Efficient Groundness Analysis in Prolog

Boolean functions can be used to express the groundness of, and trace grounding dependencies between, program variables in (constraint) logic programs. In this paper, a variety of issues pertaining to the efficient Prolog implementation of groundness analysis are investigated, focusing on the domain of definite Boolean functions, Def. The systematic design of the representation of an abstract domain is discussed in relation to its impact on the algorithmic complexity of the domain operations; the most frequently called operations should be the most lightweight. This methodology is applied to Def, resulting in a new representation, together with new algorithms for its domain operations utilising previously unexploited properties of Def -- for instance, quadratic-time entailment checking. The iteration strategy driving the analysis is also discussed and a simple, but very effective, optimisation of induced magic is described. The analysis can be implemented straightforwardly in Prolog and the use of a non-ground representation results in an efficient, scalable tool which does not require widening to be invoked, even on the largest benchmarks. An extensive experimental evaluation is givenComment: 31 pages To appear in Theory and Practice of Logic Programmin

Enhanced sharing analysis techniques: a comprehensive evaluation

Sharing, an abstract domain developed by D. Jacobs and A. Langen for the analysis of logic programs, derives useful aliasing information. It is well-known that a commonly used core of techniques, such as the integration of Sharing with freeness and linearity information, can significantly improve the precision of the analysis. However, a number of other proposals for refined domain combinations have been circulating for years. One feature that is common to these proposals is that they do not seem to have undergone a thorough experimental evaluation even with respect to the expected precision gains. In this paper we experimentally evaluate: helping Sharing with the definitely ground variables found using Pos, the domain of positive Boolean formulas; the incorporation of explicit structural information; a full implementation of the reduced product of Sharing and Pos; the issue of reordering the bindings in the computation of the abstract mgu; an original proposal for the addition of a new mode recording the set of variables that are deemed to be ground or free; a refined way of using linearity to improve the analysis; the recovery of hidden information in the combination of Sharing with freeness information. Finally, we discuss the issue of whether tracking compoundness allows the computation of more sharing information

On the practicality of global flow analysis of logic programs

This paper addresses the issue of the practicality of global flow analysis in logic program compilation, in terms of both speed and precision of analysis. It discusses design and implementation aspects of two practical abstract interpretation-based flow analysis systems: MA3, the MOO Andparallel Analyzer and Annotator; and Ms, an experimental mode inference system developed for SB-Prolog. The paper also provides performance data obtained from these implementations. Based on these results, it is concluded that the overhead of global flow analysis is not prohibitive, while the results of analysis can be quite precise and useful

Effectiveness of abstract interpretation in automatic parallelization: a case study in logic programming

We report on a detailed study of the application and effectiveness of program analysis based on abstract interpretation to automatic program parallelization. We study the case of parallelizing logic programs using the notion of strict independence. We first propose and prove correct a methodology for the application in the parallelization task of the information inferred by abstract interpretation, using a parametric domain. The methodology is generic in the sense of allowing the use of different analysis domains. A number of well-known approximation domains are then studied and the transformation into the parametric domain defined. The transformation directly illustrates the relevance and applicability of each abstract domain for the application. Both local and global analyzers are then built using these domains and embedded in a complete parallelizing compiler. Then, the performance of the domains in this context is assessed through a number of experiments. A comparatively wide range of aspects is studied, from the resources needed by the analyzers in terms of time and memory to the actual benefits obtained from the information inferred. Such benefits are evaluated both in terms of the characteristics of the parallelized code and of the actual speedups obtained from it. The results show that data flow analysis plays an important role in achieving efficient parallelizations, and that the cost of such analysis can be reasonable even for quite sophisticated abstract domains. Furthermore, the results also offer significant insight into the characteristics of the domains, the demands of the application, and the trade-offs involved

Optimality in Goal-Dependent Analysis of Sharing

We face the problems of correctness, optimality and precision for the static analysis of logic programs, using the theory of abstract interpretation. We propose a framework with a denotational, goal-dependent semantics equipped with two unification operators for forward unification (calling a procedure) and backward unification (returning from a procedure). The latter is implemented through a matching operation. Our proposal clarifies and unifies many different frameworks and ideas on static analysis of logic programming in a single, formal setting. On the abstract side, we focus on the domain Sharing by Jacobs and Langen and provide the best correct approximation of all the primitive semantic operators, namely, projection, renaming, forward and backward unification. We show that the abstract unification operators are strictly more precise than those in the literature defined over the same abstract domain. In some cases, our operators are more precise than those developed for more complex domains involving linearity and freeness. To appear in Theory and Practice of Logic Programming (TPLP

Effectiveness of combined sharing and freeness analysis using abstract interpretation

This paper presents improved unification algorithms, an implementation, and an analysis of the effectiveness of an abstract interpreter based on the sharing + freeness domain presented in a previous paper, which was designed to accurately and concisely represent combined freeness and sharing information for program variables. We first briefly review this domain and the unification algorithms previously proposed. We then improve these algorithms and correct them to deal with some cases which were not well analyzed previously, illustrating the improvement with an example. We then present the implementation of the improved algorithm and evaluate its performance by comparing the effectiveness of the information inferred to that of other interpreters available to us for an application (program parallelization) that is common to all these interpreters. All these systems have been embedded in a real parallelizing compiler. Effectiveness of the analysis is measured in terms of actual final performance of the system: i.e. in terms of the actual speedups obtained. The results show good performance for the combined domain in that it improves the accuracy of both types of information and also in that the analyzer using the combined domain is more effective in the application than any of the other analyzers it is compared to