Dynamic term size computation in logic programs via program transformation

Knowing the size of the terms to which program variables are bound at run-time in logic programs is required in a class of applications related to program optimization such as, for example, recursion elimination and granularity analysis. Such size is difficult to even approximate at compile time and is thus generally computed at run-time by using (possibly predefined) predicates which traverse the terms involved. We propose a technique based on program transformation which has the potential of performing this computation much more efficiently. The technique is based on finding program procedures which are called before those in which knowledge regarding term sizes is needed and which traverse the terms whose size is to be determined, and transforming such procedures so that they compute term sizes "on the fly". We present a systematic way of determining whether a given program can be transformed in order to compute a given term size at a given program point without additional term traversal. Also, if several such transformations are possible our approach allows finding minimal transformations under certain criteria. We also discuss the advantages and present some applications of our technique.

Design and implementation of a modular interface to integrate CLP and tabled execution

Logic programming (LP) is a family of high-level programming languages which provides high expressive power. With LP, the programmer writes the properties of the result and / or executable specifications instead of detailed computation steps. Logic programming systems which feature tabled execution and constraint logic programming have been shown to increase the declarativeness and efficiency of Prolog, while at the same time making it possible to write very expressive programs. Tabled execution avoids infinite failure in some cases, while improving efficiency in programs which repeat computations. CLP reduces the search tree and brings the power of solving (in)equations over arbitrary domains. Similarly to the LP case, CLP systems can also benefit from the power of tabling. Previous implementations which take ful advantage of the ideas behind tabling (e.g., forcing suspension, answer subsumption, etc. wherever it is necessary to avoid recomputation and terminate whenever possible) did not offer a simple, well-documented, easy-to-understand interface. This would be necessary to make the integratation of arbitrary CLP solvers into existing tabling systems possible. This clearly hinders a more widespread usage of the combination of both facilities. In this thesis we examine the requirements that a constraint solver must fulfill in order to be interfaced with a tabling system. We propose and implement a framework, which we have called Mod TCLP, with a minimal set of operations (e.g., entailment checking and projection) which the constraint solver has to provide to the tabling engine. We validate the design of Mod TCLP by a series of use cases: we re-engineer a previously existing tabled constrain domain (difference constraints) which was connected in an ad-hoc manner with the tabling engine in Ciao Prolog; we integrateHolzbauer’s CLP(Q) implementationwith Ciao Prolog’s tabling engine; and we implement a constraint solver over (finite) lattices. We evaluate its performance with several benchmarks that implement a simple abstract interpreter whose fixpoint is reached by means of tabled execution, and whose domain operations are handled by the constraint over (finite) lattices, where TCLP avoids recomputing subsumed abstractions.---ABSTRACT---La programación lógica con restricciones (CLP) y la tabulación son extensiones de la programación lógica que incrementan la declaratividad y eficiencia de Prolog, al mismo tiempo que hacen posible escribir programasmás expresivos. Las implementaciones anteriores que integran completamente ambas extensiones, incluyendo la suspensión de la ejecución de objetivos siempre que sea necesario, la implementación de inclusión (subsumption) de respuestas, etc., en todos los puntos en los que sea necesario para evitar recomputaciones y garantizar la terminación cuando sea posible, no han proporcionan una interfaz simple, bien documentada y fácil de entender. Esta interfaz es necesaria para permitir integrar resolutores de CLP arbitrarios en el sistema de tabulación. Esto claramente dificulta un uso más generalizado de la integración de ambas extensiones. En esta tesis examinamos los requisitos que un resolutor de restricciones debe cumplir para ser integrado con un sistema de tabulación. Proponemos un esquema (y su implementación), que hemos llamadoMod TCLP, que requiere un reducido conjunto de operaciones (en particular, y entre otras, entailment y proyección de almacenes de restricciones) que el resolutor de restricciones debe ofrecer al sistema de tabulación. Hemos validado el diseño de Mod TCLP con una serie de casos de uso: la refactorización de un sistema de restricciones (difference constraints) previamente conectado de un modo ad-hoc con la tabulación de Ciao Prolog; la integración del sistema de restricciones CLP(Q) de Holzbauer; y la implementación de un resolutor de restricciones sobre retículos finitos. Hemos evaluado su rendimiento con varios programas de prueba, incluyendo la implementación de un intérprete abstracto que alcanza su punto fijo mediante el sistema de tabulación y en el que las operaciones en el dominio son realizadas por el resolutor de restricciones sobre retículos (finitos) donde TCLP evita la recomputación de valores abstractos de las variables ya contenidos en llamadas anteriores.

Deriving a fixpoint computation algorithm for top-down abstract interpretation of logic programs

Bruynooghe described a framework for the top-down abstract interpretation of logic programs. In this framework, abstract interpretation is carried out by constructing an abstract and-or tree in a top-down fashion for a given query and program. Such an abstract interpreter requires fixpoint computation for programs which contain recursive predicates. This paper presents in detail a fixpoint algorithm that has been developed for this purpose and the motivation behind it. We start off by describing a simple-minded algorithm. After pointing out its shortcomings, we present a series of refinements to this algorithm, until we reach the final version. The aim is to give an intuitive grasp and provide justification for the relative complexity of the final algorithm. We also present an informal proof of correctness of the algorithm and some results obtained from an implementation.

A methodology for granularity-based control of parallelism in logic programs

Several types of parallelism can be exploited in logic programs while preserving correctness and efficiency, i.e. ensuring that the parallel execution obtains the same results as the sequential one and the amount of work performed is not greater. However, such results do not take into account a number of overheads which appear in practice, such as process creation and scheduling, which can induce a slow-down, or, at least, limit speedup, if they are not controlled in some way. This paper describes a methodology whereby the granularity of parallel tasks, i.e. the work available under them, is efficiently estimated and used to limit parallelism so that the effect of such overheads is controlled. The run-time overhead associated with the approach is usually quite small, since as much work is done at compile time as possible. Also,a number of run-time optimizations are proposed. Moreover, a static analysis of the overhead associated with the granularity control process is performed in order to decide its convenience. The performance improvements resulting from the incorporation of grain size control are shown to be quite good, specially for systems with medium to large parallel execution overheads.

Efficient term size computation for granularity control

Knowing the size of the terms to which program variables are bound at run-time in logic programs is required in a class of optimizations which includes granularity control and recursion elimination. Such size is difficult to even approximate at compile time and is thus generally computed at run-time by using (possibly predeñned) predicates which traverse the terms involved. We propose a technique which has the potential of performing this computation much more efficiently. The technique is based on ñnding program procedures which are called before those in which knowledge regarding term sizes is needed and which traverse the terms whose size is to be determined, and transforming such procedures so that they compute term sizes "on the fly". We present a systematic way of determining whether a given program can be transformed in order to compute a given term size at a given program point without additional term traversal. Also, if several such transformations are possible our approach allows ñnding minimal transformations under certain criteria. We also discuss the advantages and applications of our technique (specifically in the task of granularity control) and present some performance results.

A comparative study of methods for automatic compile-time parallelization of logic programs

This paper presents a study of the effectiveness of three different algorithms for the parallelization of logic programs based on compile-time detection of independence among goals. The algorithms are embedded in a complete parallelizing compiler, which incorporates different abstract interpretation-based program analyses. The complete system shows the task of automatic program parallelization to be practical. The trade-offs involved in using each of the algorithms in this task are studied experimentally, weaknesses of these identified, and possible improvements discussed.

Towards granularity based control of parallelism in logic programs

Several types of parallelism can be exploited in logic programs while preserving correctness and efficiency, i.e. ensuring that the parallel execution obtains the same results as the sequential one and the amount of work performed is not greater. However, such results do not take into account a number of overheads which appear in practice, such as process creation and scheduling, which can induce a slow-down, or, at least, limit speedup, if they are not controlled in some way. This paper describes a methodology whereby the granularity of parallel tasks, i.e. the work available under them, is efficiently estimated and used to limit parallelism so that the effect of such overheads is controlled. The run-time overhead associated with the approach is usually quite small, since as much work is done at compile time as possible. Also, a number of run-time optimizations are proposed. Moreover, a static analysis of the overhead associated with the granularity control process is performed in order to decide its convenience. The performance improvements resulting from the incorporation of grain size control are shown to be quite good, specially for systems with médium to large parallel execution overheads.

Analyzing logic programs with dynamic scheduling

Traditional logic programming languages, such as Prolog, use a fixed left-to-right atom scheduling rule. Recent logic programming languages, however, usually provide more flexible scheduling in which computation generally proceeds leftto- right but in which some calis are dynamically "delayed" until their arguments are sufRciently instantiated to allow the cali to run efficiently. Such dynamic scheduling has a significant cost. We give a framework for the global analysis of logic programming languages with dynamic scheduling and show that program analysis based on this framework supports optimizations which remove much of the overhead of dynamic scheduling.

Tools for Search Tree Visualization: The APT Tool

The control part of the execution of a constraint logic program can be conceptually shown as a search-tree, where nodes correspond to calis, and whose branches represent conjunctions and disjunctions. This tree represents the search space traversed by the program, and has also a direct relationship with the amount of work performed by the program. The nodes of the tree can be used to display information regarding the state and origin of instantiation of the variables involved in each cali. This depiction can also be used for the enumeration process. These are the features implemented in APT, a tool which runs constraint logic programs while depicting a (modified) search-tree, keeping at the same time information about the state of the variables at every moment in the execution. This information can be used to replay the execution at will, both forwards and backwards in time. These views can be abstracted when the size of the execution requires it. The search-tree view is used as a framework onto which constraint-level visualizations (such as those presented in the following chapter) can be attached.

Two efficient representations for set-sharing analysis in logic programs

Set-Sharing analysis, the classic Jacobs and Langen's domain, has been widely used to infer several interesting properties of programs at compile-time such as occurs-check reduction, automatic parallelization, flnite-tree analysis, etc. However, performing abstract uniflcation over this domain implies the use of a closure operation which makes the number of sharing groups grow exponentially. Much attention has been given in the literature to mitígate this key inefficiency in this otherwise very useful domain. In this paper we present two novel alternative representations for the traditional set-sharing domain, tSH and tNSH. which compress efficiently the number of elements into fewer elements enabling more efficient abstract operations, including abstract uniflcation, without any loss of accuracy. Our experimental evaluation supports that both representations can reduce dramatically the number of sharing groups showing they can be more practical solutions towards scalable set-sharing.

Towards execution time estimation for logic programs via static analysis and profiling

Effective static analyses have been proposed which infer bounds on the number of resolutions or reductions. These have the advantage of being independent from the platform on which the programs are executed and have been shown to be useful in a number of applications, such as granularity control in parallel execution. On the other hand, in distributed computation scenarios where platforms with different capabilities come into play, it is necessary to express costs in metrics that include the characteristics of the platform. In particular, it is specially interesting to be able to infer upper and lower bounds on actual execution times. With this objective in mind, we propose an approach which combines compile-time analysis for cost bounds with a one-time profiling of the platform in order to determine the valúes of certain parameters for a given platform. These parameters calíbrate a cost model which, from then on, is able to compute statically time bound functions for procedures and to predict with a significant degree of accuracy the execution times of such procedures in the given platform. The approach has been implemented and integrated in the CiaoPP system.

A generic framework for the analysis and specialization of logic programs

The relationship between abstract interpretation and partial deduction has received considerable attention and (partial) integrations have been proposed starting from both the partial deduction and abstract interpretation perspectives. In this work we present what we argüe is the first fully described generic algorithm for efñcient and precise integration of abstract interpretation and partial deduction. Taking as starting point state-of-the-art algorithms for context-sensitive, polyvariant abstract interpretation and (abstract) partial deduction, we present an algorithm which combines the best of both worlds. Key ingredients include the accurate success propagation inherent to abstract interpretation and the powerful program transformations achievable by partial deduction. In our algorithm, the calis which appear in the analysis graph are not analyzed w.r.t. the original definition of the procedure but w.r.t. specialized definitions of these procedures. Such specialized definitions are obtained by applying both unfolding and abstract executability. Our framework is parametric w.r.t. different control strategies and abstract domains. Different combinations of such parameters correspond to existing algorithms for program analysis and specialization. Simultaneously, our approach opens the door to the efñcient computation of strictly more precise results than those achievable by each of the individual techniques. The algorithm is now one of the key components of the CiaoPP analysis and specialization system.

Towards dynamic term size computation via program transformation

Knowing the size of the terms to which program variables are bound at run-time in logic programs is required in a class of applications related to program optimization such as, for example, recursion elimination and granularity analysis. Such size is difficult to even approximate at compile time and is thus generally computed at run-time by using (possibly predefined) predicates which traverse the terms involved. We propose a technique based on program transformation which has the potential of performing this computation much more efficiently. The technique is based on finding program procedures which are called before those in which knowledge regarding term sizes is needed and which traverse the terms whose size is to be determined, and transforming such procedures so that they compute term sizes "on the fly". We present a systematic way of determining whether a given program can be transformed in order to compute a given term size at a given program point without additional term traversal. Also, if several such transformations are possible our approach allows finding minimal transformations under certain criteria. We also discuss the advantages and present some applications of our technique.

Analysis of concurrent constraint logic programs with a fixed scheduling rule

The analysis of concurrent constraint programs is a challenge due to the inherently concurrent behaviour of its computational model. However, most implementations of the concurrent paradigm can be viewed as a computation with a fixed scheduling rule which suspends some goals so that their execution is postponed until some condition awakens them. For a certain kind of properties, an analysis defined in these terms is correct. Furthermore, it is much more tractable, and in addition can make use of existing analysis technology for the underlying fixed computation rule. We show how this can be done when the starting point is a framework for the analysis of sequential programs. The resulting analysis, which incorporates suspensions, is adequate for concurrent models where concurrency is localized, e.g. the Andorra model. We refine the analysis for this particular case. Another model in which concurrency is preferably encapsulated, and thus suspensions are local to parts of the computation, is that of CIAO. Nonetheless, the analysis scheme can be generalized to models with global concurrency. We also sketch how this could be done, and we show how the resulting analysis framework could be used for analyzing typical properties, such as suspensión freeness.

Combining static analysis and profiling for estimating execution times in logic programs

Effective static analyses have been proposed which allow inferring functions which bound the number of resolutions or reductions. These have the advantage of being independent from the platform on which the programs are executed and such bounds have been shown useful in a number of applications, such as granularity control in parallel execution. On the other hand, in certain distributed computation scenarios where different platforms come into play, with each platform having different capabilities, it is more interesting to express costs in metrics that include the characteristics of the platform. In particular, it is specially interesting to be able to infer upper and lower bounds on actual execution time. With this objective in mind, we propose a method which allows inferring upper and lower bounds on the execution times of procedures of a program in a given execution platform. The approach combines compile-time cost bounds analysis with a one-time profiling of the platform in order to determine the values of certain constants for that platform. These constants calibrate a cost model which from then on is able to compute statically time bound functions for procedures and to predict with a significant degree of accuracy the execution times of such procedures in the given platform. The approach has been implemented and integrated in the CiaoPP system.