a file, and restored in a subsequent session. An automatic saving and restoring can be stated respectively by adding the commands /save_state and /restore_state in the files des.ini and des.out. This way, the user can restart its session in the same state point it was left, including the deductive database, metadata information (types, constraints, SQL text, ...), system settings, all opened external databases and persistent predicates. The format of the saved stated is typically expected to change among different DES versions.

See also /restore_state Filename.

5.17.2 Local and ODBC Databases

· /dangling_relations

Display the relations that depend on others which do not exist

· /dbschema

Display the database schema: Database name, tables, views and Datalog constraints. A Datalog integrity constraint is displayed under a table if it only refers to this table, and under the Datalog integrity constraints otherwise. If a constraint is created with a CREATE TABLE Tablename statement, it is listed under the table Tablename even when it refers to other tables or views.

TAPI enabled.

Synonyms: /db_schema.

· /dbschema Name

Display the database schema for the given connection, view or table name.

TAPI enabled.

Synonyms: /db_schema Name.

· /dbschema Connection:Name

Display the database schema for the given view or table name in the given connection.

TAPI enabled.

Synonyms: /db_schema Connection:Name.

· /db_schema

Synonym for /dbschema.

· /db_schema Name

Synonym for /dbschema Name.

· /db_schema Connection:Relation

Synonym for /dbschema Connection:Relation.

/dbs_schemas Display the schema of each open database: Tables, views and constraints. TAPI enabled

· /dependent_relations [direct] [declared] Relation

Display a list of relations that depend on Relation. Relation can be either a pattern R/A or a relation R. A relation R can be either a relation name N or C:N, where C refers to a specific connection and N is a relation name. If direct is included, the dependency is only direct; otherwise, the dependency is both direct and indirect. If declared is included, only declared (typed) relations are included in the outcome. In development mode, system-generated predicates are also considered. TAPI enabled

· /describe Relation

Synonym for /db_schema Relation, where Relation can only be either a table or a view, possibly qualified with the database name (as connection:relation)

· /drop_all_tables

Drop all tables from the current database but dual if it exists. If the current connection is an external database, tables in $des are not dropped.

TAPI enabled.

· /drop_all_relations

Drop all relations from the current database but dual if it exists. If the current connection is an external database, relations in $des are not dropped.

· /drop_all_views

Drop all views from the current database but dual if it exists. If the current connection is an external database, views in $des are not dropped.

· /open_db Name [Options]

Open and set the current ODBC connection to Name, where Options=[user('Username')] [password('Password')]. Username and Password must be delimited by single quotes ('). If Name contains a blank space, it must also be enclosed in single quotes. This connection must be already defined at the OS layer.

TAPI enabled.

· /close_db

Close the current ODBC connection.

TAPI enabled.

· /close_db Name

Close the given ODBC connection.

TAPI enabled.

· /close_dbs

Close all the opened ODBC connections. Make $des the current database.

· /current_db

Display the current ODBC connection name and DSN provider.

TAPI enabled.

· /get_relation Connection Relation

Display the relation schema and data for the given connection as the Prolog term schema_data(Schema,Data), where Schema is of the form relname(col_1:type_1,...,col_n:type_n), Data is a list of tuples relname(val_1,...,val_n), col_i are column names, type_i are type names, and val_i are values of the corresponding type type_i. If Connection=$des and Relation=answer, the outcome corresponds to the answer to the last submitted query

· /is_empty relation_name

Display $true if the given relation is empty, and $false otherwise.

TAPI enabled

· /list_dbs

Display the open database connections.

TAPI enabled.

Synonym: /show_dbs.

· /list_relations

List relation (both tables and views) names.

· /list_tables

List table names.

· /list_table_schemas

List table schemas.

TAPI enabled

· /list_table_constraints Name

List table constraints for table Name.

TAPI enabled

· /list_views

List view names.

TAPI enabled

· /list_view_schemas

List view schemas.

TAPI enabled

· /parse_external_sql

Display whether parsing of SQL queries sent to external engines is enabled

· /parse_external_sql Switch

Enable or disable parsing of SQL queries sent to external engines (on or off, resp.)

· /referenced_relations Relation

Display the name of relations that are directly referenced by a foreign key in relation Relation.

TAPI enabled

· /referenced_relations Relation/Arity

Display in format Name/Arity those relations that are directly referenced by a foreign key in relation Relation/Arity.

TAPI enabled

· /refresh_db

Refresh local metadata from either the deductive or the current external database, clear the cache, and recompute the PDG and strata.

TAPI enabled.

· /relation_exists RelationName

Display $true if the given relation exists, and $false otherwise.

TAPI enabled

· /relation_modified

Display the relations modified so far (Datalog relation, SQL table or view), whether it is typed or not, as the Prolog terms connection_table(Connection, Relation), where Connection is the connection for which the relation with name Relation has been modified.
TAPI enabled

· /relation_schema RelationName

Display relation schema of RelationName.

TAPI enabled

· /show_dbs

Synonym for /list_dbs.

TAPI enabled.

· /sql_left_delimiter

Display the SQL left delimiter as defined by the current database manager (either DES or the external DBMS via ODBC).

TAPI enabled

· /sql_right_delimiter

Display the SQL left delimiter as defined by the current database manager (either DES or the external DBMS via ODBC) .

TAPI enabled

· /use_db Name

Make Name the current ODBC connection. If it is not open already, it is automatically opened.

TAPI enabled.

· /use_ddb

Shorthand for /use_db $des.

TAPI enabled.

5.17.3 Dependency Graph and Stratification

· /external_pdg

Display whether external PDG construction is enabled.

· /external_pdg Switch

Enable or disable external PDG construction (on or off) Some ODBC drivers are so slow that makes external PDG construction impractical. If disabled, tracing and debugging external databases are not possible.

· /pdg

Display the current predicate dependency graph.

TAPI enabled

· /pdg Name

Display the current predicate dependency graph restricted to the first predicate found with name Name.

TAPI enabled

· /pdg Name/Arity

Display the current predicate dependency graph restricted to the predicate with name Name and Arity.

TAPI enabled

· /rdg

Display the current relation dependency graph, i.e., the PDG restricted to show only nodes with type information (tables and views).

TAPI enabled

· /rdg Name

Display the current relation dependency graph restricted to the first relation found with name Name.

TAPI enabled

· /rdg Name/Arity

Display the current relation dependency graph restricted to the relation with name Name and Arity.

TAPI enabled

· /strata

Display the current stratification as a list of pairs (Name/Arity, Stratum).

· /strata Name

Display the current stratification restricted to predicate with name Name.

· /strata Name/Arity

Display the current stratification restricted to the predicate Name/Arity.

· /xpdg

Display the extended predicate dependency graph, which details the restricted predicates (if existing) and their dependencies.

· /xpdg Name

Display the current predicate dependency graph restricted to the predicate with name Name, detailing the restricted predicates (if existing) and their dependencies.

· /xpdg Name/Arity

Display the current predicate dependency graph restricted to the predicate Name/Arity , detailing the restricted predicates (if existing) and their dependencies.

5.17.4 Debugging and Test Case Generation

· /debug_datalog Goal [Level]

Start the debugger for the basic goal Goal at predicate or clause level, which is indicated with the options p and c for Level, respectively. Default is p. This debugger implements the framework described in SDKB 2008 paper [CGS08].

· /debug_dl Name/Arity Options

Start the debugger for the predicate Name/Arity where:

Options = [Answer]

[trust_extension([yes|no])]

[file(File)]

where the file name will be typically enclosed between single quotes (following syntax of Prolog atoms), and:

Answer = abort |

valid |

nonvalid |

missing(Tuple) |

wrong(Tuple)

Defaults are no answer and trust extension (trust_extension(yes)). If present, the answer must be the first option. It is assumed that a predicate name only occurs in the program with the same arity. This debugger implements the framework described in PPDP 2015 paper [CGS15a].
TAPI enabled

· /debug_dl_answer Question Answer

Answer a question when debugging a Datalog relation. Possible answers are abort, valid, nonvalid, missing(Tuple), and wrong(Tuple), where Tuple is of the form rel(cte₁, ..., cte_n), where rel is the relation name and each argument cte_i is a Datalog constant. Placeholders (_) are allowed for missing tuples instead of constants.
TAPI enabled

· /debug_dl_cleanup

Clean up full Datalog debugger. Typically used with TAPI, this command removes temporary data and files resulting from a debugging session.
TAPI enabled

· /debug_dl_current_question

Display the current question when debugging a Datalog relation.
TAPI enabled

· /debug_dl_explain

Explain the outcome of the last Datalog debugging session.
TAPI enabled

· /debug_dl_node_state

Display Datalog debugging node states.
TAPI enabled

· /debug_dl_set_node Name/Arity State

Set the state for a node with an unknown state. State can be valid, nonvalid, missing(Tuple), and wrong(Tuple), where Tuple is of the form rel(cte₁, ..., cte_n), where rel is the relation name and each argument cte_i is a Datalog constant. Placeholders (_) are allowed for missing tuples instead of constants.
TAPI enabled

· /debug_dl_solutions

Display Datalog debugging solutions for the current question.
TAPI enabled

· /debug_dl_statistics

Display Datalog debugging session statistics.
TAPI enabled

· /debug_sql View [Options]

Debug an SQL view where:

Options = [Answer]

[trust_tables([yes|no])] [trust_file(FileName)]

[oracle_file(FileName)] [debug([full|plain])]

[order([cardinality|topdown])]

Answer = abort |

valid |

nonvalid |

missing(PartialTuple) |

wrong(TotalTuple)

Defaults are no answer, trust tables, no trust file, full debugging, and navigation order based on relation cardinality. If present, this answer must be the first option. It might be needed to enclose FileName between single quotes.
TAPI enabled

· /debug_sql_answer Question Answer

Answer a question when debugging an SQL relation. Possible answers are abort, valid, nonvalid, missing(Tuple), and wrong(Tuple), where Tuple is of the form rel(cte₁, ..., cte_n), where rel is the relation name and each argument cte_i is an SQL constant. Placeholders (_) are allowed for missing tuples instead of constants.
TAPI enabled

· /debug_sql_current_question

Display the current question when debugging an SQL view.
TAPI enabled

· /debug_sql_node_state

Display SQL debugging node states.
TAPI enabled

· /debug_sql_set_node Node State

Set the state for a node with an unknown state. State can be either valid, nonvalid, missing(Tuple), and wrong(Tuple), where Tuple is of the form rel(cte₁, ..., cte_n), where rel is the relation name and each argument cte_i is an SQL constant. Placeholders (_) are allowed for missing tuples instead of constants.
TAPI enabled

· /debug_sql_statistics

Display SQL debugging session statistics.
TAPI enabled

· /trace_datalog Goal [Order]

Trace a Datalog goal in the given order (postorder or the default preorder).

· /trace_sql View [Order]

Trace an SQL view in the given order (postorder or the default preorder).

· /test_case View [Options]

Generate test case classes for the view View. Options may include a class and/or an action parameters. The test case class is indicated by the values all (positive-negative, the default), positive, or negative in the class parameter. The action is indicated by the values display (only display tuples, the default), replace (replace contents of the involved tables by the computed test case), or add (add the computed test case to the contents of the involved tables) in the action parameter.

· /tc_size

Display the minimum and maximum number of tuples generated for a test case.

· /tc_size Min Max

Set the minimum and maximum number of tuples generated for a test case.

· /tc_domain

Display the domain of values for test cases.

· /tc_domain Min Max

Set the domain of values for test cases between Min and Max.

5.17.5 Tabling

· /clear_et

Delete the contents of the extension table. Can be used as a directive.

· /list_et

List the contents of the extension table in lexicographical order. First, answers are displayed, then calls.

· /list_et Name

List the contents of the extension table matching Name. First, answers are displayed, then calls.

· /list_et Name/Arity

List the contents of the extension table matching the pattern Name/Arity. First, answers are displayed, then calls.

TAPI enabled.

5.17.6 Operating System

· /ashell Command

An asynchronous shell command, i.e., as /shell Command but without waiting for the process to finish and also eliding output.

· /cat Filename

Type the contents of Filename enclosed between the following lines:

%% BEGIN AbsoluteFilename %%

%% END AbsoluteFilename %%

Synonym: /type Filename.

· /cd

Set the current directory to the directory where DES was started from.

TAPI enabled.

· /cd Path

Set the current directory to Path.

TAPI enabled.

· /copy FromFile ToFile

Synonym for /cp FromFile ToFile.

· /cp FromFile ToFile

Copy the file FromFile to ToFile.

· /del Filename

Synonym for /rm FileName.

· /e Filename

Synonym for /edit Filename.

· /edit Filename

Edit Filename by calling the predefined external text editor. This editor is set with the command /set_editor.

· /dir

Synonym for /ls.

· /dir Path

Synonym for /ls Path.

· /ls

Display the contents of the current directory in alphabetical order. First, files are displayed, then directories. Use /shell dir and /shell ls for file and directory listings directly from the host OS.

Synonym: /dir.

· /ls Path

DisDisplay the contents of the given directory in alphabetical order. If Path is a file name and exists, it is displayed. Files and directories are displayed as in /ls. Use /shell dir [arguments] and /shell ls [arguments] for file and directory listings directly from the host OS.

Synonym: /dir Path.

· /pwd

Display the absolute filename for the current directory.

TAPI enabled.

· /rm FileName

Delete FileName from the file system.

Synonyms: /del.

· /set_editor

Display the current external text editor.

· /set_editor Editor

Set the current external text editor to Editor.

· /shell Command

Submit Command to the operating system shell.

Notes for platform specific issues:

o Windows users:

command.exe is the shell for Windows 98, whereas cmd.exe is the one for Windows NT/2000/2003/XP/Vista/7/8.

Filenames containing blanks must be enclosed between double quotes (").

Some non-file parameters needing double quotes might been needed to be also enclosed between single quotes ('"some parameter"') in SWI-Prolog distros.

o SICStus users:

Under Windows, if the environment variable SHELL is defined, it is expected to name a Unix like shell, which will be invoked with the option -c Command. If SHELL is not defined, the shell named by COMSPEC will be invoked with the option /C Command.

o Windows and Linux/Unix executable users:

The same note for SICStus is applied.

Synonyms: /s.

· /type Filename

Synonym for /cat Filename

5.17.7 Logging

· /ilog

Display whether immediate logging is enabled. If enabled, each log is closed before user input and opened again afterwards.

· /ilog Switch

Enable or disable immediate logging (on or off, resp.). If enabled, each log is closed before user input and opened again afterwards.

· /log

Display the current log files, if any.

· /log Filename

Set logging to the given filename overwriting the file, if exists, or creating a new one. Simultaneous logging to different logs is supported. Simply issue as many /log Filename commands as needed.

· /log Mode Filename

Set logging to the given filename and mode: write (overwriting the file, if exists, or creating a new one) or append (appending to the contents of the existing file, if exists, or creating a new one).

· /nolog

Disable logging.

· /nolog Filename

Disable logging for the given filename.

5.17.8 Informative

· /apropos Keyword

Display detailed help about Keyword, which can be a command or built-in.

Synonyms: /help.

· /builtins

List predefined operators, functions, and predicates.

· /command_assertions

List commands that can be used as assertions. A Datalog program can contain assertions :- command(arg1,...,argn), where command is the command name, and argi are its arguments.

· /development

Display whether development listings are enabled.

· /development Switch

Enable or disable development listings (on or off, resp.). These listings show the source-to-source translations needed to handle null values, Datalog outer join built-ins, and disjunctive literals.

· /display_answer

Display whether display of computed tuples is enabled.

· /display_answer Switch

Enable or disable display of computed tuples (on or off, resp.) The number of tuples is still displayed.

· /display_nbr_of_tuples

Display whether display of the number of computed tuples is enabled.

· /display_nbr_of_tuples Switch

Enable or disable display of the number of computed tuples (on or off, resp.)

· /help

Display resumed help on commands.

Shorthand: /h.

· /help Keyword

Display detailed help about Keyword, which can be a command or built-in.

Synonym: /apropos.

· /license

Display GPL and LGPL licenses.

· /prolog_system

Display the underlying Prolog engine version.

· /silent

Display whether silent batch output is either enabled or disabled.

· /silent Option

Enable or disable silent batch output messages (on or off, resp.) If this command precedes any other input, it is processed in silent mode (the command is not displayed and some displays are elided, as in particular verbose outputs).

· /status

Display the current system status, i.e., verbose mode, logging, elapsed time display, program transformation, current directory, current database and other settings.

· /verbose

Display whether verbose output is either enabled or disabled (on or off, resp.)

· /verbose Switch

Enable or disable verbose output messages (on or off, resp.) Another option, toggle, toggles its state (from on to off and vice versa).

· /version

Display the current DES system version.

5.17.9 Query Languages

· /datalog

Switch to Datalog interpreter. All subsequent queries are parsed and executed first by the Datalog engine. If it is not a Datalog query, then it is tried in order as an SQL, RA, TRC, and DRC query.

Synonyms: /des

· /datalog Query

Trigger Datalog resolution for the query Query. The query is parsed and executed in Datalog, but if a parsing error is found, it is tried in order as an SQL, RA, TRC, and DRC query.

· /des

Synonym for /datalog.

· /drc

Switch to DRC interpreter (all queries are parsed and executed in DRC).

· /drc Query

Trigger DRC evaluation for the query Query.

· /prolog

Switch to Prolog interpreter (all queries are parsed and executed in Prolog).

· /prolog Goal

Trigger Prolog’s SLD resolution for the goal Goal.

· /ra

Switch to RA interpreter (all queries are parsed and executed in RA).

· /ra RA_expression

Trigger RA evaluation for the query RA_expression.

· /sql

Switch to SQL interpreter (all queries are parsed and executed in SQL).

· /sql SQL_statement

Trigger SQL resolution for SQL_statement.

· /trc

Switch to TRC interpreter (all queries are parsed and executed in TRC).

· /trc Query

Trigger TRC evaluation for the query Query.

5.17.10 TAPI

See also Section 5.18.2 for more information.

· /tapi Input

Process Input and format its output for TAPI communication. Only a limited set of possible inputs are allowed (cf. Section 5.18).

/mtapi

Process the next input lines by TAPI. It behaves as /tapi Input, where Input are the lines following /mtapi and terminated by a single line containing $eot. Thus, "mtapi" stands for "multiline-tapi"

/tapi_log

Display whether TAPI logging is enabled. If enabled, both TAPI commands and their results are not logged

/tapi_log Switch

Enable or disable TAPI logging (on or off, resp.) If enabled, both TAPI commands and their results are not logged

· /test_tapi

Test the current TAPI connection.

TAPI enabled.

5.17.11 Settings

· /autosave

Display whether the database is automatically saved upon exiting and restored upon starting in the file des.sds (on) or not (off).

· /autosave Switch

Enable or disable automatic saving and restoring of the database (on or off, resp.) Another option, toggle, toggles its state (from on to off and vice versa). If enabled, the complete database is automatically saved upon exiting and restored upon starting in the file des.sds. Processing /autosave on adds the line /restore_state to the beginning of des.ini if the line is not in the file, and adds the line /save_state to the beginning of des.out if the line is not in the file. If either des.ini or des.out does not exist, the file is created and the corresponding line is included. Processing /autosave off deletes the line /restore_state from des.ini if they exist, and the line /save_state from des.out if they exist. If either des.ini or des.out becomes empty, the file is deleted.

· /batch

Display whether batch mode is enabled. If enabled, batch mode avoids PDG construction.

· /batch Switch

Enable or disable batch mode (on or off, resp.)

· /check

Display whether integrity constraint checking is enabled.

· /check Switch

Enable or disable integrity constraint checking (on or off, resp.)

· /compact_listings

Display whether compact listings are enabled.

· /compact_listings Switch

Enable or disable compact listings (on or off, resp.)

· /current_flag Flag

Display the current value of flag Flag, if it exists.

· /des_sql_solving

Display whether DES is forced to solve SQL queries for external DB's. If enabled, this allows to experiment with more expressive queries as, e.g., hypothetical and non-linear recursive queries targeted at an external DBMS.

· /des_sql_solving Switch

Enable or disable DES solving for SQL queries when the current database is an open ODBC connection (on or off, resp.)

· /display_banner

Display whether the system banner is displayed at startup.

· /display_banner Switch

Enable or disable the display of the system banner at startup (on or off, resp.). Only useful in a batch file des.ini or des.cnf.

· /duplicates

Display whether duplicates are enabled.

· /duplicates Switch

Enable or disable integrity constraint checking (on or off, resp.)

· /fp_info

Display whether fixpoint information is to be displayed.

· /fp_info Switch

Enable or disable display of fixpoint information, as the ET entries deduced for the current iteration (on or off, resp.)

· /host_safe

Display whether host safe mode is enabled (on) or not (off). Enabling host safe mode prevents users and applications using DES from accessing the host (typically used to shield the host from outer attacks, hide host information, protect the file system, and so on).

· /host_safe on

Enable host safe mode. Once enabled, this mode cannot be disabled.

· /hypothetical

Display whether hypothetical queries are enabled (on) or not (off) .

· /hypothetical Switch

Enable or disable hypothetical queries (on or off, resp.)

· /keep_answer_table

Display whether keeping the answer table is enabled

· /keep_answer_table Switch

Enable or disable keeping the answer table (on or off, resp.)

· /multiline

Display whether multi-line input is enabled.

· /multiline Switch

Enable or disable multi-line input (on or off resp.)

· /nulls

Display whether nulls are enabled (on) or not (off) .

· /nulls Switch

Enable or disable nulls (on or off, resp.)

· /order_answer

Display whether displayed answers are ordered by default.

· /order_answer Switch

Enable or disable a default (ascending) ordering of displayed computed tuples (on or off, resp.) This order is overridden if the user query contains either a group by specification or a call to a view with such a specification.

· /output

Display the display output mode (on, off, or only_to_log). In mode on, both console and log outputs are enabled. In mode off, no output is enabled. In mode only_to_log, only log output is enabled.

· /output Mode

Set the display output mode (on, off, or only_to_log).

· /pretty_print

Display whether pretty print listings is enabled.

· /pretty_print Switch

Enable or disable pretty print for listings (on or off, resp.)

· /prompt

Display the prompt format.

· /prompt Option

Set the format of the prompt. The value des sets the prompt to DES>. The value des_db adds the current database name DB as DES:DB>. The value plain sets the prompt to >. The value prolog sets the prompt to ?-. Note that, for the values des and des_db, if a language other than Datalog is selected, the language name preceded by a dash is also displayed before >, as DES-SQL>.

· /reorder_goals

Display whether pushing equalities to the left is enabled

· /reorder_goals Switch

Enable or disable pushing equalities to the left (on or off, resp.) Equalities in bodies are moved to the left, which in general allows more efficient computations.

· /reset

Synonym for /restore_default_status.

· /restore_default_status

Restore the status of the system to the initial status, i.e., set all user-configurable flags to their initial values, including the default database and the start-up directory. Neither the database nor the extension table are cleared

Synonyms: /reset

· /running_info

Display whether running information, such as the incremental number of consulted rules as they are read and the current batch line, is to be displayed.

· /running_info Value

Enable or disable display of running information, such as the number of consulted rules as they are read (value on) and the current batch line (value batch, which applies only when /output is set to only_to_log). The default value off disables this display

· /safe

Display whether safety transformation is enabled.

· /safe Switch

Enable or disable program transformation for unsafe rules (on or off, resp.)

· /safety_warnings

Display whether safety warnings are enabled.

· /safety_warnings Switch

Enable or disable safety warnings (on or off, resp.)

· /sandboxed

Synonym for /host_safe.

· /sandboxed on

Synonym for /host_safe on.

/set_flag Flag Expression

Set the system flag Flag to the value corresponding to evaluating Expression. An expression can be simply a constant value. Use quotes to delimit a string value (otherwise, it can be interpreted as a variable if it starts with either a capital letter or an underscore). Any system flag can be changed but unexpected behaviour can occur if thoughtlessly setting a flag.

· /show_compilations

Display whether compilations from SQL DQL statements to Datalog rules are to be displayed.

· /show_compilations Switch

Enable or disable display of extended information about compilation of SQL DQL statements to Datalog clauses (on or off, resp.)

· /show_sql

Display whether SQL compilations are to be displayed.

· /show_sql Switch

Enable or disable display of SQL compilations (on or off, resp.) SQL statements can come from either RA, or DRC, or TRC, or Datalog compilations. In this last case, they are intented to be externally processed.

· /simplification

Display whether program simplification is enabled.

· /simplification Switch

Enable or disable program simplification (on or off, resp.). Rules with equalities, true, and not BooleanValue are simplified.

· /singleton_warnings

Display whether singleton warnings are enabled.

· /singleton_warnings Switch

Enable or disable singleton warnings (on or off, resp.)

· /sql_semantic_check

Display the SQL semantic check mode (on, off or loose). Mode off means disabled, on means enabled, and loose includes more probabilities for false positives, though with more error detections. When enabled, possible semantic errors are warned

· /sql_semantic_check Mode

Set the SQL semantic check with Switch (on, off or loose). Mode off means disabled, on means enabled, and loose includes more probabilities for false positives, though with more error detections. When enabled, possible semantic errors are warned

· /system_mode

Display the current system mode, which can be either des or fuzzy.

· /system_mode Mode

Set the system mode to Mode (des or fuzzy). Switching between modes abolishes the current database. Can be used as a directive.

· /type_casting

Display whether automatic type casting is enabled.

· /type_casting Switch

Enable or disable automatic type casting (on or off, resp.) This applies to Datalog fact assertions and SQL insertions and selections. Enabling this provides a closer behaviour of SQL statement solving. Changing the status of this mode implies the recompilation of views in the local database.

· /undef_pred_warnings

Display whether undefined predicate warnings are enabled.

· /undef_pred_warnings Switch

Enable or disable undefined predicate warnings (on or off, resp.)

· /unfold

Display whether program unfolding is enabled.

· /unfold Switch

Enable or disable program unfolding (on or off, resp.) Unfolding affects to the set of rules which result from the compilation of a single source rule. Unfolding is always forced for SQL, RA, TRC and DRC compilations, irrespective of this setting.

· /unset_flag Flag

Unset the system flag with name Flag so it becomes no longer defined up to a new setting.

5.17.12 Timing

· /date

Display the current host date as specified by the command /date_format which, by default, is ISO 8601: YYYY-MM-DD for the year (YYYY), month (MM), and day (DD).

· /datetime

Display the current host date as specified by the command /date_format which, by default, is: YYYY-MM-DD for the year (YYYY), month (MM), and day (DD), and the host time as HH:Mi:SS for hours (HH), minutes (Mi), and seconds (SS) in 24-hour format according to ISO 8601.

· /date_format

Display the current date format.

· /date_format Format

Set the date format for display and insert, specifying dates as strings. Format is an unquoted string including single numeric occurrences of YYYY (year), MM (month), DD (day of the month), and a (single-char) separator between them. Default is ISO 8601: YYYY-MM-DD.

· /display_stopwatch

Display stopwatch. Precision depends on host Prolog system (1 second or milliseconds).

· /format_datetime

Display whether formatted date and time is enabled. It is disabled by default.

· /format_datetime Switch

Enable or disable formatted date and time (on or off, resp.) If disabled (as default), dates are displayed as date(year, month, day), and time is displayed as time(hour, minute, second), both with positive numbers for each term argument. If enabled, dates are displayed in the date format as specified by the command /date_format, and time as specified by /time_format.

· /format_timing

Display whether formatted timing for measured times is enabled, such as those displayed by statistics.

· /format_timing Switch

Enable or disable formatted timing for measured times, such as those displayed by statistics (on or off, resp.). Given that ms, s, m, h represent milliseconds, seconds, minutes, and hours, respectively, times less than 1 second are displayed as ms; times between 1 second and less than 60 are displayed as s.ms; times between 60 seconds and less than 60 minutes are displayed as m:s.ms; and times from 60 minutes on are displayed as h:m:s.ms

· /reset_stopwatch

Reset stopwatch. Precision depends on host Prolog system (1 second or milliseconds).

· /set_timeout

Display whether a global timeout is set.

· /set_timeout Value

Set the global timeout to Value (either in seconds as an integer or off). If an integer is provided, any input is restricted to be processed for a time period of up to this number of seconds. If the timeout is exceeded, then the execution is stopped as if an exception was raised. If Value is off, the timeout is disabled.

· /start_stopwatch

Start stopwatch. Precision depends on host Prolog system (1 second or milliseconds).

· /stop_stopwatch

Stop stopwatch. Precision depends on host Prolog system (1 second or milliseconds).

· /time

Display the current host time as HH:Mi:SS for hours (HH), minutes (Mi), and seconds (SS) in 24-hour format according to ISO 8601.

· /time Input

Process Input and display detailed elapsed time. Its output is the same as processing Input with /timing detailed.

· /timeout Seconds Input

Process Input for a time period of up to the number of seconds specified in Seconds. If the timeout is exceeded, then the execution is stopped as if an exception was raised. Timeout commands cannot be nested. In this case, the outermost command is the prevailing one.

· /timing

Display whether elapsed time display is enabled.

· /timing Option

Sets the required level of elapsed time display as disabled, enabled or detailed (off, on or detailed, resp.)

5.17.13 Statistics

· /display_statistics

Display whether statistics display is enabled.

· /display_statistics Switch

Enable or disable statistics display (on or off, resp., and disabled by default). Enabling statistics display also enables statistics collection, but disabling statistics display does not disable statistics collection. Statistics include numbers for: Fixpoint iterations, EDB (Extensional Database - Facts) retrievals, IDB (Intensional Database - Rules) retrievals, ET (Extension Table) retrievals, ET lookups, CT (Call Table) lookups, CF (Complete Computations) lookups, ET entries and CT entries. Individual statistics can be displayed in any mode with write commands and system flags (e.g., /writeln $et_entries$). . Enabling statistics incurs in a run-time overhead.

· /host_statistics Keyword

Display host Prolog statistics for Keyword (runtime or total_runtime). For runtime, this command displays the CPU time used while executing, excluding time spent in memory management tasks or in system calls since the last call to this command. For total_runtime, this command displays the total CPU time used while executing, including memory management tasks such as garbage collection but excluding system calls since the last call to this command.

· /reset_statistics

Reset deductive engine statistics

· /statistics

Display whether statistics collection is enabled or not (on or off, resp.). It also displays last statistics, if enabled.

· /statistics Switch

Enable or disable statistics collection (on or off, resp., and disabled by default). Statistics include numbers for: Fixpoint iterations, EDB (Extensional Database - Facts) retrievals, IDB (Intensional Database - Rules) retrievals, ET (Extension Table) retrievals, ET lookups, CT (Call Table) lookups, CF (Complete Computations) lookups, ET entries and CT entries. Statistics are displayed only in verbose mode, but they can be displayed in any mode with write commands and system flags (e.g., /writeln $et_entries$). Enabling statistics incurs in a run-time overhead.

5.17.14 Scripting

· /if Condition Input

Process Input if Condition holds. A condition is written as a Datalog goal, including all the primitive predicates, operators and functions. Condition may have to be enclosed between parentheses to avoid ambiguity.

· /goto Label

Set the current script position to the next line where the label Label is located. A label is defined as a single line starting with a semicolon (:) and followed by its name. If the label is not found, an error is displayed and processing continue with the next script line. This command can not be the last one in a script and does not apply to interactive mode.

· /process Filename [Parameters]

Process the contents of Filename as if they were typed at the system prompt. Extensions by default are: .sql and .ini. When looking for a file f, the following filenames are checked in this order: f, f.sql, and f.ini. A parameter is a string delimited by either blanks or double quotes (") if the parameter contains a blank. The same is applied to Filename. The value for each parameter is retrieved by the tokens $parv1$, $parv2$, ... for the first, second, ... parameter, respectively.

Synonyms: /p.

· /run Filename [Parameters]

Reminiscent of old 8 bit computers, this command allows for processing a file but retaining user input for selected commands such as /input. Process the contents of Filename as if they were typed at the system prompt. Extensions by default are: .sql and .ini. When looking for a file f, the following filenames are checked in this order: f, f.sql, and f.ini. A parameter is a string delimited by either blanks or double quotes (") if the parameter contains a blank. The same is applied to Filename. The value for each parameter is retrieved by the tokens $parv1$, $parv2$, ... for the first, second, ... parameter, respectively.

· /repeat Number Input

Repeat Input as many times as Number, where Input can be any legal input at the command prompt.

· /return

Stop processing of current script, returning a 0 code. This code is stored in the system variable $return_code$. Parent scripts continue processing

· /return Code

Stop processing of current script, returning Code. This code is stored in the system variable $return_code$. Parent scripts continue processing

· /set

Display each user variable and its corresponding value.

· /set Variable

Display the value for the user variable Variable.

· /set Variable Expression

Set the user variable Variable to the value corresponding to evaluating Expression. An expression can be simply a constant value. Use quotes to delimit a string value (otherwise, it can be interpreted as a variable if it starts with either a capital letter or an underscore). Refer to a user variable by delimiting it with dollars. If a user variable name coincides with the name of a system flag, the system flag overrides the user variable.

· /set_default_parameter Index Value

Set the default value for the i-th parameter (denoted by the number Index) to Value.

· /stop_batch

Stop batch processing. The last return code is kept. All parent scripts are stopped.

· /input Variable

Wait for a user input (terminated by Intro) to be set on the user variable Variable.

· /unset Variable

Unset the variable with name Variable so it becomes no longer defined up to a new setting.

· /write String

Write String to console. String can contain system variables as $stopwatch$ (which holds the current stopwatch time) and $total_elapsed_time$ (which holds the last total elapsed time). Strings are not needed to be delimited: the text after the command is considered as the string. (See Section 5.15 for system variables).

· /writeln String

As /write but adding a new line at the end of the string.

· /write_to_file File String

Write String to File. If File does not exist, it is created; otherwise, previous contents are not deleted and String is simply appended to File. String can contain system variables as $stopwatch$ (which holds the current stopwatch time) and $total_elapsed_time$ (which holds the last total elapsed time). Strings are not needed to be delimited: the text after File is considered as the string. (See Section 5.15 for system variables).

· /writeln_to_file File

As /write_to_file but writing a new line.

5.17.15 Miscellanea

· /csv

Display whether csv dump is enabled. If so, the output csv file name is displayed.

· /csv FileName

Enables semicolon-separated csv output of answer tuples. If FileName is off, output is disabled. If the file already exists, tuples are appended to the existing file.

· /debug_sql_bench NbrTables TableSize NbrViews MaxDepth MaxChildren FileName

With the same parameters as /generate_db, generate an SQL database instance and a mutated version. The filename for the first one is appended with _trust before the extension.

· /exit

Synonym for /halt.

Shorthand: /e.

· /generate_db NbrTables TableSize NbrViews MaxDepth MaxChildren FileName

· /halt

Quit the system.

Synonyms: /exit, /quit.

· /mparse Input

Parse the next input lines as they were directly submitted from the prompt, terminated by $eot. Return syntax errors and semantic warnings, if present in Input. TAPI enabled

· /parse Input

Parse the input as it was directly submitted from the prompt, avoiding its execution. Return syntax errors and semantic warnings, if present in Input. TAPI enabled

· /quit

Synonym for /halt.

Shorthand: /q.

· /solve Input

Solve Input as it was directly submitted from the prompt. The command, used as a directive, can submit goals during consulting a Datalog program. Can be used as a directive.

5.17.16 Implementor

· /breakpoint

Set a breakpoint: start host Prolog debugging.

· /debug

Enable debugging in the host Prolog interpreter.

· /indexing

Display whether hash indexing on memo tables is enabled.

· /indexing Switch

Enable or disable hash indexing on memo tables (on or off, resp.) Default is enabled, which shows a noticeable speed-up gain in some cases.

· /nodebug

Disable debugging in the host Prolog interpreter. Only working for source distributions.

· /nospyall

Remove all Prolog spy points in the host Prolog interpreter. Disable debugging.

· /nospy Pred[/Arity]

Remove the spy point on the given predicate in the host Prolog interpreter.

· /optimize_cc

Display whether complete computations optimization is enabled.

· /optimize_cc Switch

Enable or disable complete computations optimization (on or off, resp. and enabled by default). Fixpoint iterations and/or extensional database retrievals might been saved.

· /optimize_ep

Display whether extensional predicates optimization is enabled.

· /optimize_ep Switch

Enable or disable extensional predicates optimization (on or off, resp. and enabled by default). Fixpoint iterations and extensional database retrievals are saved for extensional predicates as a single linear fetching is performed for computing them.

· /optimize_nrp

Display whether non-recursive predicates optimization is enabled.

· /optimize_nrp Switch

Enable or disable non-recursive predicates optimization (on or off, resp. and enabled by default). Memoing is only performed for top-level goals.

· /optimize_st

Display whether stratum optimization is enabled.

· /optimize_st Switch

Enable or disable stratum optimization (on or off, resp. and enabled by default). Extensional table lookups are saved for non-recursive predicates calling to recursive ones, but more tuples might be computed if the non-recursive call is filtered, as in this case an open call is submitted instead (i.e., not filtered).

· /spy Pred[/Arity]

Set a spy point on the given predicate in the host Prolog interpreter.

· /system Goal

Submit Goal to the underlying Prolog system.

· /terminate

Terminate the current DES session without halting the host Prolog system

Synonym: /t.

5.17.17 Fuzzy

· /fuzzy_answer_subsumption

Display whether fuzzy answer subsumption is enabled.

· /fuzzy_answer_subsumption Switch

Enable or disable fuzzy answer subsumption (on or off, resp. and enabled by default). Enabling fuzzy answer subsumption prunes answers for the same tuple with less approximation degrees, in general saving computations.

· /fuzzy_expansion

Display current fuzzy expansion: bpl (Bousi~Prolog) or des (DES). For each fuzzy equation P~Q=D, the first one generates as many rules for Q as rules for P, whereas for the second one, generates only one rule for Q.

· /fuzzy_expansion Value

Set the fuzzy expansion as of the given system: bpl (Bousi~Prolog) or des (DES). If changed, the database is cleared. The value bpl is for experimental purposes and may develop unexpected behaviour when retracting either clauses or equations. Can be used as a directive.

· /fuzzy_relation

Display each fuzzy relation and its properties.

· /fuzzy_relation ListOfProperties

Synonym for /fuzzy_relation ~ ListOfProperties.

· /fuzzy_relation Relation ListOfProperties

Set the relation name with its properties given as a list of: reflexive, symmetric and transitive. If a property is not given, its counter-property is assumed (irreflexive for reflexive, asymmetric for symmetric, and intransitive for transitive). Can be used as a directive.

· /fuzzy_rel ListOfProperties

Synonym for /fuzzy_relation ~ ListOfProperties.

· /lambda_cut

Display current lambda cut value, a float between 0.0 and 1.0. It defines a threshold for approximation degrees of answers.

· /lambdacut

Synonym for /lambda_cut.

· /lambda_cut Value

Set the lambda cut value, a float between 0.0 and 1.0. It defines a threshold for approximation degrees of answers. Can be used as a directive.

· /lambdacut Value

Synonym for /lambda_cut Value.

· /list_fuzzy_equations

List fuzzy proximity equations of the form X~Y=D, meaning that the symbol X is similar to the symbol Y with approximation degree D. Equivalent to /list_fuzzy_equations ~.

· /list_fuzzy_equations Relation

List fuzzy equations of the form X Relation Y = D, meaning that the symbol (either a predicate or constant) X is related under Relation to the symbol Y with approximation degree D.

· /list_t_closure

List the t-closure of the similarity relation ~ as fuzzy proximity equations of the form X~Y=D, meaning that the symbol X is similar to the symbol Y with approximation degree D. Equivalent to /list_t_closure ~. Can be used as a directive.

· /list_t_closure Relation

List the t-closure of the relation Relation as fuzzy equations of the form X Relation Y=D, meaning that the symbol X is similar to the symbol Y with approximation degree D. Can be used as a directive.

· /t_closure_comp

Display the way for computing the t-closure of fuzzy relations, which can be either datalog or prolog. While the former uses the deductive engine for computing this t-closure, the latter uses a more-efficient, specific-purpose Floyd–Warshall algorithm

· /t_closure_comp Value

Set the way for computing the t-closure of fuzzy relations, which can be either datalog or prolog. Can be used as a directive.

· /t_closure_entries

Synonym for /t_closure_entries ~.

· /t_closure_entries Relation

Display the number of entries in the t-closure of Relation. The system flag $t_closure_entries$ is updated each time this command is executed

· /t_norm

Synonym for /t_norm ~.

· /t_norm Value

Synonym for /t_norm ~ Value. Can be used as a directive.

· /t_norm Relation

Display the current t-norm for Relation, which can be: goedel, lukasiewicz, product, hamacher, nilpotent, where min is synonymous for goedel, and luka for lukasiewicz. Can be used as a directive.

· /t_norm Relation Value

Set the current t-norm for Relation, which can be: goedel, lukasiewicz, product, hamacher, nilpotent, where min is synonymous for goedel, and luka for lukasiewicz. Can be used as a directive.

· /transitivity

Synonym for /transitivity ~.

· /transitivity Value

Synonym for /transitivity ~ Value. Can be used as a directive.

· /transitivity Relation

· /transitivity Relation Value

· /weak_unification

Display current weak unification algorithm: a1 (Sessa) or a3 (Block-based). The algorithm a3, though a bit slower at run-time, is complete for proximity relations. However, it shows exponential time complexity for compilation.

· /weak_unification Value

Set the weak unification algorithm: a1 (Sessa) or a3 (Block-based). If changed, the database is cleared. The algorithm a3, though a bit slower at run-time, is complete for proximity relations. However, it shows exponential time complexity for compilation. Can be used as a directive.

5.18 Textual API

Rather than providing a Prolog underlying system dependent API, DES provides a textual API (TAPI, Textual Application Programming Interface) for its communication to external applications. It can used via standard input and output streams, as provided by the OS.

Such interface has been guided by the demands of the ACIDE GUI (Graphical User Interface) in order to allow users to interact with the system via a Java application. This way, it is possible to inspect and modify the database schema and table contents, being managed by DES and by external data sources as RDBMS's, spreadsheets, or CSV (Comma-Separated Values) plain files connected by an ODBC connection. This TAPI can be used from any application wrote in any language and running on any platform, provided that it can handle input and output standard streams.

Several existing commands, statements and queries can be processed via this interface. As well, new commands and statements have been added to support the GUI requirements described above. Input syntax is as for DES, whereas answers follow a concrete format for easing their parsing. Any input to this interface must be prepended by the command /tapi, and cannot be spread beyond a single line, as shown next:

Input: /tapi /test_tapi

Output: $success

Notice that after the command /tapi, another command follows: /test_tapi, which is only intended to test whether a successful connection between the external application and DES can be established. If so, the answer $success is sent to the output stream. The usual DES command prompt is not sent, as well as no extra blank lines (even if compact listings are disabled, cf. Section 5.17.11). Any input which is not TAPI enabled after /tapi can also be submitted in the DES command prompt, and follows the usual DES output, instead of the TAPI-oriented way.

TAPI commands can be tested at the system prompt, such as:

DES> /tapi /test_tapi

$success

A typical scenario for accessing DES from an external application is to start a process from this application and connecting adequately input and output streams. If run on Windows, use the console application des.exe for such process; otherwise, use des (both provided in the binary distribution for several operating systems).

5.18.1 Notes about the Interface

· Text in font Courier New are for textual input and output. Italized Courier New stands for input that the TAPI user must provide with a concrete input. For example, description for dropping a table includes: /tapi drop table table_name, where table_name is the placeholder for your concrete table to be dropped.

· Lines starting with % are remarks which are not needed to be included (they are only for explanatory purposes).

· Types returned by a database or predicate handled by DES include:

Where N is an integer greater than 0.

· Types returned by ODBC databases depend on the concrete external DBMS.

· Character strings as returned by DES are enclosed between single quotes. This allows in particular to distinguish these strings from the null value, which can occur in any data type.

· Datalog identifiers in TAPI inputs must be enclosed between single quotes should they contain special characters (as blanks, commas and quotes). If an identifier contains a single quote, this must be written twice as, e.g., 'pete''s' , which represents pete's.

· DDL (Data Definition Language) statements for SQL and Datalog include:

o CREATE TABLE (SQL)

o CREATE VIEW (SQL)

o RENAME (SQL)

o :-strong_constraint (Datalog)

· DQL (Data Query Language) SQL statements include:

o SELECT

o WITH

· Any input to command /tapi is processed as a DES input. However, output is only formatted for those commands and queries as listed in sections 5.18.2 and . So, feeding unsupported inputs to /tapi might produce unexpected results. Users of TAPI are expected to ask for other commands and/or statements needed for their concrete applications. Feedback is welcome.

5.18.1.1 Identifiers

As SQL identifiers can contain special characters which can be missed with other language constructors, they are enclosed between delimiters in such a case. This document contains an abbreviated notation: name and column_name, for table and views in the former, and columns in the second. When an SQL identifier is written as part of a TAPI input, they must be enclosed between the characters L and R (left and right delimiters, respectively). Characters for such delimiters depend on the external DBMS. For instance, MS Access requires [ and ], resp., but standard SQL defines double quotes for both (") (MS Access does not support this).

In order to know what are such characters for the current connection, one can submit the following commands:

/tapi /sql_left_delimiter

/tapi /sql_right_delimiter

Datalog identifiers suffer a similar situation but they are enclosed between single quotes (if needed). For example:

/tapi /listing 't'

5.18.1.2 Kinds of Answers

Any input can return either a successful answer (with a syntax described for each supported command and statement) or an error. There are several kinds of answers:

· Regular:

o Successful answer with no return data:

$success

o Error:
One or more consecutive error blocks of the form:

$error

code

text

...

text

ended by:

$eot

Where code is the error code and text is its textual description, which can consist of several lines. Last line is the text for denoting end of transmission. Error codes are digits starting by either 0 (denoting an exception error), or 1 (denoting a warning), or 2 (denoting an extended informative message).

· Boolean:

Only one line, either one of the following:

$true
$false

If an error occurs, it is output as in the regular answer.

· Defined specifically for a given command or statement.

If an error occurs, it is output as in the regular answer.

5.18.2 TAPI-enabled Commands

This section shows most supported command for TAPI communication. Specific commands used for SQL and Datalog debugging are described in their respective sections.

· Command:

/listing

Answer:

Loaded rules delimited by separator and a final line containing $eot:

rule_1_1

...

rule_1_m

...

rule_n_1

...

rule_n_m

$eot

Remarks:

Note that a single rule may expand to several lines if pretty print is enabled.

All forms of this command are supported (with arguments name, arity, ...)

Example:

/tapi /listing

p(0).

p(X) :-

p(Y),

X=Y+1.

$eot

· Command:

/listing_asserted

Remarks:

As /listing above but only for asserted rules.

All forms of this command are supported (with arguments name, arity, ...)

· Command:

/list_et

Answer:

Extension table contents. Each entry is preceded by the separator $ and follows the relation name and as many lines as tuple arguments (i.e., arity).

$answers

name

value

...

value

...

$calls

name

value

...

value

...

$eot

Remarks:

Note that a single rule may span several lines if pretty print is enabled.

All forms of this command are supported (with arguments name and arity).

Example:

/tapi /list_et

$answers

'a'

$calls

_8902

_8910

_8911

$eot

Compare this with the same command with no TAPI:

DES> /list_et

Answers:

{

p(a),

t(1,3),

t(2,4)

}

Info: 2 tuples in the answer table.

Calls:

{

p(A),

t(A,B)

}

Info: 2 tuples in the call table.

· Command:

/list_sources Name/Arity

Answer:

Rule sources for predicate Name/Arity. There are two possible sources: Consulted from a file, and asserted at the prompt. Each entry of the former form is preceded by a line containing $file, followed by the file name, the start line, and the end line. Each entry of the latter form is preceded by a line containing $asserted, followed by a line with its assertion time.

$asserted

'time'

...

$file

'fileName'

line

...

$eot

Example:

/tapi /list_sources father/2

$asserted

'2025,3,11,13,45,19'

$file

'c:/des/desdevel/examples/family.dl'

$file

'c:/des/desdevel/examples/family.dl'

$file

'c:/des/desdevel/examples/family.dl'

$file

'c:/des/desdevel/examples/family.dl'

$eot

· Command:

/sql_left_delimiter

Answer:

Only one line with a single character corresponding to the SQL left delimiter as defined by the database manager (either DES or the external DBMS via ODBC).

Example assuming an ODBC connection to MS Access:

Input:

/tapi /sql_left_delimiter

Output:

[

· Command:

/sql_right_delimiter

Answer:

Only one line with a single character corresponding to the SQL right delimiter as defined by the database manager (either DES or the external DBMS via ODBC).

Example assuming an ODBC connection to MS Access:

Input:

/tapi /sql_right_delimiter

Output:

]

· Command:

/cd

Answer:

Only one line with the full path DES was started from.

Example:

Input:

/tapi /cd

Output:

c:/des

· Command:

/cd Path

Answer:

Only one line with the full new path.

Example:

Input:

/tapi /cd examples

Output:

c:/des/examples

· Command:

/consult File

/c File

/[File]

Answer:

Information about the loaded program and a final line containing $eot.

Examples:

Input:

/tapi /[family]

Output:

Info: 11 rules consulted.

$eot

Input:

/tapi /c family,fact

Output:

Warning: N > 0 may raise a computing exception if non-ground at run-time.

Warning: N1 is N - 1 may raise a computing exception if non-ground at run-time.

Warning: F is N * F1 may raise a computing exception if non-ground at run-time.

Warning: Next rule is unsafe because of variable(s):

[F,N]

fac(N,F) :-

N > 0,

N1 is N - 1,

fac(N1,F1),

F is N * F1.

Info: 13 rules consulted.

$eot

· Command:

/reconsult Files

/r Files

/[+Files]

Answer:

Information about the loaded program and a final line containing $eot.

Example:

Input:

/tapi /[+family]

Output:

Info: 11 rules consulted.

$eot

· Command:

/test_tapi

Answer:

Regular.

Remarks:

This command is used to test the current connection.

Example:

Input:

/tapi /test_tapi

Output:

$success

/tapi /use_db db

Arguments:

db: Database connection name. Not delimited.

Answer:

Regular.

Remarks:

Example:

Input:

/tapi /use_db test

Output:

$success

· Command:

/open_db db

Arguments:

db: Database connection name. Not delimited.

Answer:

Regular.

Remarks:

This command is used to open an ODBC connection (cf. Section 0).

Example:

Input:

/tapi /open_db test

Output:

$success

/tapi /show_dbs

Answer:

...

$eot

Remarks:

0).

Example:

Input:

/tapi /show_dbs

Output:

$des

test

tablas

$eot

· Command:

/close_db

Answer:

Regular.

Remarks:

This command is used to close the current ODBC connection (cf. Section 0).

Example:

Input:

/close_db

Output:

$success

· Command:

/current_db

Answer:

Two lines: the first one containing the current ODBC connection name and the second one the external DBMS (cf. Section 0).

Remarks:

This command is used to get the current ODBC connection name (cf. Section 0).

Example:

Input, assuming that the ODBC connection test is already opened:

/tapi /current_db

Output:

test

access

· Command:

/relation_exists relation_name

Arguments:

relation_name: Relation (table, view or predicate) name, which must be enclosed between delimiters if needed.

Answer:

Boolean.

Remarks:

This command returns $true if the given relation exists, and $false otherwise.

Example:

Input:

/tapi /relation_exists "v"

Output:

$true

· Command:

ddl_query

Answer:

Regular.

Remarks:

This DDL statement returns $success upon a successful processing.

Example:

Input:

/tapi create table [t]([a] int)

Output:

$success

· Command:

/dependent_relations pattern

Where pattern can be either relation_name or relation_name/arity, where relation_name stands for a relation name and arity for its arity.

Answer:

relation_name

...

relation_name

$eot

Where relation_name stands for relation names.

Remarks:

Display the names of relations that directly depend on the given relation. Relations are returned alphabetically sorted.

Example:

Input, considering that views z1 y z2 reference table t:

/tapi /dependent_relations "t"

Output:

$eot

· Command:

/list_table_schemas

Answer:

table_name(column_name:type,..., column_name:type)

...

table_name(column_name:type,..., column_name:type)

$eot

Where table_name stands for table names, column_name is a column name, type is the column type, and $eot is the end of the transmission.

Remarks:

Return table schemas.

Tables are returned alphabetically sorted.

Example:

Input:

/tapi /list_table_schemas

Output:

t(a:int)

$eot

· Command:

/list_view_schemas

Answer:

view(column_name:type,..., column_name:type)

...

view(column_name:type,..., column_name:type)

$eot

Where view_name stands for view names, column_name is a column name, type is the column type, and $eot is the end of the transmission.

Remarks:

Return view schemas.

Views are returned alphabetically sorted.

Example:

Input:

/tapi /list_view_schemas

Output:

v(a:int,b:varchar(20))

$eot

· Command:

/list_table_constraints table_name

Arguments:

table_name: Table name (enclosed between SQL delimiters, if needed).

Answer:

...

$eot

Where $ is a delimiter for different kinds of integrity constraints, NN is a single line with the names of columns with existence constraint, PK is a single line with the primary key constraint, CK are candidate keys, FK are foreign keys, FD are functional dependencies, IC are user-defined integrity constraints, and $eot is the end of transmission.

Remarks:

List table constraints.

If there are no constraints of a given type, no line is written.

Example:

Input:

/tapi /list_table_constraints "s"

Output (no existence constraint, primary key {b}, no candidate key, foreign key {s.[a]} → {t.[a]}, functional dependency a → b, and user-defined integrity constraint :- t(X),s(X,X).):

s.[a] -> t.[a]

[a] -> [b]

:- t(X),s(X,X).

$eot

· Command:

/relation_schema relation_name

Arguments:

relation_name: Relation name (either a table or view), which must be enclosed between SQL delimiters if needed.

Answer:

relation_kind

relation_name

column_name

type

column_name

type

...

column_name

type

$eot

Remarks:

Return relation schema of relation_name. First line in the answer is the kind of relation (either $table for a table or $view for a view), followed by its name in the second line. Next and successive pair of lines contain the column name and column type.

Example:

Input:

/tapi /relation_schema "t"

Output:

$table

int

$eot

· Command:

/drop_ic constraint

Arguments:

constraint: Constraint following Datalog syntax (cf. Section 4.1.18.8).

Answer:

Regular.

Example:

Input:

/tapi /drop_ic :-pk('s',['b'])

Output:

$success

· Command:

/dbschema view_name

Arguments:

view_name: View name as an SQL identifier, which needs to be enclosed between SQL delimiters if needed.

Answer:

relation_kind

relation_name

column_name

type

...

column_name

type

SQL

...

SQL

Datalog

...

Datalog

$eot

Remarks:

First line in the answer is the kind of relation ($view), followed by its name in the second line. Next and successive pair of lines contain the column name and its type. Next lines contain the SQL definition of the view, starting with a line containing the delimiter $. Next lines contain the Datalog definition of the view, starting with a line containing the delimiter $. Finally, end of transmission is the last line.

Both Datalog and SQL outputs are displayed depending on whether pretty print is disabled or not (cf. Section ), i.e., each statement or rule can be in a single line or multiple lines.

Example:

Input:

/tapi /dbschema "v"

Output:

$view

int

varchar(20)

SELECT ALL *

FROM (t

NATURAL INNER JOIN

s);

$eot

· Command:

/is_empty relation_name

Arguments:

relation_name: Relation name (either a table or a view), which must be enclosed between SQL delimiters if needed.

Answer:

Boolean.

Remarks:

Return $true is relation relation_name is empty (i.e., it contains no tuples in its meaning) and $false otherwise.

Example:

Input:

/tapi /is_empty "t"

Output:

$false

· Command:

/pdg optional_argument

Arguments:

optional_argument: An optional argument, either a predicate name or name/arity pattern.

Answer:

node

...

kind

node

...

$eot

Remarks:

Return nodes in the current PDG, one per line, then arcs. An arc is output as three consecutive lines: the first one (kind) is the type of the arc (+ or -), and the second and third are the ending and starting nodes, resp.

Example:

Input:

/tapi /pdg

Output:

a/0

b/0

c/0

d/0

b/0

c/0

b/0

d/0

c/0

b/0

a/0

b/0

$eot

· Command:

/mparse

Arguments:

No argument.

Answer:

$error

code

text

...

text

...

$error

code

text

...

text

$eot

Remarks:

After issuing this command, the system reads the next lines up to the one containing $eot (or end of stream). These lines are parsed (only SQL DQL and DML queries supported up to now) and not executed. Return either a syntax error, one or more semantic errors or, if there are no errors, return $eot. A syntax error with location information separate it with a line containing $ (not all errors return this location information). A syntax error can be followed by informative messages (error code 2).

Examples:

Input:

/tapi /mparse

select s.a

from t,s

$eot

Output:

$error

[Sem] Columns of relation "t" are not used.

$error

[Sem] Missing join condition for [t,s].

$eot

Input:

/tapi /mparse

select s.a

from t+s

$eot

Output:

$error

(SQL) Expected comma or (SQL) Expected end of SELECT statement near:

select s.a

from t

$eot

Input:

/tapi /mparse

select t.b,s.c

from t join s on t.a=s.a

$eot

Output:

$eot

Input:

/tapi /mparse

select *

from employee

$eot

Output:

$error

Unknown table or view 'employee'.

$error

Possible relation (respect case): [employees]

$eot

· Command:

/parse sql_dql_query

Arguments:

sql_dql_query: An SQL DQL query to be only parsed, not executed.

Answer:

$error

code

text

...

text

...

$error

code

text

...

text

$eot

Remarks:

Return either a syntax error, one or more semantic errors or, if there are no errors, return $eot. See also /mparse

Example:

Input:

/tapi select t.a from t,s

Output:

$error

[Sem] Columns of relation "s" are not used.

$error

[Sem] Missing join condition for [t,s].

$eot

· Command:

/save_state [[force] Filename]

Arguments:

Filename: The file name for storing the current state (it can include a relative or absolute path. Double quotes can be used to surround paths with blanks).

Answer:

Regular.

Remarks:

The option force can be used only when a file name is provided. See also /restore_state

Examples:

Input:

/tapi /save_state s1.sds

Output:

$success

Input:

/tapi /save_state s2.sds

Output:

$error

error(permission_error(open,source_sink,c:/s2.sds),permission_error(open(c:/s2.sds,write,_5681),open,file,c:/s2.sds,not writeable))

$eot

· Command:

/restore_state [Filename]

Arguments:

Filename: The file name for restoring a previous saved state (it can include a relative or absolute path. Double quotes can be used to surround paths with blanks).

Answer:

Regular.

Remarks:

5.18.3 TAPI-enabled Queries

This section shows each supported query for TAPI communication.

· Query:

sql_ddl_query

Where sql_ddl_query can be any SQL DDL query (cf. Section 4.2.4).

Answer:

Regular.

Examples:

Input:

/tapi create table t(a int)

Output:

$success

Input:

/tapi rename table t to q

Output:

$success

· Query:

sql_dml_query

Where sql_dml_query can be any SQL DML query (cf. Section 4.2.5).

Answer:

If successful, one single line with the number of affected tuples.

Examples:

Input:

/tapi insert into [t] values(3)

Output:

Input:

/tapi insert into [t] values('3')

Output:

$error

Type mismatch [number(integer)] (table declaration)

$eot

· Query:

sql_dql_query

Where sql_dql_query can be any SQL DQL query (cf. Section 4.2.6).

Answer:

relation_name

column_name

type

...

column_name

type

value

...

value

...

value

...

value

$eot

Where relation_name is the name of the answer relation, column_name is a column name, type is the column type, value is the column value, $ is the record delimiter and $eot is the end of the transmission.

Remarks:

This DQL statement returns in the first line the name of the answer relation, the first column name and its type in the next two lines, and so for all of its columns. Then, each or the tuples in the relation preceded by the record delimiter ($). Last line is the end of transmission.

Examples:

Input, considering that table s contains tuples {(1,'abc'), (null,'def'), (null,null)}:

/tapi select * from [s]

Output:

answer

s.a

int

s.b

varchar(20)

'abc'

null

'def'

null

$eot

Input, considering an empty table s:

/tapi select * from [s]

Output:

answer

s.a

int

s.b

varchar(20)

$eot

5.18.4 TAPI-enabled Assertions

This section shows each supported assertion for TAPI communication.

· Predefined constraints (type, primary key, existence, primary key, candidate key, foreign key, functional dependency):

predefined_constraint

Answer:

Regular.

Remarks:

Only one constraint can be issued. Sequences of constraints (separated by colons) are not supported.

Examples:

Input:

/tapi :-pk(t,[a])

Output:

$success

Input:

/tapi :-pk(t,[b])

Output:

$error

Unknown column 'b'.

$eot

5.19 Sandboxing: Enabling Host Safety

Some applications (whether built with TAPI access or otherwise) require isolating the host system from OS accesses which may corrupt it. Typically, this scenario raises in web applications, where a limited set of features from DES are required. In particular, accesses to the host file system should not be permitted in this cases. To this end, the command /host_safe on (or its synonymous /sandboxed on) allows the system to be tuned for this security shield to prevent outer attacks, hide host information, protect the file system, and so on.

Host safety is ensured by disabling sensible commands. On the one hand, there are several command categories for which all their commands are disabled. On the other hand, there are some other commands that have been disabled even when belonging to assumed-safe categories, as follows:

o Unsafe categories:

§ Operating System

§ Logging

§ Miscellanea

§ Implementor

o Unsafe commands:

§ /autosave

§ /open_db

§ /restore_ddb

§ /restore_state

§ /save_ddb

§ /save_state

§ /set_flag

§ /use_ddb

5.20 ISO Escape Character Syntax

Special characters in constants and user identifiers can be specified by prepending a backslash to an escape-sequence. This feature depends on its support by the underlying Prolog system, so that the reader is referenced to read the corresponding entry in the manual of such system.

Currently, escape-sequences can only be specified in Datalog files to be either consulted or reconsulted, but neither at the command prompt nor in files to be processed.

Common escape-sequences are:

· \a
Alarm (ASCII character code 7)

· \b
Backspace (ASCII character code 8)

· \d
Delete (ASCII character code 127)

· \e
Escape (ASCII character code 27)

· \f
Form feed (ASCII character code 12)

· \n
Line feed/Newline (ASCII character code 10)

· \r
Carriage return (ASCII character code 13). Go to the start of the line, without feeding a new line

· \t
Horizontal tab (ASCII character code 9)

· \v
Vertical tab (ASCII character code 11)

· \xhex-digit...\
A character code represented by the hexadecimal digits.

5.21 Database Instance Generator

Sometimes, it is convenient to have some sample databases for testing or benchmarking. Here, we provide a database instances generator tool that is able to randomly generate databases given a series of parameters. The following command generates such database instances:

/generate_db NbrTables TableSize NbrViews MaxDepth MaxChildren FileName

These parameters specify the number of tables (NbrTables) and its rows (TableSize), the maximum number of views (NbrViews), the height of the computation tree (i.e., the maximum number of view descendants in a rooted genealogic line) (MaxDepth), the maximum number of children for views (MaxChildren), and the output filename (FileName). The output file is an SQL script which can be processed to build the database, where the SQL dialect is tailored to the current open database. This database is required to support INTERSECT and EXCEPT clauses (incidentally, MySQL and Access do not). Upon successful command execution, the database instance is created in the current database (either the default local database $des or whatever external other which has been opened via ODBC and made the current one). Should any error exists, the system flag error is automatically set to 1 (its default value is 0).

Tables are named t1, t2, ... and their column names are a, b, ... and types are the same for all the columns as specified in the flag gen_column_type. The first column is a primary key. Tuples in each table are of the form {(1,N,R¹₁,R¹₂), (2,N-1,R²₁,R²₂), ... }, where the first and the second value has been chosen arbitrarily as an increasing and a decreasing progression respectively, Rⁱ_j represents random integers, and N is the number of rows as specified in the parameter TableSize.

With respect to views, first, a computation tree structure committing to the applicable parameters is randomly generated. Then, an SQL query for each node in the tree is built where each child of the node is made to occur in a FROM clause of the query. The query is randomly selected to be a basic query or a set query. The WHERE condition firstly correlates each involved relation and then randomly applies a condition. Each view receives the name vi where i is an increasing integer from 1 on (v1 is always the root name and numbers are assigned in preorder in the computation tree). Views have column names a, b, ... as the tables. Each generated view is tested to deliver more than one tuple if possible by randomly enlarging the result set if necessary (i.e., by relaxing the WHERE condition or changing a more restricting set operator (INTERSECT, EXCEPT) for a less restricting one (UNION)). However, it still can be the case that some of the views return no tuples at all.

The next picture illustrates the dependency graph for a database which has been generated with the following commands:

DES> /set_flag random_seed 1234567890

DES> /generate_db 3 5 10 3 3 p.sql

The shape of the database depends on the randomizer, but the same result can be obtained with the same random seed. To this end, you can use the flag random_seed as used above to reproduce the same results as depicted.

There are other parameters that can be set by setting system flags as follows:

· gen_number_of_table_columns(Number). % Number of columns in both tables and views. Default: 4. Minimum: 2

· gen_column_type(InternalType). % Type of the columns. Default: number(integer). Possible other values: number(float), string(varchar), string(varchar(N)), string(char(N)), where N is the number of characters

· gen_children_density(Percent). % Probability (0-100) of having MaxChildren in each node. Default: 70

Any of these flags can be modified with the command: /set_flag FlagName Value. For example, the following will set the number of columns to 2:

/set_flag gen_number_of_table_columns 2

5.22 Notes about the Implementation of DES

DES is implemented with the original ideas found in [Diet87, TS86, FD92], that deal with termination issues of Prolog programs. These ideas have been already used in the deductive database community. Our implementation uses extension tables for achieving a top–down driven bottom–up approach. In its current form, it can be seen as an extension of the work in [Diet87, FD92] in the sense that, in addition, we deal with negation, undefined (although incomplete) information, nulls, aggregates, Top-N queries, hypothetical reasoning, restricted predicates and more. Also, the implementation follows a different approach: Instead of compiling rules, they are interpreted.

DES does not pretend to be an efficient system but a system capable of showing the nice aspects of the more powerful form of logic we can find in Datalog systems w.r.t. relational database systems.

5.22.1 Tabling[20]

DES uses an extension table which stores answers to goals previously computed, as well as their calls. For the ease of the introduction, we assume an answer table and a call table to store answers and calls, respectively. Answers may be positive or negative, that is, if a call to a positive goal p succeeds, then the fact p is added as an answer to the answer table; if a negated goal not p succeeds, then the fact not p is added. Calls are also added to the call table whenever they are solved. This allows us to detect whether a call has been previously solved and we can use the results in the extension table (if any).

The algorithm which implements this idea is schematized next:

% Already called. Call table with an entry for the current call

memo(G) :-

build(G,Q), % Build in Q the same call with fresh variables

called(Q), % Look for a unifiable call in CT for the current call

subsumes(Q,G), % Test whether CT call subsumes the current call

!, %

et_lookup(G). % If so, use the results in answer table (ET)

% New call. Call table without an entry for the current call

memo(G) :-

assertz(called(G)), % Assert the current call to CT

( (et_lookup(G)) % First call returns all previous answers in ET

;

(solve_goal(G), % Solve the current call using applicable rules

build(G,Q), % Build in Q the same call with fresh variables

no_subsumed_by_et(Q), % Test whether there is no entry in ET for Q

et_assert(G), % If so, assert the current result in ET

et_changed)). % Flag the change

This algorithm, first, tests whether there is a previous call that subsumes[21] the current call. There are two possibilities: 1) there is such a previous call: then, use the result in the answer table, if any. It is possible that there is no such a result (for instance, when computing the goal p in the program p :- p) and we cannot derive any information, 2) otherwise, process the new call knowing that there is no call or answer to this call in the extension table. So, firstly store the current call and then, solve the goal with the program rules (recursively applying this algorithm). Once the goal has been solved (if succeeded), store the computed answer if there is no any previous answer subsuming the current one (note that, through recursion, we can deliver new answers for the same call). This so–called memoization process is implemented with the predicate memo/1 in the file des.pl of the distribution, and will also be referred to as a memo function in the rest of this manual.

Negative facts are produced when a negative goal is proven by means of negation as failure (closed world assumption). In this situation, a goal as not p which succeeds produces the fact not p which is added to the answer table, just the same as proving a positive goal.

The command /list_et shows the current state of the extension table, both for answers and calls already obtained by solving one or more queries (incidentally, recall that you can focus on the contents of the extension table for a given predicate, cf. Section 5.17.5). This command is useful for the user when asking for the meaning of relations, and for the developer for examining the last calls being performed. Before executing any query, the extension table is empty; after executing a query, at least the call is not empty. Also, the extension table is empty after the execution of a temporary view.[22] The extension table contains the calls made during the last fixpoint iteration (see next section for details); the calls are cleared before each iteration whereas the answers are kept. The command /clear_et clears the extension table contents, both for calls and answers.

5.22.2 Fixpoint Computation

The tabling mechanism is insufficient in itself for computing all of the possible answers to a query. The rationale behind this comes from the fact that the computed information is not complete when solving a given goal, because it can use incomplete information from the goals in its defining rules (these goals can be mutually recursive). Therefore, we have to ensure that we produce all the possible information by finding a fixpoint of the memo function. The algorithm implementing this is depicted next:

solve_star(Q,St) :-

repeat,

(remove_calls, % Clear CT

et_not_changed, % Flag ET as not changed

solve(Q,St), % Solve the call to Q using memoization at stratum St

fail % Request all alternatives

;

no_change, % If no more alternatives, start a new iteration

!, fail). % Otherwise, fail and exit

First, the call table is emptied in order to allow the system to try to obtain new answers for a given call, preserving the previous computed answers. Then, the memo function is applied, possibly providing new answers. If the answer table remains the same as before after this last memo function application, we are done. Otherwise, the memo function is reapplied as many times as needed until we find a stable answer table (with no changes in the answer table). The answer table contains the meaning of the query (plus perhaps other meanings for the relations used in the computation of the given query).

The fixpoint is found in finite time because the memo function is monotonic in the sense that we only add new entries each time it is called while keeping the old ones. Repeatedly applying the memo function to the answer table delivers a finite answer table since the number of new facts that can be derived from a Datalog program is finite (recall that there are no compound terms such as s^k(z)). On the one hand, the number of positive facts which can be inferred are finite because there is a finite number of ground facts which can be used in a given proof, and proofs have finite depth provided that tabling prevents recomputations of older nodes in the proof tree. On the other hand, the number of negative facts which can be inferred is also finite because they are proved using negation as failure. (Failures are always finite because they are proved trying to get a success.) Finally, there are facts that cannot be proved to be true or false because of recursion. These cases are detected by the tabling mechanism which prevent infinite recursion such as in p :- p.

It is also possible that both a positive and a negative fact have been inferred for a given call. Then, an undefined fact replaces the contradictory information. The implementation simply removes the contradictory facts and informs about the undefinedness. As already indicated (see Section 6.8.1), the algorithm for determining undefinedness is incomplete.

5.22.3 Dependency Graphs and Stratification: Negation, Outer Joins, and Aggregates

Each time a program is consulted or modified (i.e., via submitting a temporary view or changing the database), a predicate dependency graph is built [ZCF+97]. This graph shows the dependencies, through positive and negative atoms, among predicates in the program. Also, a negative dependency is added for each outer join goal and aggregate goal.

This dependency graph is useful for finding a stratification for the program [ZCF+97]. A stratification collects predicates into numbered strata (1..N). A basic bottom-up computation would solve all of the predicates in stratum 1, then 2, and so on, until the meaning of the whole program is found. With our approach, we only resort to compute by stratum when a negative dependency occurs in the predicate dependency graph restricted to the query; nevertheless, each predicate that is actually needed is solved by means of the extension table mechanism described in the previous section. As a consequence, many computations are avoided w.r.t. a naïve bottom-up implementation. See also next section on optimizations.

Outer join and aggregate goals are also collected into strata as if they were negative atoms in order to have their answer set completely defined and therefore ensure termination of the computation algorithm in presence of null values (for outer joins) and incomplete set of values (for aggregates).

5.22.4 Optimizations

Though, as already said, DES is not targeted at performance, it uses the (slower in most systems) Prolog dynamic database, it does not allow user-defined indexes, implemented algorithms are not the best ones, several tasks are redone sparingly (although they can be actually saved), and so on. Once that said, there has been still a minor room for optimizing performance so that projects of the size DES is intended for can be successfully achieved. Below, we list some of such optimizations that can be enabled or disabled at user request (this feature is more oriented to the system implementors for knowing the impact on performance of such optimizations). Each optimization is listed in a subsection along with the command (between brackets) that is used for disabling or enabling it (with the switch off and on, respectively).

5.22.4.1 Complete Computations (/optimize_cc)

Each call during the computation of a stratum (stratum saturation) is remembered in addition to its outcome (in the answer table). Even when the calls are removed in each fixpoint iteration (recall Section 5.22.2), most general ones do persist as a collateral data structure to be used for saving computations should any of them is called again during either computing a higher stratum or a subsequent query solving. 'cc' stands for completed computation, so that if a call is marked as a completed computation, it is not even tried if called again. This means the following two points: 1) During the computation of the memo function, calls already computed are not tried to be solved again, and only the entries in the memo table are returned. 2) Moreover, computing the memo function is completely avoided if a subsuming already-computed call can be found. In the first case, that saves solving goals in computing the memo function. In the second case, that completely saves fixpoint computation.

The following system session shows how this optimization works. First, we enable statistics collection, enable verbose output to automatically display statistics results, disable all the optimizations, assert the fact p(1) and submit the query p(X):

DES> /statistics on

DES> /verbose on

DES> /optimize_cc off

Info: Complete computations optimization is off.

DES> /optimize_ep off

Info: Extensional predicate optimization is off.

DES> /optimize_nrp off

Info: Non-recursive predicates optimization is off.

DES> /optimize_st off

Info: Stratum optimization is already disabled.

DES> /assert p(1)

Info: Rule asserted.

DES> p(X)

Info: Parsing query...

Info: DL query successfully parsed.

Info: Solving query p(X)...

Info: Displaying query answer...

Info: Sorting answer...

{

p(1)

}

Info: 1 tuple computed.

Info: Fixpoint iterations: 2

Info: EDB retrievals : 2

Info: IDB retrievals : 0

Info: ET retrievals : 4

Info: ET look-ups : 6

Info: CT look-ups : 2

Info: CF look-ups : 0

Info: ET entries : 1

Info: CT entries : 1

As the statistics show, 2 fixpoint iterations have been needed to deduce the output. In the first one, the rule p(1) is read for the first time. Then, in the second iteration, it is read again and as the answer table has not changed, then this means that the fixpoint has been reached. The information display EDB retrievals shows those two fact reads (where EDB stands for Extensional Database).

If the same query is submitted again:

DES> p(X)

Info: Parsing query...

Info: DL query successfully parsed.

Info: Solving query p(X)...

Info: Displaying query answer...

Info: Sorting answer...

{

p(1)

}

Info: 1 tuple computed.

Info: Fixpoint iterations: 1

Info: EDB retrievals : 1

Info: IDB retrievals : 0

Info: ET retrievals : 4

Info: ET look-ups : 4

Info: CT look-ups : 1

Info: CF look-ups : 0

Info: ET entries : 1

Info: CT entries : 1

then only 1 iteration is needed to reach the fixpoint, and only one EDB retrieval is done, as the answer table contained an entry for p(1) already for the same call. This illustrates point 1 above.

Now let's enable the optimization, previously deleting the contents of the answer table so that we are in the same starting situation again:

DES> /clear_et

Info: Extension table cleared.

DES> /optimize_cc on

Info: Complete flag optimization is on.

DES> p(X)

Info: Parsing query...

Info: DL query successfully parsed.

Info: Solving query p(X)...

Info: Displaying query answer...

Info: Sorting answer...

{

p(1)

}

Info: 1 tuple computed.

Info: Fixpoint iterations: 2

Info: EDB retrievals : 2

Info: IDB retrievals : 0

Info: ET retrievals : 4

Info: ET look-ups : 6

Info: CT look-ups : 2

Info: CF look-ups : 1

Info: ET entries : 1

Info: CT entries : 1

As before, 2 fixpoint iterations and 2 EDB retrievals are needed. But, if we submit again the query:

DES> p(X)

Info: Parsing query...

Info: DL query successfully parsed.

Info: Solving query p(X)...

Info: Displaying query answer...

Info: Sorting answer...

{

p(1)

}

Info: 1 tuple computed.

Info: Fixpoint iterations: 0

Info: EDB retrievals : 0

Info: IDB retrievals : 0

Info: ET retrievals : 2

Info: ET look-ups : 2

Info: CT look-ups : 0

Info: CF look-ups : 1

Info: ET entries : 1

Info: CT entries : 1

then, as the computation for the goal p(X) is complete, then no fixpoint iterations are needed. For the same reason, no EDB retrievals are needed, as just the contents of the memo table are returned. This illustrates point 2 above.

5.22.4.2 Extensional Predicates (/optimize_ep)

Extensional predicates are not needed to be iteratively computed. So, no fixpoint computation is needed for them. They are known from the predicate dependency graph simply because they occur in the graph without incoming arcs. For them, a linear fetching is enough to derive their meanings. 'ep' stands for 'extensional predicates'.

In the following system session we illustrate this with the fact p(1):

DES> /clear_et

Info: Extension table cleared.

DES> /optimize_ep on

Info: Extensional predicate optimization is on.

DES> p(X)

Info: Parsing query...

Info: DL query successfully parsed.

Info: Solving query p(X)...

Info: Displaying query answer...

Info: Sorting answer...

{

p(1)

}

Info: 1 tuple computed.

Info: Fixpoint iterations: 1

Info: EDB retrievals : 1

Info: IDB retrievals : 0

Info: ET retrievals : 2

Info: ET look-ups : 3

Info: CT look-ups : 0

Info: CF look-ups : 1

Info: ET entries : 1

Info: CT entries : 1

where there are 1 fixpoint iteration and only one EDB retrieval. This optimization is independent from the completed computations optimization.

Successive calls will render the same behaviour as in the previous section, unless the complete computations optimization is enabled:

DES> p(X)

Info: Parsing query...

Info: DL query successfully parsed.

Info: Solving query p(X)...

Info: Displaying query answer...

Info: Sorting answer...

{

p(1)

}

Info: 1 tuple computed.

Info: Fixpoint iterations: 0

Info: EDB retrievals : 0

Info: IDB retrievals : 0

Info: ET retrievals : 2

Info: ET look-ups : 2

Info: CT look-ups : 0

Info: CF look-ups : 1

Info: ET entries : 1

Info: CT entries : 1

where no fixpoint iterations and no EDB retrievals are needed.

Extensional Database (/optimize_edb)

p(2) to the meaning of p with the rule p(X):-p(Y),Y<2,X=Y+1.

DES> /optimize_cc off

DES>

DES> /optimize_ep off

DES>

DES> /optimize_edb off

DES>

DES> /optimize_nrp off

DES>

DES> /optimize_st off

DES>

DES> /optimize_sn off

DES>

DES> /assert p(1)

Info: Computing strata...

Info: Rule asserted.

DES>

DES> /assert p(X):-p(Y),Y<2,X=Y+1

Info: Computing strata...

Info: Rule asserted.

DES>

DES> p(X)

Info: Parsing query...

Info: Query successfully parsed.

Info: Solving query p(X)...

Info: Displaying query answer...

Info: Sorting answer...

{

p(1),

p(2)

}

Info: 2 tuples computed.

Info: Fixpoint iterations: 2

Info: EDB retrievals : 2

Info: IDB retrievals : 2

Info: ET retrievals : 11

Info: ET look-ups : 10

Info: CT look-ups : 4

Info: CF look-ups : 0

p(1) is retrieved once because of its single defining EDB rule (fact). This result is used next for solving the IDB rule. In the next iteration, again an EDB retrieval is needed which is again used for the IDB rule. As there is no more tuples added to the answer table, then the computation stops (cf. Section 5.22.1).

DES> /optimize_edb on

DES>

DES> /clear_et

Info: Extension table cleared.

DES>

DES> p(X)

Info: Parsing query...

Info: Query successfully parsed.

Info: Solving query p(X)...

Info: Displaying query answer...

Info: Sorting answer...

{

p(1),

p(2)

}

Info: 2 tuples computed.

Info: Fixpoint iterations: 2

Info: EDB retrievals : 1

Info: IDB retrievals : 2

Info: ET retrievals : 10

Info: ET look-ups : 9

Info: CT look-ups : 4

Info: CF look-ups : 0

Although successive calls to p(X) will need the same fixpoint iterations and EDB retrieval, if the complete computations optimization is enabled, no fixpoint iterations nor EDB retrievals would be needed, as explained at the end of the previous section.

5.22.4.3 Non-recursive Predicates (/optimize_nrp)

Each non-recursive predicate can be extracted out from the fixpoint iterative cycle because its meaning can be computed by requesting all its solutions at once. Further fixpoint iterations won't develop new tuples, so this would be useless. In fact, this is true for each non-recursive rule of any predicate (being recursive or not). Though, this optimization is not available yet.

The following example shows the predicate p as composed of a fact and a rule. First, it is computed with all optimizations disabled:

DES> /assert p(1)

DES> /assert p(X):-X=1+1

DES> p(X)

Info: Parsing query...

Info: DL query successfully parsed.

Info: Solving query p(X)...

Info: Displaying query answer...

Info: Sorting answer...

{

p(1),

p(2)

}

Info: 2 tuples computed.

Info: Fixpoint iterations: 2

Info: EDB retrievals : 2

Info: IDB retrievals : 2

Info: ET retrievals : 8

Info: ET look-ups : 8

Info: CT look-ups : 2

Info: CF look-ups : 0

Info: ET entries : 2

Info: CT entries : 1

Then, enabling non-recursive predicates optimization and submitting the same query:

DES> /optimize_nrp on

Info: Non-recursive predicates optimization is on.

DES> /clear_et

DES> p(X)

{

p(1),

p(2)

}

Info: 2 tuples computed.

Info: Fixpoint iterations: 1

Info: EDB retrievals : 1

Info: IDB retrievals : 1

Info: ET retrievals : 4

Info: ET look-ups : 4

Info: CT look-ups : 0

Info: CF look-ups : 0

Info: ET entries : 2

Info: CT entries : 0

In only one fixpoint iteration the meaning is computed for which 1 EDB and 1 IDB retrievals are needed (the fact and rule, respectively).

5.22.4.4 Stratum (/optimize_st)

Predicates which contain no recursive rules but calls to recursive predicates do not need to be computed in the same iterative fixpoint computation. If this optimization is enabled, such predicates are isolated from recursive ones in another stratum, so that iterative cycles are saved for them. This situation occurs, for instance, when compiling SQL queries to Datalog, as the intermediate relation answer is introduced. Next system session illustrates this:

DES> :-type(p(a:int))

DES> /display_answer off

DES> /display_nbr_of_tuples off

DES> /timing on

DES> /running_info off

DES> /assert p(1)

DES> /assert p(X):-p(Y),X=Y+1,Y<500

DES> select * from p

Info: Solving query answer(A)...

answer(p.a:int) ->

Info: Fixpoint iterations: 500

Info: EDB retrievals : 500

Info: IDB retrievals : 1000

Info: ET retrievals : 627246

Info: ET look-ups : 252999

Info: CT look-ups : 1500

Info: CF look-ups : 0

Info: ET entries : 1000

Info: CT entries : 2

Info: Total elapsed time: 02.755 s.

DES> /optimize_st on

DES> select * from p

Info: Solving query answer(A)...

Info: Computing by stratum of [p(A)].

answer(p.a:int) ->

Info: Fixpoint iterations: 2

Info: EDB retrievals : 502

Info: IDB retrievals : 504

Info: ET retrievals : 381248

Info: ET look-ups : 128757

Info: CT look-ups : 1006

Info: CF look-ups : 0

Info: ET entries : 1000

Info: CT entries : 2

Info: Total elapsed time: 01.888 s.

With this optimization enabled, less extension table lookups are needed and the result is therefore computed faster. However, note that non-termination might raise when breaking strata if using the metapredicate top: This is because top requires the amount of tuples as indicated from its goal argument. If this goal is isolated in a higher stratum, no top constraint is propagated to the lower stratum, as in:

DES> :- type(p(a:int))

DES> /assert p(1)

DES> /assert p(X):-p(Y),X=Y+1

DES> select top 2 * from p

answer(p.a:int) ->

{

answer(1),

answer(2)

}

Info: 2 tuples computed.

DES> /optimize_st on

DES> select top 2 * from p

... non-terminating query

That is, as the SQL query had been compiled to:

answer(A) :-

top(10,p(A)).

then, the predicate answer/1 is located at stratum 2 and the predicate p/1 at stratum 1:

DES> /strata

[(p/1,1),(answer/1,2)]

and DES tries to solve first the goal p(X) (not top(10,p(A)))[23] which proves to be non-terminating as there is no top constraint on p. Further releases might cope with this issue.

5.22.5 Indexing (/indexing)

There is no provision for user indexes up to now. However, indexing on memo tables can be enabled or disabled at user request. There are three tables which are indexed: the answer table, the call table, and the complete computation table. The first one stores the computed results for the calls during query solving and it is used in the tabling scheme for avoiding to recompute already known goals. The second one stores the calls so that it is possible to know whether a subsuming call has been done already. The third table stores for each call whether its computation has been either completed or not.

The next system session shows a speed-up of almost 3× when enabling indexing.

DES> /timing on

DES> /indexing off

DES> /pretty_print off

DES> /display_answer off

DES> p(X):-X=1;p(Y),Y<500,X=Y+1

Info: Processing:

p(X)

in the program context of the exploded query:

p(X) :- X=1.

p(X) :- p(Y),Y<500,X=Y+1.

Info: 500 tuples computed.

Info: Total elapsed time: 03.540 s.

DES> /indexing on

DES> p(X):-X=1;p(Y),Y<500,X=Y+1

Info: Processing:

p(X)

in the program context of the exploded query:

p(X) :- X=1.

p(X) :- p(Y),Y<500,X=Y+1.

Info: 500 tuples computed.

Info: Total elapsed time: 01.279 s.

5.22.6 Porting to Unsupported Systems

DES is implemented in several Prolog files:

· des.pl contains the common predicates for all of the platforms (both Prolog interpreters and operating systems) following the Prolog ISO standard.

· des_ini.pl contains initialization directives for loading files at system start-up.

· des_dcg.pl contains the definition of DCG expansion (which varies from one Prolog system to another).

· des_sql.pl contains the SQL processor.

· des_ra.pl contains the RA processor.

· des_drc.pl contains the DRC processor.

· des_trc.pl contains the TRC processor.

· des_commands.pl defines system commands.

· des_help.pl includes the help system.

· des_common.pl includes predicates used by several files.

· des_types.pl contains the type checking, inference and casting systems.

· des_atts.pl for allowing attributed variables in the context of types.

· des_modes.pl implements the mode information system for Datalog predicates.

· des_persistence.pl implements persistence of Datalog predicates on external SQL databases via ODBC connections.

· des_fuzzy.pl implements a fuzzy system.

· des_trace.pl implements a naïve declarative tracer.

· des_dl_debug.pl contains the Datalog declarative debugger.

· des_sql_debug.pl contains the SQL declarative debugger.

· des_sql_semantic.pl contains the SQL semantic checker.

· debug/des_pchr.pl is a CHR program for debugging Datalog predicates and used by des_dl_debug.pl.

· des_tc.pl contains the SQL test case generator code.

· des_dbigen.pl contains the SQL database instance random generator.

· des_glue.pl contains Prolog system specific code, which vary from a system to another.

Adapting the predicates found in the last file should not pose problems, provided that the Prolog interpreter and operating system feature some required characteristics. In particular, finite domain constraints with positive and negative integers is a must for supporting several features of DES, such as type inference and test case generation. Also, attributed variables are required. Finally, file-system-related built-ins. If you plan to port DES to other systems not described here, you will have to modify the system specific Prolog file to suit your system. If so, and if you want to figure as one of the system contributors, please send an e–mail message with the code and reference information to: fernan@sip.ucm.es, accepting that your contribution will be under the GNU Lesser General Public License. (See the appendix for details.)

6. Examples

The DES distribution contains the directory examples, with many program examples and scripts. Next, a few of them are explained. Unless explicitly noted, all queries have been solved after the commands /verbose off and /pretty_print off have been executed.

6.1 Relational Operations (files relop.{dl,sql,ra,drc,trc})

The program relop.dl is intended to show how to mimic with Datalog rules the basic relational operations that can be found in the file relop.sql. It contains three relations (a, b, and c), which are used as arguments of relational operations. In order to have loaded this program and be able to submit queries you can consult it with /c relop. In the remarks below, relational operator symbols are represented with ASCII characters, as =|x| to denote the left outer join , the letter x to simply denote the Cartesian product, and the letter U for the set union.

% (Extended) Relational Algebra Operations

% pi(X)(c(X,Y)) : Projection of the first argument of c

projection(X) :- c(X,Y).

% sigma(X=a2)(a) : Selecting tuples from a such that its first argument is a2

selection(X) :- a(X), X=a2.

% a x b : Cartesian product of relations a and b

cartesian(X,Y) :- a(X), b(Y).

% a |x| b : Natural inner join of relations a and b

inner_join(X) :- a(X), b(X).

% a =|x| b : Left outer join of relations a and b

left_join(X,Y) :- lj(a(X), b(Y), X=Y).

% a |x|= b : Right outer join of relations a and b

right_join(X,Y) :- rj(a(X), b(Y), X=Y).

% a =|x|= b : Full outer join of relations a and b

full_join(X,Y) :- fj(a(X), b(Y), X=Y).

% a U b : Set union of relations a and b

union(X) :- a(X) ; b(X).

% a - b: Set difference of relations a and b

difference(X) :- a(X), not b(X).

Once the program is consulted, you can query it with, for example:

DES> projection(X)

{

projection(a1),

projection(a2)

}

Info: 2 tuples computed.

The result of a query is the meaning of the view, i.e., the fact set for the query derived from the program whether intensionally or extensionally. In the above example, projection(X) corresponds to the projection of the first argument of relation c.

The second view in Section 4.1.5 returns:

Info: Processing:

a(X) :- b(X).

{

a(a1),

a(a2),

a(a3),

a(b1),

a(b2)

}

Info: 5 tuples computed.

For abolishing this program and execute the SQL statements in relop.sql, you can type /abolish and /process relop.sql. Note that the extension can be omitted in the /process command.

Here, we depart from the Datalog interpreter and, if you are to submit SQL queries, it is useful to switch to the SQL interpreter via the command /sql as inputs will be parsed only by the SQL parser. Otherwise, it will be tried to be identified as a Datalog input, and then as an SQL input.

Note that in the file relop.sql listed below, strings are enclosed between apostrophes. This is not needed in the Datalog language. In order to execute the contents of this file, type /process relop.sql.

% Switch to SQL interpreter

/sql

% Creating tables

create or replace table a(a);

create or replace table b(b);

create or replace table c(a,b);

% Listing the database schema

/dbschema

% Inserting values into tables

insert into a values ('a1');

insert into a values ('a2');

insert into a values ('a3');

insert into b values ('b1');

insert into b values ('b2');

insert into b values ('a1');

insert into c values ('a1','b2');

insert into c values ('a1','a1');

insert into c values ('a2','b2');

% Testing the just inserted values

select * from a;

select * from b;

select * from c;

% Projection

select a from c;

% Selection

select a from a where a='a2';

% Cartesian product

select * from a,b;

% Inner Join

select a from a inner join b on a.a=b.b;

% Left Join

select * from a left join b on a.a=b.b;

% Right Join

select * from a right join b on a.a=b.b;

% Full Join

select * from a full join b on a.a=b.b;

% Union

select * from a union select * from b;

% Difference

select * from a except select * from b;

If we have created the relations in Datalog, we cannot access them from SQL unless they had been either defined as tables or views or declared with types. For example, following the first alternative and after consulting the file relop.dl, we can submit:

create table a(a varchar);

And, then, accessing with an SQL statement the tuples that were asserted in Datalog:

DES> select * from a;

answer(a.a) ->

{

answer(a1),

answer(a2),

answer(a3)

}

Info: 3 tuples computed.

Otherwise, an error is submitted:

Error: Unknown table or view 'a'.

Following the second alternative, and after consulting the file relop.dl, we can declare types for a:

DES> /datalog :-type(a,[a:varchar])

DES> select * from a

answer(a.a) ->

{

answer(a1),

answer(a2),

answer(a3)

}

Info: 3 tuples computed.

Files relop.trc and relop.drc include the relational operations expressed as queries in these files. To process any of these files you have to proceed similar to SQL: /p relop.trc, for instance. As an example or TRC, the following computes the set union of two relations:

DES-TRC> {X|a(X) or b(X)};

answer(a:string) ->

{

answer(a1),

answer(a2),

answer(a3),

answer(b1),

answer(b2)

}

Info: 5 tuples computed.

6.2 Paths in a Graph (files paths.{dl,sql,ra})

This program[24] introduces the use of recursion in DES by defining the graph in Figure 2 and the set of tuples <origin, destination> such that there is a path from origin to destination.

Figure 2. Paths in a Graph

The file paths.dl contains the following Datalog code, which can be consulted with /c paths:

% Paths in a Graph

edge(a,b).

edge(a,c).

edge(b,a).

edge(b,d).

path(X,Y) :- path(X,Z), edge(Z,Y).

path(X,Y) :- edge(X,Y).

The query path(X,Y) yields the following answer:

{

path(a,a),

path(a,b),

path(a,c),

path(a,d),

path(b,a),

path(b,b),

path(b,c),

path(b,d)

}

Info: 8 tuples computed.

The file paths.sql contains the SQL counterpart code, which can be executed with /process paths.sql:

create table edge(origin,destination);

insert into edge values('a','b');

insert into edge values('a','c');

insert into edge values('b','a');

insert into edge values('b','d');

create view paths(origin,destination) as

with

recursive path(origin,destination) as

(select * from edge)

union

(select path.origin,edge.destination

from path,edge

where path.destination = edge.origin)

select * from path;

So, you can get the same answer as before with the SQL statement:

DES> select * from paths;

answer(paths.origin, paths.destination) ->

{

answer(a,a),

answer(a,b),

answer(a,c),

answer(a,d),

answer(b,a),

answer(b,b),

answer(b,c),

answer(b,d)

}

Info: 8 tuples computed.

Another shorter formulation is allowed in DES with the following view definition:

create view path(origin,destination) as

select * from

(select * from edge)

union

(select path.origin,edge.destination

from path,edge

where path.destination=edge.origin)

You can finally compare this with the RA formulation:

paths(origin,destination) :=

select true (edge)

union

project paths.origin,edge.destination

(edge zjoin paths.destination = edge.origin paths);

6.3 Shortest Paths (file spaths.{dl,sql,ra})

Thanks to aggregate predicates, one can code the following version of the shortest paths problem (file spaths.dl), which uses the same definition of edge as in the previous example:

path(X,Y,1) :-

edge(X,Y).

path(X,Y,L) :-

path(X,Z,L0),

edge(Z,Y),

count(edge(A,B),Max),

L0<Max,

L is L0+1.

sp(X,Y,L) :-

min(path(X,Y,Z),Z,L).

Note that the infinite computation that may raise from using the built-in is/2 is avoided by limiting the total length of a path to the number of edges in the graph.

The following query returns all the possible paths and their corresponding minimal distances:

DES> sp(X,Y,L)

{

sp(a,a,2),

sp(a,b,1),

sp(a,c,1),

sp(a,d,2),

sp(b,a,1),

sp(b,b,2),

sp(b,c,2),

sp(b,d,1)

}

Info: 8 tuples computed.

Below is the SQL formulation for the same problem (file spaths.sql) :

DES> create or replace view spaths(origin,destination,length) as with recursive path(origin,destination,length) as

(select edge.*,1 from edge)

union

(select path.origin,edge.destination,path.length+1

from path,edge

where path.destination=edge.origin and

path.length<(select count(*) from edge))

select origin,destination,min(length) from path group by origin,destination;

DES> select * from spaths

answer(spaths.origin, spaths.destination, spaths.length) ->

{

answer(a,a,2),

answer(a,b,1),

answer(a,c,1),

answer(a,d,2),

answer(b,a,1),

answer(b,b,2),

answer(b,c,2),

answer(b,d,1)

}

Info: 8 tuples computed.

A possible RA formulation follows:

max_length(max_length) :=

group_by [] count(*) true (edge);

path(origin,destination,length) :=

project origin,destination,1 (edge)

union

project path.origin,edge.destination,path.length+1

(

path

zjoin path.destination=edge.origin and

path.length<max_length

(edge product max_length)

);

spaths(origin,destination,length) :=

group_by origin,destination origin,destination,min(length) true

(path);

And its query:

/ra select true (spaths);

6.4 Family Tree (files family.{dl,sql,ra})

This (yet another classic) program defines the family tree shown in Figure 3, the set of tuples <parent,child> such that parent is a parent of child (the relation parent), the set of tuples <ancestor,descendant> such that ancestor is an ancestor of descendant (the relation ancestor), the set of tuples <father,child> such that father is the father of child (the relation father), and the set of tuples <mother,child> such that mother is the mother of child (the relation mother).

Figure 3. Family Tree

The file family.dl contains the following Datalog code, which can be consulted with /c family:

father(tom,amy).

father(jack,fred).

father(tony,carolII).

father(fred,carolIII).

mother(grace,amy).

mother(amy,fred).

mother(carolI,carolII).

mother(carolII,carolIII).

parent(X,Y) :- father(X,Y).

parent(X,Y) :- mother(X,Y).

ancestor(X,Y) :- parent(X,Y).

ancestor(X,Y) :- parent(X,Z), ancestor(Z,Y).

The query ancestor(tom,X) yields the following answer (that is, it computes the set of descendants of tom):

{

ancestor(tom,amy),

ancestor(tom,carolIII),

ancestor(tom,fred)

}

Info: 3 tuples computed.

Solving the view:

son(S,F,M) :- father(F,S),mother(M,S).

yields the following answer, computing the set of sons:

Info: Processing:

son(S,F,M) :- father(F,S),mother(M,S).

{

son(amy,tom,grace),

son(carolII,tony,carolI),

son(carolIII,fred,carolII),

son(fred,jack,amy)

}

Info: 4 tuples computed.

The file family.sql contains the SQL counterpart code, which can be executed with /process family.sql:

create table father(father,child);

insert into father values('tom','amy');

insert into father values('jack','fred');

insert into father values('tony','carolII');

insert into father values('fred','carolIII');

create table mother(mother,child);

insert into mother values('grace','amy');

insert into mother values('amy','fred');

insert into mother values('carolI','carolII');

insert into mother values('carolII','carolIII');

create view parent(parent,child) as

select * from father

union

select * from mother;

create or replace view ancestor(ancestor,descendant) as

select parent,child from parent

union

select parent,descendant from parent,ancestor

where parent.child=ancestor.ancestor;

The two example queries above can be formulated in SQL as:

select * from ancestor where ancestor='tom';

select child,father,mother

from father,mother

where father.child=mother.child;

And also as RA queries as:

/ra select ancestor='tom' (ancestor);

project child,father,mother

(father zjoin father.child=mother.child mother);

6.5 Basic Recursion Problem (file recursion.dl)

This example is intended to show that queries involving recursive predicates do terminate thanks to DES fixpoint solving, by contrast with Prolog’s usual SLD resolution.

p(0).

p(X) :- p(X).

p(1).

The query p(X) returns the inferred facts from the program irrespective of the apparent infinite recursion in the second rule. (Note that the Prolog goal p(1) does not terminate. You can easily check it out with /prolog p(1).)

6.6 Transitive Closure (files tranclosure.{dl,sql,ra})

With this example, we show a possible use of mutual recursion by means of a Datalog program that defines the transitive closure of the relations p and q[25]. It can be consulted with /c tranclosure.

p(a,b).

p(c,d).

q(b,c).

q(d,e).

pqs(X,Y) :- p(X,Y).

pqs(X,Y) :- q(X,Y).

pqs(X,Y) :- pqs(X,Z),p(Z,Y).

pqs(X,Y) :- pqs(X,Z),q(Z,Y).

The query pqs(X,Y) returns the whole set of inferred facts that model the transitive closure.

File tranclosure.sql contains the SQL counterpart code, which can be executed with /process tranclosure.sql:

create table p(x,y);

insert into p values ('a','b');

insert into p values ('c','d');

create table q(x,y);

insert into q values ('b','c');

insert into q values ('d','e');

create view pqs(x,y) as

select * from p

union

select * from q

union select pqs.x,p.y from pqs,p where pqs.y=p.x

union select pqs.x,q.y from pqs,q where pqs.y=q.x;

The query select * from pqs returns the same answer as before.

The file tranclosure.ra contains the RA formulation:

pqs(x,y) :=

union

project pqs.x,p.y (pqs zjoin pqs.y=p.x p)

union

project pqs.x,q.y (pqs zjoin pqs.y=q.x q);

/ra select true (pqs)

6.7 Mutual Recursion (files mutrecursion.{dl,sql,ra})

The following program shows a basic example about mutual recursion:

p(a).

p(b).

q(c).

q(d).

p(X) :- q(X).

q(X) :- p(X).

Submitting the goal p(X), we get:

{

p(a),

p(b),

p(c),

p(d)

}

Info: 4 tuples computed.

which is the same set of values for arguments for the query q(X). The file mrtc.dl is a combination of this example and that of the previous section.

The file mutrecursion.sql contains the SQL counterpart code, which can be executed with /process mutrecursion.sql:

/sql

/assert p(a)

/assert p(b)

/assert q(c)

/assert q(d)

-- View q must be given a prototype for view p to be defined

create view q(x) as select * from q;

create or replace view p(x) as select * from q;

create or replace view q(x) as select * from p;

Note that it is needed to build a void view for q in order to have it declared when defining the view p. The void view is then replaced by its actual definition. The contents of both views can be tested to be equal with:

select * from p;

select * from q;

File mutrecursion.ra contains the RA formulation:

-- View q must be given a prototype for view p to be defined

q(x) := select true (q);

p(x) := select true (q);

q(x) := select true (p);

select true (p);

select true (q);

6.8 Farmer-Wolf-Goat-Cabbage Puzzle (file puzzle.dl)

This example[26] shows the classic Farmer–Wolf–Goat–Cabbage puzzle (also Missionaries and Cannibals as another rewritten form). The farmer, wolf, goat, and cabbage are all on the north shore of a river and the problem is to transfer them to the south shore. The farmer has a boat which he can row taking at most one passenger at a time. The goat cannot be left with the wolf unless the farmer is present. The cabbage, which counts as a passenger, cannot be left with the goat unless the farmer is present. The following program models the solution to this puzzle. The relation state/4 defines the valid states under the specification (i.e., those situations in which there is no danger for any of the characters in our story; a state in which the goat is left alone with the cabbage may result in an eaten cabbage) and imposes that there is a previous valid state from which we depart from. The arguments of this relation are intended to represent (from left to right) the position (north –n– or south –s– shore) of the farmer, wolf, goat, and cabbage. We use the relation safe/4 to verify that a given configuration of positions is valid. The relation opp/2 simply states that north is the opposite shore of south and vice versa.

% Initial state

state(n,n,n,n).

% Farmer takes Wolf

state(X,X,U,V) :-

safe(X,X,U,V),

opp(X,X1),

state(X1,X1,U,V).

% Farmer takes Goat

state(X,Y,X,V) :-

safe(X,Y,X,V),

opp(X,X1),

state(X1,Y,X1,V).

% Farmer takes Cabbage

state(X,Y,U,X) :-

safe(X,Y,U,X),

opp(X,X1),

state(X1,Y,U,X1).

% Farmer goes by himself

state(X,Y,U,V) :-

safe(X,Y,U,V),

opp(X,X1),

state(X1,Y,U,V).

% Opposite shores (n/s)

opp(n,s).

opp(s,n).

% Farmer is with Goat

safe(X,Y,X,V).

% Farmer is not with Goat

safe(X,X,X1,X) :- opp(X,X1).

If we submit the query state(s,s,s,s), we get the expected result:

{

state(s,s,s,s)

}

Info: 1 tuple computed.

That is, the system has proved that there is a serial of transfers between shores which finally end with the asked configuration (this problem is not modelled to show this serial). If we ask for the extension table contents regarding the relation state/4 (with the command /list_et state/4), we get for the answers:

{

state(n,n,n,n),

state(n,n,n,s),

state(n,n,s,n),

state(n,s,n,n),

state(n,s,n,s),

state(s,n,s,n),

state(s,n,s,s),

state(s,s,n,s),

state(s,s,s,n),

state(s,s,s,s)

}

Info: 10 tuples in the answer set.

This is the complete set of valid states which includes all of the valid paths from state(n,n,n,n) to state(s,s,s,s). However, the order of states to reach the latter is not given, but we can find it by observing this relation, i.e.:

state(n,n,n,n) ® Farmer takes Goat to south shore ®

state(s,n,s,n) ® Farmer returns to north shore ®

state(n,n,s,n) ® Farmer takes Wolf to south shore ®

state(s,s,s,n) ® Farmer takes Goat to north shore ®

state(n,s,n,n) ® Farmer takes Cabbage to south shore ®

state(s,s,n,s) ® Farmer returns to north shore ®

state(n,s,n,s) ® Farmer takes Goat to south shore ®

state(s,s,s,s) Final safe state

Observe that there is two states in the relation state/4 which do not form part of the previous path:

state(s,n,s,s)

state(n,n,n,s)

These states come from another possible path:[27]

state(n,n,n,n) ® Farmer takes Goat to south shore ®

state(s,n,s,n) ® Farmer returns to north shore ®

state(n,n,s,n) ® Farmer takes Cabbage to south shore ®

state(s,n,s,s) ® Farmer takes Goat to north shore ®

state(n,n,n,s) ® Farmer takes Wolf to south shore ®

state(s,s,s,n) ® Farmer takes Goat to north shore ®

state(s,s,n,s) ® Farmer returns to north shore ®

state(n,s,n,s) ® Farmer takes Goat to south shore ®

state(s,s,s,s) Final safe state

6.8.1 Dealing with paths (file puzzle1.dl)

As just illustrated, the sequence of movements needed to find a feasible solution can be inferred from the answer table. Nonetheless, it is possible to outcome such sequences even when there is no provision for data structures. The idea is to code sequences of movements into a single plain type, as an integer. We can resort, for instance, to build a decimal number whose digits, as read from right to left, indicate the selected movement in the sequence. If we number the movement alternatives from 1 to 4 (in the same order as rules occur at the program text) the first solution above can be coded as 2412342, and the second one as 2432142.

Modelling in this way, we can rewrite the predicate state by adding a first argument as the sequence needed to reach a given state, and the steps already performed. This is useful to build the code as adding a number (identifying the alternative rule) multiplied by the n-th power of ten, where n is the number of steps already done. The following two example rules illustrates this:

% 0. Initial state

state(0,0,n,n,n,n).

% 1. Farmer takes Wolf

state(C,S,X,X,U,V) :-

safe(X,X,U,V),

opp(X,X1),

state(C1,S1,X1,X1,U,V),

S is S1+1,

bound(B),

S<B,

C is C1+1*10**S1.

Solving the new program yields:

DES> state(C,S,s,s,s,s)

{

state(2412342.0,7,s,s,s,s),

state(2432142.0,7,s,s,s,s)

}

Info: 2 tuples computed.

Which is explained as follows:

* Solution 1: state(2412342.0,7,s,s,s,s)

0: Initial state

North: Farmer,Goat,Cabbage,Wolf

South: empty

2: Farmer takes goat to the South shore

North: Cabbage,Wolf

South: Farmer,Goat

4: Farmer returns to North shore

North: Farmer,Cabbage,Wolf

South: Goat

3: Farmer takes cabbage to the South shore

North: Wolf

South: Farmer,Cabbage,Goat

2: Farmer takes goat to the North shore

North: Farmer,Goat,Wolf

South: Cabbage

1: Farmer takes wolf to the South shore

North: Goat

South: Farmer,Cabbage,Wolf

4: Farmer returns to North shore

North: Farmer,Goat

South: Cabbage,Wolf

2: Farmer takes goat to the South shore

North: empty

South: Farmer,Goat,Cabbage,Wolf

* Solution 2: state(2432142.0,7,s,s,s,s)

0: Initial state

North: Farmer,Goat,Cabbage,Wolf

South: empty

2: Farmer takes goat to the South shore

North: Cabbage,Wolf

South: Farmer,Goat

4: Farmer returns to North shore

North: Farmer,Cabbage,Wolf

South: Goat

1: Farmer takes wolf to the South shore

North: Cabbage

South: Farmer,Goat,Wolf

2: Farmer takes goat to the North shore

North: Farmer,Goat,Cabbage

South: Wolf

3: Farmer takes cabbage to the South shore

North: Goat

South: Farmer,Cabbage,Wolf

4: Farmer returns to North shore

North: Farmer,Goat

South: Cabbage,Wolf

2: Farmer takes goat to the South shore

North: empty

South: Farmer,Goat,Cabbage,Wolf

6.9 Paradoxes (files russell.{dl,sql,ra})

When negation is used, we can find paradoxes, such as the Russell’s paradox (the barber in a town shaves every person who does not shave himself) shown in the next example (please note that this example is not stratified and, in general, we cannot ensure correctness for non-stratifiable programs):

DES> /verbose on

Info: Verbose output is on.

DES> /c russell

Info: Consulting russell...

man(barber).

man(mayor).

shaves(barber,M) :-

man(M),

not shaves(M,M).

shaved(M) :-

shaves(barber,M).

end_of_file.

Info: 4 rules consulted.

Info: Computing predicate dependency graph...

Info: Computing strata...

Warning: Non stratifiable program.

If we submit the query shaves(X,Y), we get the positive facts as well as a set of undefined inferred information (in our example, whether the barber shaves himself), as follows (here, verbose output is enabled):

DES> shaves(X,Y)

Warning: Unable to ensure correctness for this query.

{

shaves(barber,mayor)

}

Info: 1 tuple computed.

Undefined:

{

shaves(barber,barber)

}

Info: 1 tuple undefined.

If we look at the extension table contents by submitting the command /list_et, we get as answers:

Answers:

{

man(barber),

man(mayor),

not shaves(mayor,mayor),

shaves(barber,mayor)

}

Info: 4 tuples in the answer set.

We can see that, in particular, we have proved additional negative information (the mayor does not shaves himself) and that no information is given for the undefined facts. The current implementation uses an incomplete algorithm for finding such undefined facts. We can see this incompleteness by adding the following rule:

shaved(M) :- shaves(barber,M).

The query shaved(M) returns:

Warning: Unable to ensure correctness for this query.

{

shaved(mayor)

}

Info: 1 tuple computed.

That is, the system is unable to prove that shaved(barber) is undefined.

If you look at the predicate dependency graph and the stratification of the program:

DES> /pdg

Nodes: [man/1,shaved/1,shaves/2]

Arcs : [shaves/2-shaves/2,shaves/2+man/1,shaved/1+shaves/2]

DES> /strata

[non-stratifiable]

you get the predicate dependency graph shown in Figure 4, and you are informed that the program is non-stratifiable. This figure shows a negation in a cycle, so that the program is not stratifiable. (The system warned of this situation when the program was loaded.)

Figure 4. Predicate Dependency Graph for russell.dl

However, even when a program is non-stratifiable, there may exist a query with an associated predicate dependency subgraph so that negation does not occur in any cycle. For instance, this occurs with the query man(X) in this program:

DES> man(X)

Info: Stratifiable subprogram found for the given query.

{

man(barber),

man(mayor)

}

Info: 2 tuples computed.

Here, the system recomputed the strata for the predicate dependency subgraph, and informed that it found a stratifiable subprogram for such a query. In this simple case, no more negations were involved in the subgraph, but more elaborated dependencies can be found in other examples (cf. sections 6.10 and 6.11).

Stratification may be needed for programs without negation as long as a temporary view contains a negated goal. Consider the following view under the program relop.dl (rules in the program with negation are not present in the subgraph for the query d(X)):

DES> d(X) :- a(X), not b(X)

Info: Processing:

d(X) :- a(X),not b(X).

{

d(a2),

d(a3)

}

Info: 2 tuples computed.

In this view, the query d(X) is solved with a solve-by-stratum algorithm, described in Section 5.22.3. In this case, this means that the goal b(X) is solved before obtaining the meaning of d(X) because b is in a lower stratum than d and it is needed for the computation of d.

The basic paradox p:-not p can be found in the file paradox.dl, whose model is undefined as you can test with the query p.

6.10 Parity (file DLDebugger/parity.dl)

This example program[28] is intended to compute the parity of a given base relation br(X), i.e., it can determine whether the number of elements in the relation (cardinality) is even or odd by means of the predicates br_is_even, and br_is_odd, respectively. The predicate next defines an ascending chain of elements in br based on their textual ordering, where the first link of the chain connects the distinguished node nil to the first element in br. The predicates even and odd define the even, resp. odd, elements in the chain. The predicate has_preceding defines the elements in br such that there are previous elements to a given one (the first element in the chain has no preceding elements). The rule defining this predicate includes an intended error (fourth rule in the example) which will be used in Section 6.13 to show how it is caught by the declarative debugger.

% Pairs of non-consecutive elements in br

between(X,Z) :-

br(X), br(Y), br(Z), X<Y, Y<Z.

% Consecutive elements in the sequence, starting at nil

next(X,Y) :-

br(X), br(Y), X<Y, not between(X,Y).

next(nil,X) :-

br(X), not has_preceding(X).

% Values having preceding values in the sequence

has_preceding(X) :-

br(X), br(Y), Y>X. % Error: Y>X should be Y<X

% Values in an even position of the sequence, including nil

even(nil).

even(Y) :-

odd(X), next(X,Y).

% Values in an odd position of the sequence

odd(Y) :-

even(X), next(X,Y).

% Succeeds if the cardinality of the sequence is even

br_is_even :-

even(X), not next(X,Y).

% Succeeds if the cardinality of the sequence is odd

br_is_odd :-

odd(X), not next(X,Y).

% Base relation

br(a).

br(b).

6.11 Grammar (file grammar.dl)

Parsers can also be coded as Datalog programs. In this example[29], a simple left-recursive grammar analyser is coded for the following grammar rules.

A –> a

A –> Ab

A –> Aa

It was tested with the input string "ababa", which is coded with the relation t(F,T,L), F for the position of token T that ends at position L.

t(1,a,2).

t(2,b,3).

t(3,a,4).

t(4,b,5).

t(5,a,6).

a(F,L) :- t(F,a,L).

a(F,L) :- a(F,M), t(M,b,L).

a(F,L) :- a(F,M), t(M,a,L).

DES> a(1,6)

{

a(1,6)

}

Info: 1 tuple computed.

6.12 Fibonacci (file fib.{dl,sql,ra})

The all-time classics Fibonacci program[30] can be coded in DES thanks to arithmetic built-ins. It can be formulated as follows:

fib(0,1).

fib(1,1).

fib(N,F) :-

N>1,

N2 is N-2,

fib(N2,F2),

N1 is N-1,

fib(N1,F1),

F is F2+F1.

Since DES is implemented with extension tables, computing high Fibonacci numbers is possible with linear complexity:

DES> fib(1000,F)

{

fib(1000,70330367711422815821835254877183549770181269836358732742604905087154537118196933579742249494562611733487750449241765991088186363265450223647106012053374121273867339111198139373125598767690091902245245323403501)

}

Info: 1 tuple computed.

Also, it is possible to formulate this in SQL, even when the next view features non-linear recursion (file fib.sql):

create view fib(n,f) as

select 0,1

union

select 1,1

union

select fib1.n+1,fib1.f+fib2.f

from fib fib1, fib fib2

where fib1.n=fib2.n+1 and fib1.n<10;

As well, next there is a possible RA formulation (file fib.ra):

fib(n,f) :=

project 0,1 (dual)

union

project 1,1 (dual)

union

project fib1.n+1,fib1.f+fib2.f

(rename fib1(n1,f1) (fib)

zjoin

n1=n2+1 and n1<10

rename fib2(n2,f2) (fib));

6.13 Hanoi Towers (file hanoi.dl)

Another well-known toy puzzle is the towers of Hanoi, which can be coded as:

hanoi(1,A,B,C).

hanoi(N,A,B,C) :-

N>1,

N1 is N-1,

hanoi(N1,A,C,B),

hanoi(N1,C,B,A).

We can submit the following query for 10 discs:

DES> hanoi(10,a,b,c)

{

hanoi(10,a,b,c)

}

Info: 1 tuple computed.

Note that the answer to this query does not reflect the movements of the discs, which can be otherwise shown as the intermediate results kept in the extension table:

DES> /list_et hanoi

Answers:

{

hanoi(1,a,c,b),

hanoi(1,b,a,c),

hanoi(1,c,b,a),

hanoi(2,a,b,c),

hanoi(2,b,c,a),

hanoi(2,c,a,b),

hanoi(3,a,c,b),

hanoi(3,b,a,c),

hanoi(3,c,b,a),

hanoi(4,a,b,c),

hanoi(4,b,c,a),

hanoi(4,c,a,b),

hanoi(5,a,c,b),

hanoi(5,b,a,c),

hanoi(5,c,b,a),

hanoi(6,a,b,c),

hanoi(6,b,c,a),

hanoi(6,c,a,b),

hanoi(7,a,c,b),

hanoi(7,b,a,c),

hanoi(7,c,b,a),

hanoi(8,a,b,c),

hanoi(8,b,c,a),

hanoi(8,c,a,b),

hanoi(9,a,c,b),

hanoi(9,c,b,a),

hanoi(10,a,b,c)

}

Info: 27 tuples in the answer set.

...

6.14 Other Examples

The directory examples includes some other examples such as bom.dl (bill of materials) and trains.dl (train connections) which show more example applications including negation. Other examples are orbits.dl (a solar system tiny database), sg.dl (same generation for a family database), tc.dl (transitive closure), and empTraining.{ra,sql} (taken from [Diet01]). Also, there are other directories, such as persistent, which contains examples for persisting predicates; the folder ontology, which includes examples of authoring ontologies and some documentation; fuzzy, with Fuzzy Datalog examples; hypothetical, with Hypothetical Datalog examples; and DLDebugger and SQLDebugger, which include examples for debugging Datalog programs and SQL views, respectively.

7. Contributions

This section collects the contributions from external developers up to now:

· Fuzzy Datalog.
Authors: Pascuál Julián-Iranzo and Fernando Sáenz-Pérez
Date: 2/2017
Description: Fuzzy extension of Datalog including fuzzy relations and weak unification
License: LGPL
Contact: Fernando Sáenz-Pérez

· Datalog Declarative Debugger with Wrong and Missing Answers.
Authors: Rafael Caballero-Roldán, Yolanda García-Ruiz, and Fernando Sáenz-Pérez
Date: 8/2015
Description: Tool for the declarative debugging of Datalog programs with wrong and missing answers
License: LGPL
Contact: Fernando Sáenz-Pérez

· SQL Declarative Debugger.
Authors: Rafael Caballero-Roldán, Yolanda García-Ruiz, and Fernando Sáenz-Pérez
Date: 5/2011 (upgraded version with Wrong and Missing Answers since DES 3.0)
Description: Tool for the declarative debugging of Datalog programs with wrong and missing answers
License: LGPL
Contact: Fernando Sáenz-Pérez

· Test Case Generator.
Authors: Rafael Caballero-Roldán, Yolanda García-Ruiz, and Fernando Sáenz-Pérez
Date: 10/2009 (upgraded version supported since DES 1.8.0)
Description: Tool for generating test cases for SQL views
License: LGPL
Contact: Yolanda García-Ruiz (Implementor)

· Datalog Declarative Debugger.
Authors: Rafael Caballero-Roldán, Yolanda García-Ruiz, and Fernando Sáenz-Pérez
Date: 5/2007
Description: Tool for the declarative debugging of Datalog programs (brand-new version with Wrong and Missing Answers since DES 4.0)
License: LGPL
Contact: Yolanda García-Ruiz (Implementor)

ACIDE (A Configurable Development Environment).
Authors: Diego Cardiel Freire, Juan José Ortiz Sánchez, Delfín Rupérez Cañas (SI 2006/2007), Miguel Martín Lázaro (SI 2007/2008), and Javier Salcedo Gómez (SI 2010/2011), Pablo Gutiérrez García-Pardo, Elena Tejeiro Pérez de Ágreda, Andrés Vicente del Cura (SI 2012/2013), Fernando Ordás Lorente, Juan Jesús Marqués Ortiz, Semíramis Gutiérrez Quintana (SI 2013/2014), Sergio Domínguez Fuentes (SI 2014/2015), and Sergio García Rodríguez (TFG 2019/2020) led by Fernando Sáenz-Pérez.
Date: 3/2007 (ACIDE 0.1, first version), 11/2008 (ACIDE 0.7), 7/2011 (ACIDE 0.8), 12/2012 (ACIDE 0.9) , 4/2013 (ACIDE 0.10) , 7/2013 (ACIDE 0.11), 12/2013 (ACIDE 0.12), 2/2014 (ACIDE 0.13), 3/2014 (ACIDE 0.14) , 4/2014 (ACIDE 0.15), 8/2014 (ACIDE 0.16) , 12/2015 (ACIDE 0.17), 1/2021 (ACIDE 0.18 - current version).
Description: This project is aimed to provide a multiplatform configurable integrated development environment which can be configured in order to be used with any development system such as interpreters, compilers and database systems. Features of this system include: project management, multi-file editing, syntax colouring, and parsing on-the-fly (which informs of syntax errors when editing programs prior to the compilation).
License: GPL.
Project Web Page: http://acide.sourceforge.net/

· Emacs development environment.
Author: Markus Triska.
Date: 2/22/2007
Description: Provides an integration of DES into Emacs. Once a Datalog file has been opened, you can consult it by pressing F1 and submit queries and commands from Emacs. This works at least in combination with SWI-Prolog (it depends on the –s switch); other systems may require slight modifications.
License: GPL.
Project Web Page: http://stud4.tuwien.ac.at/~e0225855/index.html
Contact: markus.triska@gmx.at
Installation: Copy des.el (in the contributors web page) to your home directory and add to your .emacs:

(load "~/des")

; adapt the following path as necessary:

(setq des-prolog-file "~/des/systems/swi/des.pl")

(add-to-list 'auto-mode-alist '("\\.dl$" . des-mode))

Restart Emacs, open a *.dl file to load it into a DES process (this currently only works with SWI-Prolog). If the region is active, F1 consults the text in the region. You can then interact with DES as on a terminal.

8. Caveats and Limitations

· Datalog:

o No compound terms as arguments in user relations

o Termination is ensured up to arithmetic and hypotheses. There is no provision for numerical bounds (although top-N queries can be used to limit the number of returned tuples)

o No database updates via Datalog rules are allowed (program asserts and retracts)

o Rules in consulted files must end with a dot, in contrast to command prompt inputs in single-line mode, where the dot is optional. Rules in a consulted file may span on multiple lines and an ending dot is mandatory, irrespective of the multi-line mode

o Differential naïve optimization is experimental

· SQL:

o User identifiers (including tables, views, column names) are case sensitive for the local database. Language keywords can be written in either upper or lower or mixed case

o Case sensitiveness for external databases depends on the RDBMS and its ODBC connection (e.g., DB2 uses uppercase user identifiers, even when they are declared in lowercase)

o SQL in DES is set-oriented (instead of bag/multiset as the standard) by default. Nonetheless, duplicates can be enabled with /duplicates on. This command can be added to the file des.ini in the DES start path

o Even enabling automatic type casting (with the command /type_casting on), the type system is stronger than other SQL implementations (e.g., an integer division div only accepts integers as arguments)

o DES features a strong type system which may deal unexpected results to SQL users, as in:

DES> select 1 union select 1.0

Error: Type mismatch number(integer) vs. number(float).

As a numeric constant is assumed to be float if it includes a decimal part, and integer otherwise, both constants are of different types and a type error is raised. However, DES can behave similar to SQL systems by relaxing type equality to type compatibility with the command /type_casting on for automatic type casting, therefore allowing queries as above, returning in this case the most general type

o Duplicates in conjunction with SQL set operators and disjunctions are not equivalent to SQL implementations. Further versions may make match them

o No Datalog built-in predicate is allowed as an SQL identifier for a relation with the same arity (as, e.g., the table name count with two columns)

o No ADL (Access Data Language) sentences are provided

o Batch updates and deletions are not atomic

o Nulls and null-related operations do not exactly follow the SQL standard

o Strings may become evaluated if they match primitive functions

o Lack of some types, such as boolean

o See also Section 5.1.10 regarding ODBC connections

· Test case generator:

o Test case generation is not supported for ODBC connections, up to now

· Miscellanea:

o Enabling duplicates can notably harm performance for recursive predicates (cf. Fibonacci example) because duplicate sources are also rules (in addition to facts)

o Users should not write predicate identifiers starting with the symbol '$'. Otherwise, unexpected behaviour might happen

o The function rand (without seed) may deliver the same outcome for different solutions of a goal/statement

· Prolog systems' specific issues:

o SWI-Prolog distributions do not allow arithmetic expressions involving log/2

o Each underlying Prolog system has its own pros and cons when accessing external databases

9. Release Notes

This section lists release notes of the current DES version. Former release notes can be found in the document release_notes_history_DES6.8.pdf, which can be downloaded from https://des.sourceforge.io/html/download.html.

9.1 Version 6.8 of DES (released on June, 15th, 2025)

· Enhancements:

o Enhanced SQL semantic analysis with functional dependencies to uncover common pitfalls

o Added the value loose for the command /sql_semantic_check, which includes more probabilities for false positives, though with more error detections

o Avoided some rechecking in SQL semantic warnings

o Experimental semi-naïve optimization for linear recursive predicates

o Intermediate files from a Datalog debugging session are removed. Via TAPI, an ad-hoc command is used for this purpose

o Enhanced full Datalog debugger by avoiding some subset questions derived from former user answers

o Reduced set of automatic questions in the full Datalog debugger

o Included dealing with an abort answer in the command /debug_dl

o Updated help for /debug_dl

o Wrong and missing data can be specified in the command /debug_dl_set_node

o New semantics for non-deterministic functions and impure deterministic functions (and counterpart function predicates)

o Setting fuzzy mode disables non-Datalog languages. As well, setting a non-Datalog language in fuzzy mode selects (crisp-)Datalog

o Commands /ls and /dir accepts a filename as argument. Also, extended help provided for these commands

o New predicate and function substr with no length

o Added support for the ALL and ANY quantifiers in the HAVING clause

o Syntax of PostgreSQL simplified recursive views is supported (the same as already provided by DES but adding a RECURSIVE keyword)

o SQL IS NULL operation extended to deal with expressions

o The function cast can receive an expression as its first argument

o Added exception to show internal errors when processing SQL queries

o Uppercase ODBC connection names in commands do not need to be enclosed between single quotes (unless they contain a blank space)

o ODBC connections become case-insensitive

o Only one pass in the extensional table for fetching completed entries during fixpoint computation

o Top-level goals which have been previously completed are not reprocessed (no fixpoint computation for them)

o Completed top-N goals become cached in the extension table

o Along user inputs, the extension table is only cleared for affected predicates

o Function rand/1 is solved once for each call, avoiding resetting the seed along fixpoint computation

o The command /fp_info also displays statistics at each fixpoint iteration if they are enabled

o When rules are removed (either manually or by the system when removing intermediate predicates), only entries in the extension table corresponding to those rules are removed, instead of clearing all the table

o Host safety (sandboxing) extended to files out of the start path, which are not allowed to be accessed

o New commands:

§ /debug_dl_cleanup Clean up full Datalog debugger. Typically used with TAPI, this command removes temporary data and files resulting from a debugging session. TAPI enabled

§ /debug_dl_set_node Name/Arity State Set the state for a node. State can be valid, nonvalid, missing(Tuple), and wrong(Tuple), where Tuple is of the form rel(cte₁, ..., cte_n), where rel is the relation name and each argument cte_i is an SQL constant. Placeholders (_) are allowed for missing tuples instead of constants. TAPI enabled

§ /debug_dl_solutions Display Datalog debugging solutions for the current question. TAPI enabled

§ /list_predicate_classes List classes of predicates: local (local database, either typed or not), deductive database (typed local), mixed database (both in the external and deductive databases), external database (only from an external connection), user (all predicates but built-ins), extensional (only facts or tables), recursive (in a recursive cycle), non-recursive (in no recursive cycle), non-dependent on recursive (not in a recursive cycle and non-dependent on a recursive predicate), restricted (with a restricted rule at least), dependent on restricted, non-completeable (its extension table cannot be closed), non-cacheable (with no entries in the extension table), semi-naïve optimized (amenable for this optimization)

§ /nodebug Disable debugging in the host Prolog interpreter. Only working for source distributions

§ /parse_external_sql Display whether parsing of SQL queries sent to external engines is enabled

§ /parse_external_sql Switch Enable or disable parsing of SQL queries sent to external engines (on or off, resp.)

§ /reset_statistics Reset deductive engine statistics

§ /unset Var Unset the user variable Var so it becomes no longer defined up to a new setting

§ /unset_flag FlagName Unset the system flag with name FlagName so it becomes no longer defined up to a new setting

§ /xpdg Display the extended predicate dependency graph, which details the restricted predicates (if existing) and their dependencies

§ /xpdg Name Display the current predicate dependency graph restricted to predicate with name Name, detailing the restricted predicates (if existing) and their dependencies

§ /xpdg Name/Arity Display the current predicate dependency graph restricted to predicate Name/Arity, detailing the restricted predicates (if existing) and their dependencies

· Changes:

o The commands /drop_all_relations and /drop_all_tables apply the CASCADE option

o The command /get_relation renders null internal representation as null for non-TAPI invocations. Otherwise, it displays null internal representations

o Predicates depending on non-deterministic functions (such as rand and current_time) are not cached along user inputs

o Non-deterministic functions (such as rand and current_time) are evaluated only once for each solving path. This is relevant in two scenarios: providing different values for different depth calls along recursion, and different values for different choice points

o Modified semantics of top-N queries: results are not affected by literal ordering

· Fixed bugs:

o The file des_pchr.pl was not located where expected and the debugging session could not proceed

o Some functions incorrectly propagated semantic bindings, leading to false positives for inconsistent conditions in SQL semantic checking

o Some false positives in semantic warnings for EXCEPT, UNION, DIVISION and IN SQL operators

o False positive in semantic warnings with COUNT DISTINCT when several relations were joined

o False positive in semantic warnings for columns without aggregates in the HAVING conditions

o False positive in semantic warnings for conditions over grouped columns occurring in the HAVING clause without an aggregate

o Expressions in disjunctive bodies were not translated

o Applying the full debugger to a Datalog predicate that is not the root in the PDG of a program did not find the erroneous predicate

o Some relations enclosed between parentheses were not parsed

o Some built-in predicate calls were not reordered to avoid instantiation exceptions. Some corner cases led to incomplete answers

o Some uses of string casting yield to type errors

o ODBC connections to Oracle failed

o With ALTER TABLE it was possible to add existing column names

o Type errors in expressions as arguments of built-in infix operators

o The command /current_flag failed when applied to a user flag

o Dropping delimited tables in Oracle would fail

o Datalog constant e (Euler number) raised an exception in comparison queries (bug introduced in version 6.7)

o Selecting a string matching a built-in in SQL might fail

o Open answers led exceptions

o Non-ground goals in a top-n call might return incomplete answers for recursive predicates in the goal solving path

o Incorrect pending choice point led /fp_info on to display spurious text

o The extension table was not cleared when disabling duplicates

o Some statistics related to the extension table were not updated when inserting, deleting and updating in SQL statements

o Under TAPI listings, an exception was raised for foreign keys with more than one attribute

10. Acknowledgements

The author wishes to thank Jan Wielemaker both for providing such an amazing free Prolog system and for his restless supporting help. Mats Carlsson and Per Mildner, at SICS, supported the development providing help, by adding new features to the ODBC library, and providing hints on Spider usage for code analysis. Paulo Moura provided help with Logtalk linter to uncover code issues. Also, thanks to all the people providing feedback, since they are guiding DES to suit more demanded requirements and in particular, to the students of the subject Databases at UCM since 2012. Contributors are specially acknowledged: Markus Triska, for developing the Emacs IDE and also author of the SWI-Prolog clpfd library. ACIDE was developed and improved by Diego Cardiel Freire, Juan José Ortiz Sánchez, Delfín Rupérez Cañas, Miguel Martín Lázaro, Javier Salcedo Gómez, Pablo Gutiérrez García-Pardo, Elena Tejeiro Pérez de Ágreda, Andrés Vicente del Cura, Fernando Ordás Lorente, Juan Jesús Marqués Ortiz, Semíramis Gutiérrez Quintana, Sergio Domínguez Fuentes, Sergio García Rodríguez, Carlos González Torres and Cristina Lara López. Javier Amado Lázaro improved the SQL semantic analysis. Sergio García-Jiménez developed DESODBC, an ODBC driver to access DES from other applications. Thanks to Yolanda García and Rafael Caballero for making possible to declaratively debug Datalog and SQL databases. They are also key authors in the inclusion of test case generation for SQL views. In particular, Yolanda took the implementation effort supported by Rafael. Pascual Julián-Iranzo provided all the help and formal support to develop Fuzzy Datalog. Gabriel Aranda López and Sonia Estévez Martín generated Mac OS X Snow Leopard and Leopard executables, respectively, for versions up to DES 2.6. Enrique Martín Martín fixed the Linux distribution of DES 1.5.0. Fernando Sáenz-López designed and drew the system logo. Finally, thanks to the Spanish MINECO projects SAFER (PID2019-104735RB-C42), CAVI-ART (TIN2013-44742-C4-3-R), CAVI-ART-2 (TIN2017-86217-R), Madrid regional projects BLOQUES-CM (P2018/TCS-4339), and N-GREENS Software-CM (S2013/ICE-2731), UCM grant GR3/14-910502, FAST-STAMP (TIN2008-06622-C03-01), Prometidos-CM (S2009TIC-1465), GPD-UCM (UCM-BSCH-GR35/10-A-910502) and FADoSS-UCM (910398) which supported this work in the context of the University Complutense of Madrid, and its departments: Artificial Intelligence and Software Engineering, and Computer Systems and Programming.

[1] Interestingly, both Datalog and standard SQL are both Turing complete (see for instance a proof for SQL in [PSQL15] which implements a tag system), but no one would use it as a general-purpose language in practical applications.

[2] See section 5 for more details about commands.

[3] The meaning of a relation is the set of facts inferred both extensionally and intensionally from the program.

[5] In file negation.dl, located at the examples distribution directory. Adapted from [RSSWF97].

[6] We discarded the term finite domain predicate to refer to these kind of predicates in order to avoid a possible confusion with finite domain constraints, as this Datalog dialect is not a constraint database in the sense of [Rev02].

[7] One can roughly think of the restricting rules of p as belonging to a different predicate with the same arity but with name -p.

[8] However, note that our approach differs from [Bon90] in at least the following: We allow for rules in the assumption (not only facts), and variables in any assumed rule are not shared out of the rule.

[9] Depending on the selected weak unification algorithm, other arguments are included in the compilations.

[10] Note that Q cannot appear without a data generator (otherwise, it would be an unsafe rule -c.f. Section 5.3.1); in this case, quality/1 represents all the possible values that the quality of a restaurant may take.

[11] Recall that the quality is computed by a rule involving the users, their comments, and the confidences.

[12] We depart here from the usual convention of having three language parts because we separate statements that retrieve tuples (DQL) from the statements that modify tuples (DML).

[14] Note that in this example, the schema for indc has been also provided, but it can be omitted.

[15] Though, more precisely, in Prolog this is the symbol used for non-unifiable pair of terms, whereas \== checks syntax disequality.

[16] Pure Datalog programs are normal logic programs (i.e., function-free) in which all rules are Horn clauses, and a program signature is built with the symbols in the program (no built-in is considered to be part of a pure Datalog program).

[18] However, it is possible that different SQL dialects cannot be appropriately debugged. In particular, for features which are not covered by the SQL grammar in Subsection 4.2.13.

[19] That is, executing the view using as input data for the tables those in the PTC.

[20] For a complementary understanding of this section, the reader is advised to read [Diet87].

[21] A term T1 subsumes a term T2 if T1 is “more general” than T2 and both terms are unifiable, e.g.: p(X,Y) subsumes p(a,Z), p(X,Y) subsumes p(U,V), p(X,Y) subsumes p(U,U), but p(U,U) neither subsumes p(a,b) nor p(X,Y).

[22] The contents of the extension table in this case should be restored instead of being cleared; left for further improvements.

[23] And secondly it would try the goal answer(X), although in this case it is unable because of the non-terminating first goal.

[27] Remember that the system returns all of the possible solutions.