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.

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.

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.

Lower bound cost estimation for logic programs

It is generally recognized that information about the runtime cost of computations can be useful for a variety of applications, including program transformation, granularity control during parallel execution, and query optimization in deductive databases. Most of the work to date on compile-time cost estimation of logic programs has focused on the estimation of upper bounds on costs. However, in many applications, such as parallel implementations on distributed-memory machines, one would prefer to work with lower bounds instead. The problem with estimating lower bounds is that in general, it is necessary to account for the possibility of failure of head unification, leading to a trivial lower bound of 0. In this paper, we show how, given type and mode information about procedures in a logic program, it is possible to (semi-automatically) derive nontrivial lower bounds on their computational costs. We also discuss the cost analysis for the special and frequent case of divide-and-conquer programs and show how —as a pragmatic short-term solution —it may be possible to obtain useful results simply by identifying and treating divide-and-conquer programs specially.

Non-failure analysis for logic programs

We provide a method whereby, given mode and (upper approximation) type information, we can detect procedures and goals that can be guaranteed to not fail (i.e., to produce at least one solution or not termínate). The technique is based on an intuitively very simple notion, that of a (set of) tests "covering" the type of a set of variables. We show that the problem of determining a covering is undecidable in general, and give decidability and complexity results for the Herbrand and linear arithmetic constraint systems. We give sound algorithms for determining covering that are precise and efiicient in practice. Based on this information, we show how to identify goals and procedures that can be guaranteed to not fail at runtime. Applications of such non-failure information include programming error detection, program transiormations and parallel execution optimization, avoiding speculative parallelism and estimating lower bounds on the computational costs of goals, which can be used for granularity control. Finally, we report on an implementation of our method and show that better results are obtained than with previously proposed approaches.

Optimized algorithms for the incremental analysis of logic programs

Global analysis of logic programs can be performed effectively by the use of one of several existing efficient algorithms. However, the traditional global analysis scheme in which all the program code is known in advance and no previous analysis information is available is unsatisfactory in many situations. Incrementa! analysis of logic programs has been shown to be feasible and much more efficient in certain contexts than traditional (non-incremental) global analysis. However, incremental analysis poses additional requirements on the fixpoint algorithm used. In this work we identify these requirements, present an important class of strategies meeting the requirements, present sufficient a priori conditions for such strategies, and propose, implement, and evalúate experimentally a novel algorithm for incremental analysis based on these ideas. The experimental results show that the proposed algorithm performs very efficiently in the incremental case while being comparable to (and, in some cases, considerably better than) other state-of-the-art analysis algorithms even for the non-incremental case. We argüe that our discussions, results, and experiments also shed light on some of the many tradeoffs involved in the design of algorithms for logic program analysis.

Implementation of multiple specialization in logic programs

We study the múltiple specialization of logic programs based on abstract interpretation. This involves in general generating several versions of a program predícate for different uses of such predícate, making use of information obtained from global analysis performed by an abstract interpreter, and finally producing a new, "multiply specialized" program. While the topic of múltiple specialization of logic programs has received considerable theoretical attention, it has never been actually incorporated in a compiler and its effects quantified. We perform such a study in the context of a parallelizing compiler and show that it is indeed a relevant technique in practice. Also, we propose an implementation technique which has the same power as the strongest of the previously proposed techniques but requires little or no modification of an existing abstract interpreter.

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.

Extracting non-strict independent and-parallelism using sharing and freeness information

Logic programming systems which exploit and-parallelism among non-deterministic goals rely on notions of independence among those goals in order to ensure certain efficiency properties. "Non-strict" independence (NSI) is a more relaxed notion than the traditional notion of "strict" independence (SI) which still ensures the relevant efficiency properties and can allow considerable more parallelism than SI. However, all compilation technology developed to date has been based on SI, because of the intrinsic complexity of exploiting NSI. This is related to the fact that NSI cannot be determined "a priori" as SI. This paper filis this gap by developing a technique for compile-time detection and annotation of NSI. It also proposes algorithms for combined compiletime/ run-time detection, presenting novel run-time checks for this type of parallelism. Also, a transformation procedure to eliminate shared variables among parallel goals is presented, aimed at performing as much work as possible at compile-time. The approach is based on the knowledge of certain properties regarding the run-time instantiations of program variables —sharing and freeness— for which compile-time technology is available, with new approaches being currently proposed. Thus, the paper does not deal with the analysis itself, but rather with how the analysis results can be used to parallelize programs.

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.

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.

B-LOG: A branch and bound methodology for the parallel execution of logic programs

We propose a computational methodology -"B-LOG"-, which offers the potential for an effective implementation of Logic Programming in a parallel computer. We also propose a weighting scheme to guide the search process through the graph and we apply the concepts of parallel "branch and bound" algorithms in order to perform a "best-first" search using an information theoretic bound. The concept of "session" is used to speed up the search process in a succession of similar queries. Within a session, we strongly modify the bounds in a local database, while bounds kept in a global database are weakly modified to provide a better initial condition for other sessions. We also propose an implementation scheme based on a database machine using "semantic paging", and the "B-LOG processor" based on a scoreboard driven controller.

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.

Estimating the computational cost of logic programs

Information about the computational cost of programs is potentially useful for a variety of purposes, including selecting among different algorithms, guiding program transformations, in granularity control and mapping decisions in parallelizing compilers, and query optimization in deductive databases. Cost analysis of logic programs is complicated by nondeterminism: on the one hand, procedures can return múltiple Solutions, making it necessary to estímate the number of solutions in order to give nontrivial upper bound cost estimates; on the other hand, the possibility of failure has to be taken into account while estimating lower bounds. Here we discuss techniques to address these problems to some extent.