Strict and non-strict independent and-parallelism in logic programs: Correctness, efficiency, and compile-time conditions.

This paper presents some fundamental properties of independent and-parallelism and extends its applicability by enlarging the class of goals eligible for parallel execution. A simple model of (independent) and-parallel execution is proposed and issues of correctness and efficiency discussed in the light of this model. Two conditions, "strict" and "non-strict" independence, are defined and then proved sufficient to ensure correctness and efñciency of parallel execution: if goals which meet these conditions are executed in parallel the solutions obtained are the same as those produced by standard sequential execution. Also, in absence of failure, the parallel proof procedure does not genérate any additional work (with respect to standard SLD-resolution) while the actual execution time is reduced. Finally, in case of failure of any of the goals no slow down will occur. For strict independence the results are shown to hold independently of whether the parallel goals execute in the same environment or in sepárate environments. In addition, a formal basis is given for the automatic compile-time generation of independent and-parallelism: compile-time conditions to efficiently check goal independence at run-time are proposed and proved sufficient. Also, rules are given for constructing simpler conditions if information regarding the binding context of the goals to be executed in parallel is available to the compiler.

On the correctness and efficiency of independent and-parallelism in logic programs

This paper presents and proves some fundamental results for independent and-parallelism (IAP). First, the paper treats the issues of correctness and efficiency: after defining strict and non-strict goal independence, it is proved that if strictly independent goals are executed in parallel the solutions obtained are the same as those produced by standard sequential execution. It is also shown that, in the absence of failure, the parallel proof procedure doesn't genérate any additional work (with respect to standard SLDresolution) while the actual execution time is reduced. The same results hold even if non-strictly independent goals are executed in parallel, provided a trivial rewriting of such goals is performed. In addition, and most importantly, treats the issue of compile-time generation of IAP by proposing conditions, to be written at compile-time, to efficiently check strict and non-strict goal independence at run-time and proving the sufficiency of such conditions. It is also shown how simpler conditions can be constructed if some information regarding the binding context of the goals to be executed in parallel is available to the compiler trough either local or program-level analysis. These results therefore provide a formal basis for the automatic compile-time generation of IAP. As a corollary of such results, the paper also proves that negative goals are always non-strictly independent, and that goals which share a first occurrence of an existential variable are never independent.

On correctness in RDF stream processor benchmarking

Two complementary benchmarks have been proposed so far for the evaluation and continuous improvement of RDF stream processors: SRBench and LSBench. They put a special focus on different features of the evaluated systems, including coverage of the streaming extensions of SPARQL supported by each processor, query processing throughput, and an early analysis of query evaluation correctness, based on comparing the results obtained by different processors for a set of queries. However, none of them has analysed the operational semantics of these processors in order to assess the correctness of query evaluation results. In this paper, we propose a characterization of the operational semantics of RDF stream processors, adapting well-known models used in the stream processing engine community: CQL and SECRET. Through this formalization, we address correctness in RDF stream processor benchmarks, allowing to determine the multiple answers that systems should provide. Finally, we present CSRBench, an extension of SRBench to address query result correctness verification using an automatic method.

B-Neck: A Distributed and Quiescent Max-Min Fair Algorithm

The problem of fairly distributing the capacity of a network among a set of sessions has been widely studied. In this problem, each session connects via a single path a source and a destination, and its goal is to maximize its assigned transmission rate (i.e., its throughput). Since the links of the network have limited bandwidths, some criterion has to be defined to fairly distribute their capacity among the sessions. A popular criterion is max-min fairness that, in short, guarantees that each session i gets a rate λi such that no session s can increase λs without causing another session s' to end up with a rate λs/ <; λs. Many max-min fair algorithms have been proposed, both centralized and distributed. However, to our knowledge, all proposed distributed algorithms require control data being continuously transmitted to recompute the max-min fair rates when needed (because none of them has mechanisms to detect convergence to the max-min fair rates). In this paper we propose B-Neck, a distributed max-min fair algorithm that is also quiescent. This means that, in absence of changes (i.e., session arrivals or departures), once the max min rates have been computed, B-Neck stops generating network traffic. Quiescence is a key design concept of B-Neck, because B-Neck routers are capable of detecting and notifying changes in the convergence conditions of max-min fair rates. As far as we know, B-Neck is the first distributed max-min fair algorithm that does not require a continuous injection of control traffic to compute the rates. The correctness of B-Neck is formally proved, and extensive simulations are conducted. In them, it is shown that B-Neck converges relatively fast and behaves nicely in presence of sessions arriving and departing.

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.

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.

Independence in CLP Languages

Studying independence of goals has proven very useful in the context of logic programming. In particular, it has provided a formal basis for powerful automatic parallelization tools, since independence ensures that two goals may be evaluated in parallel while preserving correctness and eciency. We extend the concept of independence to constraint logic programs (CLP) and prove that it also ensures the correctness and eciency of the parallel evaluation of independent goals. Independence for CLP languages is more complex than for logic programming as search space preservation is necessary but no longer sucient for ensuring correctness and eciency. Two additional issues arise. The rst is that the cost of constraint solving may depend upon the order constraints are encountered. The second is the need to handle dynamic scheduling. We clarify these issues by proposing various types of search independence and constraint solver independence, and show how they can be combined to allow dierent optimizations, from parallelism to intelligent backtracking. Sucient conditions for independence which can be evaluated \a priori" at run-time are also proposed. Our study also yields new insights into independence in logic programming languages. In particular, we show that search space preservation is not only a sucient but also a necessary condition for ensuring correctness and eciency of parallel execution.

Improving abstract interpretations by combining domains

This article considers static analysis based on abstract interpretation of logic programs over combined domains. It is known that analyses over combined domains provide more information potentially than obtained by the independent analyses. However, the construction of a combined analysis often requires redefining the basic operations for the combined domain. A practical approach to maintain precision in combined analyses of logic programs which reuses the individual analyses and does not redefine the basic operations is illustrated. The advantages of the approach are that proofs of correctness for the new domains are not required and implementations can be reused. The approach is demonstrated by showing that a combined sharing analysis — constructed from "old" proposals — compares well with other "new" proposals suggested in recent literature both from the point of view of efficiency and accuracy.

Compile-time derivation of variable dependency using abstract interpretation

Traditional schemes for abstract interpretation-based global analysis of logic programs generally focus on obtaining procedure argument mode and type information. Variable sharing information is often given only the attention needed to preserve the correctness of the analysis. However, such sharing information can be very useful. In particular, it can be used for predicting runtime goal independence, which can eliminate costly run-time checks in and-parallel execution. In this paper, a new algorithm for doing abstract interpretation in logic programs is described which concentrates on inferring the dependencies of the terms bound to program variables with increased precisión and at all points in the execution of the program, rather than just at a procedure level. Algorithms are presented for computing abstract entry and success substitutions which extensively keep track of variable aliasing and term dependence information. In addition, a new, abstract domain independent ñxpoint algorithm is presented and described in detail. The algorithms are illustrated with examples. Finally, results from an implementation of the abstract interpreter are presented.

A flexible (C)LP-based approach to the analysis of object-oriented programs

Static analyses of object-oriented programs usually rely on intermediate representations that respect the original semantics while having a more uniform and basic syntax. Most of the work involving object-oriented languages and abstract interpretation usually omits the description of that language or just refers to the Control Flow Graph(CFG) it represents. However, this lack of formalization on one hand results in an absence of assurances regarding the correctness of the transformation and on the other it typically strongly couples the analysis to the source language. In this work we present a framework for analysis of object-oriented languages in which in a first phase we transform the input program into a representation based on Horn clauses. This allows on one hand proving the transformation correct attending to a simple condition and on the other being able to apply an existing analyzer for (constraint) logic programming to automatically derive a safe approximation of the semantics of the original program. The approach is flexible in the sense that the first phase decouples the analyzer from most languagedependent features, and correct because the set of Horn clauses returned by the transformation phase safely approximates the standard semantics of the input program. The resulting analysis is also reasonably scalable due to the use of mature, modular (C)LP-based analyzers. The overall approach allows us to report results for medium-sized programs.

Efficient negation using abstract interpretation

While negation has been a very active área of research in logic programming, comparatively few papers have been devoted to implementation issues. Furthermore, the negation-related capabilities of current Prolog systems are limited. We recently presented a novel method for incorporating negation in a Prolog compiler which takes a number of existing methods (some modified and improved by us) and uses them in a combined fashion. The method makes use of information provided by a global analysis of the source code. Our previous work focused on the systematic description of the techniques and the reasoning about correctness and completeness of the method, but provided no experimental evidence to evalúate the proposal. In this paper, we report on an implementation, using the Ciao Prolog system preprocessor, and provide experimental data which indicates that the method is not only feasible but also quite promising from the efficiency point of view. In addition, the tests have provided new insight as to how to improve the proposal further. Abstract interpretation techniques are shown to offer important improvements in this application.

Validating Ontologies with OOPS!

Ontology quality can be affected by the difficulties involved in on-tology modelling which may imply the appearance of anomalies in ontologies. This situation leads to the need of validating ontologies, that is, assessing their quality and correctness. Ontology validation is a key activity in different ontol-ogy engineering scenarios such as development and selection. This paper con-tributes to the ontology validation activity by proposing a web-based tool, called OOPS!, independent of any ontology development environment, for de-tecting anomalies in ontologies. This tool will help developers to improve on-tology quality by automatically detecting potential errors.

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.

Non-strict independent and-parallelism

This paper presents and develops a generalized concept of Non-Strict Independent And Parallelism (NSIAP). NSIAP extends the applicability of Independent And- Parallelism (IAP) by enlarging the class of goals which are eligible for parallel execution. At the same time it maintains IAP's ability to run non-deterministic goals in parallel and to preserve the computational complexity expected in the execution of the program by the programmer. First, a parallel execution framework is defined and some fundamental correctness results, in the sense of equivalence of solutions with the sequential model, are discussed for this framework. The issue of efficiency is then considered. Two new definitions of NSI are given for the cases of puré and impure goals respectively and efficiency results are provided for programs parallelized under these definitions which include treatment of the case of goal failure: not only is reduction of execution time guaranteed (modulo run-time overheads) in the absence of failure but it is also shown that in the worst case of failure no speed-down will occur. In addition to applying to NSI, these results carry over and complete previous results shown in the context of IAP which did not deal with the case of goal failure. Finally, some practical examples of the application of the NSIAP concept to the parallelization of a set of programs are presented and performance results, showing the advantage of using NSI, are given.

Determination of variable dependence information through abstract interpretation

Traditional schemes for abstract interpretation-based global analysis of logic programs generally focus on obtaining procedure argument mode and type information. Variable sharing information is often given only the attention needed to preserve the correctness of the analysis. However, such sharing information can be very useful. In particular, it can be used for predicting run-time goal independence, which can eliminate costly run-time checks in and-parallel execution. In this paper, a new algorithm for doing abstract interpretation in logic programs is described which infers the dependencies of the terms bound to program variables with increased precisión and at all points in the execution of the program, rather than just at a procedure level. Algorithms are presented for computing abstract entry and success substitutions which extensively keep track of variable aliasing and term dependence information. The algorithms are illustrated with examples.