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.

Data-Flow analysis of prolog programs with extra-logical features

Abstract interpretation-based data-flow analysis of logic programs is at this point relatively well understood from the point of view of general frameworks and abstract domains. On the other hand, comparatively little attention has been given to the problems which arise when analysis of a full, practical dialect of the Prolog language is attempted, and only few solutions to these problems have been proposed to date. Such problems relate to dealing correctly with all builtins, including meta-logical and extra-logical predicates, with dynamic predicates (where the program is modified during execution), and with the absence of certain program text during compilation. Existing proposals for dealing with such issues generally restrict in one way or another the classes of programs which can be analyzed if the information from analysis is to be used for program optimization. This paper attempts to fill this gap by considering a full dialect of Prolog, essentially following the recently proposed ISO standard, pointing out the problems that may arise in the analysis of such a dialect, and proposing a combination of known and novel solutions that together allow the correct analysis of arbitrary programs using the full power of the language.

Embedding logical frameworks in scala

El Framework Lógico de Edimburgo ha demostrado ser una poderosa herramienta en el estudio formal de sistemas deductivos, como por ejemplo lenguajes de programación. Sin embargo su principal implementación, el sistema Twelf, carece de expresividad, obligando al programador a escribir código repetitivo. Este proyecto presenta una manera alternativa de utilizar Twelf: a través de un EDSL (Lenguaje Embebido de Dominio Específico) en Scala que permite representar firmas del Framework Lógico, y apoyándonos en Twelf como backend para la verificación, abrimos la puerta a diversas posibilidades en términos de metaprogramación. El código fuente, así como instrucciones para instalar y configurar, está accesible en https://github.com/akathorn/elfcala. ---ABSTRACT---The Edinburgh Logical Framework has proven to be to be a powerful tool in the formal study of deductive systems, such as programming languages. However, its main implementation, the Twelf system, lacks expressiveness, requiring the programmer to write repetitive code. This project presents an alternative way of using Twelf: by providing a Scala EDSL (Embedded Domain Specific Language) that can encode Logical Framework signatures and relying on Twelf as a backend for the verification, we open the door to different possibilities in terms of metaprogramming. The source code, along with instructions to install and configure, is accessible at https://github.com/akathorn/elfcala

Parallel execution of Prolog programs: a survey

Since the early days of logic programming, researchers in the field realized the potential for exploitation of parallelism present in the execution of logic programs. Their high-level nature, the presence of nondeterminism, and their referential transparency, among other characteristics, make logic programs interesting candidates for obtaining speedups through parallel execution. At the same time, the fact that the typical applications of logic programming frequently involve irregular computations, make heavy use of dynamic data structures with logical variables, and involve search and speculation, makes the techniques used in the corresponding parallelizing compilers and run-time systems potentially interesting even outside the field. The objective of this article is to provide a comprehensive survey of the issues arising in parallel execution of logic programming languages along with the most relevant approaches explored to date in the field. Focus is mostly given to the challenges emerging from the parallel execution of Prolog programs. The article describes the major techniques used for shared memory implementation of Or-parallelism, And-parallelism, and combinations of the two. We also explore some related issues, such as memory management, compile-time analysis, and execution visualization.

A New End-User Composition Model to Empower Knowledge Workers to Develop Rich Internet Applications

Enabling real end-user programming development is the next logical stage in the evolution of Internetwide service-based applications. Even so, the vision of end users programming their own web-based solutions has not yet materialized. This will continue to be so unless both industry and the research community rise to the ambitious challenge of devising an end-to-end compositional model for developing a new age of end-user web application development tools. This paper describes a new composition model designed to empower programming-illiterate end users to create and share their own off-the-shelf rich Internet applications in a fully visual fashion. This paper presents the main insights and outcomes of our research and development efforts as part of a number of successful European Union research projects. A framework implementing this model was developed as part of the European Seventh Framework Programme FAST Project and the Spanish EzWeb Project and allowed us to validate the rationale behind our approach.

Knowledgeable Feedback via a Cast of Virtual Characters with Different Competences

DynaLearn (http://www.DynaLearn.eu) develops a cognitive artefact that engages learners in an active learning by modelling process to develop conceptual system knowledge. Learners create external representations using diagrams. The diagrams capture conceptual knowledge using the Garp3 Qualitative Reasoning (QR) formalism [2]. The expressions can be simulated, confronting learners with the logical consequences thereof. To further aid learners, DynaLearn employs a sequence of knowledge representations (Learning Spaces, LS), with increasing complexity in terms of the modelling ingredients a learner can use [1]. An online repository contains QR models created by experts/teachers and learners. The server runs semantic services [4] to generate feedback at the request of learners via the workbench. The feedback is communicated to the learner via a set of virtual characters, each having its own competence [3]. A specific feedback thus incorporates three aspects: content, character appearance, and a didactic setting (e.g. Quiz mode). In the interactive event we will demonstrate the latest achievements of the DynaLearn project. First, the 6 learning spaces for learners to work with. Second, the generation of feedback relevant to the individual needs of a learner using Semantic Web technology. Third, the verbalization of the feedback via different animated virtual characters, notably: Basic help, Critic, Recommender, Quizmaster & Teachable agen

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.

Run-time Scalable Architecture for Deblocking Filtering in H.264/AVC-SVC Video Codecs

Systems relying on fixed hardware components with a static level of parallelism can suffer from an underuse of logical resources, since they have to be designed for the worst-case scenario. This problem is especially important in video applications due to the emergence of new flexible standards, like Scalable Video Coding (SVC), which offer several levels of scalability. In this paper, Dynamic and Partial Reconfiguration (DPR) of modern FPGAs is used to achieve run-time variable parallelism, by using scalable architectures where the size can be adapted at run-time. Based on this proposal, a scalable Deblocking Filter core (DF), compliant with the H.264/AVC and SVC standards has been designed. This scalable DF allows run-time addition or removal of computational units working in parallel. Scalability is offered together with a scalable parallelization strategy at the macroblock (MB) level, such that when the size of the architecture changes, MB filtering order is modified accordingly

Partial order and contextual net semantics for atomic and locally atomic CC programs

We present two concurrent semantics (i.e. semantics where concurrency is explicitely represented) for CC programs with atomic tells. One is based on simple partial orders of computation steps, while the other one is based on contextual nets and it is an extensión of a previous one for eventual CC programs. Both such semantics allow us to derive concurrency, dependency, and nondeterminism information for the considered languages. We prove some properties about the relation between the two semantics, and also about the relation between them and the operational semantics. Moreover, we discuss how to use the contextual net semantics in the context of CLP programs. More precisely, by interpreting concurrency as possible parallelism, our semantics can be useful for a safe parallelization of some CLP computation steps. Dually, the dependency information may also be interpreted as necessary sequentialization, thus possibly exploiting it for the task of scheduling CC programs. Moreover, our semantics is also suitable for CC programs with a new kind of atomic tell (called locally atomic tell), which checks for consistency only the constraints it depends on. Such a tell achieves a reasonable trade-off between efficiency and atomicity, since the checked constraints can be stored in a local memory and are thus easily accessible even in a distributed implementation.

Identification of logically related heap regions

This paper introduces a novel technique for identifying logically related sections of the heap such as recursive data structures, objects that are part of the same multi-component structure, and related groups of objects stored in the same collection/array. When combined withthe lifetime properties of these structures, this information can be used to drive a range of program optimizations including pool allocation, object co-location, static deallocation, and region-based garbage collection. The technique outlined in this paper also improves the efficiency of the static analysis by providing a normal form for the abstract models (speeding the convergence of the static analysis). We focus on two techniques for grouping parts of the heap. The first is a technique for precisely identifying recursive data structures in object-oriented programs based on the types declared in the program. The second technique is a novel method for grouping objects that make up the same composite structure and that allows us to partition the objects stored in a collection/array into groups based on a similarity relation. We provide a parametric component in the similarity relation in order to support specific analysis applications (such as a numeric analysis which would need to partition the objects based on numeric properties of the fields). Using the Barnes-Hut benchmark from the JOlden suite we show how these grouping methods can be used to identify various types of logical structures allowing the application of many region-based program optimizations.

A static heap analysis for shape and connectivity: Unified memory analysis: The base framework

Modeling the evolution of the state of program memory during program execution is critical to many parallehzation techniques. Current memory analysis techniques either provide very accurate information but run prohibitively slowly or produce very conservative results. An approach based on abstract interpretation is presented for analyzing programs at compile time, which can accurately determine many important program properties such as aliasing, logical data structures and shape. These properties are known to be critical for transforming a single threaded program into a versión that can be run on múltiple execution units in parallel. The analysis is shown to be of polynomial complexity in the size of the memory heap. Experimental results for benchmarks in the Jolden suite are given. These results show that in practice the analysis method is efflcient and is capable of accurately determining shape information in programs that créate and manipúlate complex data structures.

From eventual to atomic and locally atomic CC programs: A concurrent semantics

We present a concurrent semantics (i.e. a semantics where concurrency is explicitely represented) for CC programs with atomic tells. This allows to derive concurrency, dependency, and nondeterminism information for such languages. The ability to treat failure information puts CLP programs also in the range of applicability of our semantics: although such programs are not concurrent, the concurrency information derived in the semantics may be interpreted as possible parallelism, thus allowing to safely parallelize those computation steps which appear to be concurrent in the net. Dually, the dependency information may also be interpreted as necessary sequentialization, thus possibly exploiting it to schedule CC programs. The fact that the semantical structure contains dependency information suggests a new tell operation, which checks for consistency only the constraints it depends on, achieving a reasonable trade-off between efficiency and atomicity.

ACE: And/or-parallel copying-based execution of logic programs

In this paper we present a novel execution model for parallel implementation of logic programs which is capable of exploiting both independent and-parallelism and or-parallelism in an efficient way. This model extends the stack copying approach, which has been successfully applied in the Muse system to implement or-parallelism, by integrating it with proven techniques used to support independent and-parallelism. We show how all solutions to non-deterministic andparallel goals are found without repetitions. This is done through recomputation as in Prolog (and in various and-parallel systems, like &-Prolog and DDAS), i.e., solutions of and-parallel goals are not shared. We propose a scheme for the efficient management of the address space in a way that is compatible with the apparently incompatible requirements of both and- and or-parallelism. We also show how the full Prolog language, with all its extra-logical features, can be supported in our and-or parallel system so that its sequential semantics is preserved. The resulting system retains the advantages of both purely or-parallel systems as well as purely and-parallel systems. The stack copying scheme together with our proposed memory management scheme can also be used to implement models that combine dependent and-parallelism and or-parallelism, such as Andorra and Prometheus.

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

Abstract is not available.

Towards structured state threading in prolog

It is very often the case that programs require passing, maintaining, and updating some notion of state. Prolog programs often implement such stateful computations by carrying this state in predicate arguments (or, alternatively, in the internal datábase). This often causes code obfuscation, complicates code reuse, introduces dependencies on the data model, and is prone to incorrect propagation of the state information among predicate calis. To partly solve these problems, we introduce contexts as a consistent mechanism for specifying implicit arguments and its threading in clause goals. We propose a notation and an interpretation for contexts, ranging from single goals to complete programs, give an intuitive semantics, and describe a translation into standard Prolog. We also discuss a particular light-weight implementation in Ciao Prolog, and we show the usefulness of our proposals on a series of examples and applications, including code directiy using contexts, DCGs, extended DCGs, logical loops and other custom control structures.