Relational and Allegorical Semantics for Constraint Logic Programming

El cálculo de relaciones binarias fue creado por De Morgan en 1860 para ser posteriormente desarrollado en gran medida por Peirce y Schröder. Tarski, Givant, Freyd y Scedrov demostraron que las álgebras relacionales son capaces de formalizar la lógica de primer orden, la lógica de orden superior así como la teoría de conjuntos. A partir de los resultados matemáticos de Tarski y Freyd, esta tesis desarrolla semánticas denotacionales y operacionales para la programación lógica con restricciones usando el álgebra relacional como base. La idea principal es la utilización del concepto de semántica ejecutable, semánticas cuya característica principal es el que la ejecución es posible utilizando el razonamiento estándar del universo semántico, este caso, razonamiento ecuacional. En el caso de este trabajo, se muestra que las álgebras relacionales distributivas con un operador de punto fijo capturan toda la teoría y metateoría estándar de la programación lógica con restricciones incluyendo los árboles utilizados en la búsqueda de demostraciones. La mayor parte de técnicas de optimización de programas, evaluación parcial e interpretación abstracta pueden ser llevadas a cabo utilizando las semánticas aquí presentadas. La demostración de la corrección de la implementación resulta extremadamente sencilla. En la primera parte de la tesis, un programa lógico con restricciones es traducido a un conjunto de términos relacionales. La interpretación estándar en la teoría de conjuntos de dichas relaciones coincide con la semántica estándar para CLP. Las consultas contra el programa traducido son llevadas a cabo mediante la reescritura de relaciones. Para concluir la primera parte, se demuestra la corrección y equivalencia operacional de esta nueva semántica, así como se define un algoritmo de unificación mediante la reescritura de relaciones. La segunda parte de la tesis desarrolla una semántica para la programación lógica con restricciones usando la teoría de alegorías—versión categórica del álgebra de relaciones—de Freyd. Para ello, se definen dos nuevos conceptos de Categoría Regular de Lawvere y _-Alegoría, en las cuales es posible interpretar un programa lógico. La ventaja fundamental que el enfoque categórico aporta es la definición de una máquina categórica que mejora e sistema de reescritura presentado en la primera parte. Gracias al uso de relaciones tabulares, la máquina modela la ejecución eficiente sin salir de un marco estrictamente formal. Utilizando la reescritura de diagramas, se define un algoritmo para el cálculo de pullbacks en Categorías Regulares de Lawvere. Los dominios de las tabulaciones aportan información sobre la utilización de memoria y variable libres, mientras que el estado compartido queda capturado por los diagramas. La especificación de la máquina induce la derivación formal de un juego de instrucciones eficiente. El marco categórico aporta otras importantes ventajas, como la posibilidad de incorporar tipos de datos algebraicos, funciones y otras extensiones a Prolog, a la vez que se conserva el carácter 100% declarativo de nuestra semántica. ABSTRACT The calculus of binary relations was introduced by De Morgan in 1860, to be greatly developed by Peirce and Schröder, as well as many others in the twentieth century. Using different formulations of relational structures, Tarski, Givant, Freyd, and Scedrov have shown how relation algebras can provide a variable-free way of formalizing first order logic, higher order logic and set theory, among other formal systems. Building on those mathematical results, we develop denotational and operational semantics for Constraint Logic Programming using relation algebra. The idea of executable semantics plays a fundamental role in this work, both as a philosophical and technical foundation. We call a semantics executable when program execution can be carried out using the regular theory and tools that define the semantic universe. Throughout this work, the use of pure algebraic reasoning is the basis of denotational and operational results, eliminating all the classical non-equational meta-theory associated to traditional semantics for Logic Programming. All algebraic reasoning, including execution, is performed in an algebraic way, to the point we could state that the denotational semantics of a CLP program is directly executable. Techniques like optimization, partial evaluation and abstract interpretation find a natural place in our algebraic models. Other properties, like correctness of the implementation or program transformation are easy to check, as they are carried out using instances of the general equational theory. In the first part of the work, we translate Constraint Logic Programs to binary relations in a modified version of the distributive relation algebras used by Tarski. Execution is carried out by a rewriting system. We prove adequacy and operational equivalence of the semantics. In the second part of the work, the relation algebraic approach is improved by using allegory theory, a categorical version of the algebra of relations developed by Freyd and Scedrov. The use of allegories lifts the semantics to typed relations, which capture the number of logical variables used by a predicate or program state in a declarative way. A logic program is interpreted in a _-allegory, which is in turn generated from a new notion of Regular Lawvere Category. As in the untyped case, program translation coincides with program interpretation. Thus, we develop a categorical machine directly from the semantics. The machine is based on relation composition, with a pullback calculation algorithm at its core. The algorithm is defined with the help of a notion of diagram rewriting. In this operational interpretation, types represent information about memory allocation and the execution mechanism is more efficient, thanks to the faithful representation of shared state by categorical projections. We finish the work by illustrating how the categorical semantics allows the incorporation into Prolog of constructs typical of Functional Programming, like abstract data types, and strict and lazy functions.

Parallelizing irregular and pointer-based computations automatically: perspectives from logic and constraint programming

Irregular computations pose sorne of the most interesting and challenging problems in automatic parallelization. Irregularity appears in certain kinds of numerical problems and is pervasive in symbolic applications. Such computations often use dynamic data structures, which make heavy use of pointers. This complicates all the steps of a parallelizing compiler, from independence detection to task partitioning and placement. Starting in the mid 80s there has been significant progress in the development of parallelizing compilers for logic pro­gramming (and more recently, constraint programming) resulting in quite capable paralle­lizers. The typical applications of these paradigms frequently involve irregular computations, and make heavy use of dynamic data structures with pointers, since logical variables represent in practice a well-behaved form of pointers. This arguably makes the techniques used in these compilers potentially interesting. In this paper, we introduce in a tutoríal way, sorne of the problems faced by parallelizing compilers for logic and constraint programs and provide pointers to sorne of the significant progress made in the area. In particular, this work has resulted in a series of achievements in the areas of inter-procedural pointer aliasing analysis for independence detection, cost models and cost analysis, cactus-stack memory management, techniques for managing speculative and irregular computations through task granularity control and dynamic task allocation such as work-stealing schedulers), etc.

Incremental analysis of constraint logic programs

Global analyzers traditionally read and analyze the entire program at once, in a nonincremental way. However, there are many situations which are not well suited to this simple model and which instead require reanalysis of certain parts of a program which has already been analyzed. In these cases, it appears inecient to perform the analysis of the program again from scratch, as needs to be done with current systems. We describe how the xed-point algorithms used in current generic analysis engines for (constraint) logic programming languages can be extended to support incremental analysis. The possible changes to a program are classied into three types: addition, deletion, and arbitrary change. For each one of these, we provide one or more algorithms for identifying the parts of the analysis that must be recomputed and for performing the actual recomputation. The potential benets and drawbacks of these algorithms are discussed. Finally, we present some experimental results obtained with an implementation of the algorithms in the PLAI generic abstract interpretation framework. The results show signicant benets when using the proposed incremental analysis algorithms.

Global analysis of constraint logic programs

This article presents and illustrates a practical approach to the dataow analysis of constraint logic programming languages using abstract interpretation. It is rst argued that from the framework point of view it suces to propose relatively simple extensions of traditional analysis methods which have already been proved useful and practical and for exist. This is shown by proposing a simple extension of Bruynooghes traditional framework which allows it to analyze constraint logic programs. Then and using this generalized framework two abstract domains and their required abstract functions are presented the rst abstract domain approximates deniteness information and the second one freeness. Finally an approach for cobining those domains is proposed The two domains and their combination have been implemented and used in the analysis of CLP and Prolog III applications. Results from this implementation showing its performance and accuracy are also presented

Some challenges for constraint programming

We propose a number of challenges for future constraint programming systems, including improvements in implementation technology (using global analysis based optimization and parallelism), debugging facilities, and the extensión of the application domain to distributed, global programming. We also briefly discuss how we are exploring techniques to meet these challenges in the context of the development of the CIAO constraint logic programming system.

Strategic directions in constraint programming

An abstract is not available.

CLP Projection for Constraint Handling Rules

This paper introduces and studies the notion of CLP projection for Constraint Handling Rules (CHR). The CLP projection consists of a naive translation of CHR programs into Constraint Logic Programs (CLP). We show that the CLP projection provides a safe operational and declarative approximation for CHR programs. We demónstrate moreover that a confluent CHR program has a least model, which is precisely equal to the least model of its CLP projection (closing henee a ten year-old conjecture by Abdenader et al.). Finally, we illustrate how the notion of CLP projection can be used in practice to apply CLP analyzers to CHR. In particular, we show results from applying AProVE to prove termination, and CiaoPP to infer both complexity upper bounds and types for CHR programs.

Combined static and dynamic assertion-based debugging of constraint logic programs

We propose a general framework for assertion-based debugging of constraint logic programs. Assertions are linguistic constructions for expressing properties of programs. We define several assertion schemas for writing (partial) specifications for constraint logic programs using quite general properties, including user-defined programs. The framework is aimed at detecting deviations of the program behavior (symptoms) with respect to the given assertions, either at compile-time (i.e., statically) or run-time (i.e., dynamically). We provide techniques for using information from global analysis both to detect at compile-time assertions which do not hold in at least one of the possible executions (i.e., static symptoms) and assertions which hold for all possible executions (i.e., statically proved assertions). We also provide program transformations which introduce tests in the program for checking at run-time those assertions whose status cannot be determined at compile-time. Both the static and the dynamic checking are provably safe in the sense that all errors flagged are definite violations of the pecifications. Finally, we report briefly on the currently implemented instances of the generic framework.

Interfacing prolog and VRML and its application to constraint visualization

A number of data description languages initially designed as standards for trie WWW are currently being used to implement user interfaces to programs. This is done independently of whether such programs are executed in the same or a different host as trie one running the user interface itself. The advantage of this approach is that it provides a portable, standardized, and easy to use solution for the application programmer, and a familiar behavior for the user, typically well versed in the use of WWW browsers. Among the proposed standard description languages, VRML is a aimed at representing three dimensional scenes including hyperlink capabilities. VRML is already used as an import/export format in many 3-D packages and tools, and has been shown effective in displaying complex objects and scenarios. We propose and describe a Prolog library which allows parsing and checking VRML code, transforming it, and writing it out as VRML again. The library converts such code to an internal representation based on first order terms which can then be arbitrarily manipulated. We also present as an example application the use of this library to implement a novel 3-D visualization for examining and understanding certain aspects of the behavior of CLP(FD) programs.

A framework for assertion-based debugging in constraint logic programming

We propose a general framework for assertion-based debugging of constraint logic programs. Assertions are linguistic constructions which allow expressing properties of programs. We define assertion schemas which allow writing (partial) specifications for constraint logic programs using quite general properties, including user-defined programs. The framework is aimed at detecting deviations of the program behavior (symptoms) with respect to the given assertions, either at compile-time or run-time. We provide techniques for using information from global analysis both to detect at compile-time assertions which do not hold in at least one of the possible executions (i.e., static symptoms) and assertions which hold for all possible executions (i.e., statically proved assertions). We also provide program transformations which introduce tests in the program for checking at run-time those assertions whose status cannot be determined at compile-time. Both the static and the dynamic checking are provably safe in the sense that all errors flagged are definite violations of the specifications. Finally, we report on an implemented instance of the assertion language and framework.

Towards a concurrent semantics-based analysis of CC and CLP. principles and practice of constraint programming

Abstract is not available.

Some methodological issues in the design of CIAO - A generic, parallel concurrent constraint system

We informally discuss several issues related to the parallel execution of logic programming systems and concurrent logic programming systems, and their generalization to constraint programming. We propose a new view of these systems, based on a particular definition of parallelism. We argüe that, under this view, a large number of the actual systems and models can be explained through the application, at different levéis of granularity, of only a few basic principies: determinism, non-failure, independence (also referred to as stability), granularity, etc. Also, and based on the convergence of concepts that this view brings, we sketch a model for the implementation of several parallel constraint logic programming source languages and models based on a common, generic abstract machine and an intermedíate kernel language.

Independence in constraint logic programs

Studying independence of literals, variables, and substitutions has proven very useful in the context of logic programming (LP). Here we study independence in the broader context of constraint logic programming (CLP). We show that a naive extrapolation of the LP definitions of independence to CLP is unsatisfactory (in fact, wrong) for two reasons. First, because interaction between variables through constraints is more complex than in the case of logic programming. Second, in order to ensure the efUciency of several optimizations not only must independence of the search space be considered, but also an orthogonal issue - "independence of constraint solving." We clarify these issues by proposing various types of search independence and constraint solver independence, and show how they can be combined to allow different independence-related optimizations, from parallelism to intelligent backtracking. Sufficient conditions for independence which can be evaluated "a-priori" at run-time are also proposed. Our results suggest that independence, provided a suitable definition is chosen, is even more useful in CLP than in LP.

Abstract verification and debugging of constraint logic programs

The technique of Abstract Interpretation [13] has allowed the development of sophisticated program analyses which are provably correct and practical. The semantic approximations produced by such analyses have been traditionally applied to optimization during program compilation. However, recently, novel and promising applications of semantic approximations have been proposed in the more general context of program verification and debugging [3],[10],[7].

Automatic parallelization of irregular and pointer-based computations: perspectives from logic and constraint programming

Irregular computations pose some of the most interesting and challenging problems in automatic parallelization. Irregularity appears in certain kinds of numerical problems and is pervasive in symbolic applications. Such computations often use dynamic data structures which make heavy use of pointers. This complicates all the steps of a parallelizing compiler, from independence detection to task partitioning and placement. In the past decade there has been significant progress in the development of parallelizing compilers for logic programming and, more recently, constraint programming. The typical applications of these paradigms frequently involve irregular computations, which arguably makes the techniques used in these compilers potentially interesting. In this paper we introduce in a tutorial way some of the problems faced by parallelizing compilers for logic and constraint programs. These include the need for inter-procedural pointer aliasing analysis for independence detection and having to manage speculative and irregular computations through task granularity control and dynamic task allocation. We also provide pointers to some of the progress made in these áreas. In the associated talk we demónstrate representatives of several generations of these parallelizing compilers.