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

A Practical View on Renaming

We revisit variable renaming from a practitioner's point of view, presenting concepts we found useful in dealing with operational semantics of pure Prolog. A concept of relaxed core representation is introduced, upon which a concept of prenaming is built. Prenaming formalizes the intuitive practice of renaming terms by just considering the necessary bindings, where now some passive "bindings" x/x may be necessary as well. As an application, a constructive version of variant lemma for implemented Horn clause logic has been obtained. There, prenamings made it possible to incrementally handle new (local) variables.Comment: In Proceedings WLP'15/'16/WFLP'16, arXiv:1701.0014

experimental evaluation of numerical domains for inferring ranges

Abstract Among the numerical abstract domains for detecting linear relationships between program variables, the polyhedra domain is, from a purely theoretical point of view, the most precise one. Other domains, such as intervals, octagons and parallelotopes, are less expressive but generally more efficient. We focus our attention on interval constraints and, using a suite of benchmarks, we experimentally show that, in practice, polyhedra may often compute results less precise than the other domains, due to the use of the widening operator

Exploiting Linearity in Sharing Analysis of Object-oriented Programs

AbstractWe propose a new sharing analysis of object-oriented programs based on abstract interpretation. Two variables share when they are bound to data structures which overlap. We show that sharing analysis can greatly benefit from linearity analysis. We propose a combined domain including aliasing, linearity and sharing information. We use a graph-based representation of aliasing information which naturally encodes sharing and linearity information, and define all the necessary operators for the analysis of a Java-like language

Efficient top-down set-sharing analysis using cliques

Abstract. We study the problem of efficient, scalable set-sharing analysis of logic programs. We use the idea of representing sharing information as a pair of abstract substitutions, one of which is a worst-case sharing representation called a clique set, which was previously proposed for the case of inferring pair-sharing. We use the clique-set representation for (1) inferring actual set-sharing information, and (2) analysis within a top-down framework. In particular, we define the new abstract functions required by standard top-down analyses, both for sharing alone and also for the case of including freeness in addition to sharing. We use cliques both as an alternative representation and as widening, defining several widening operators. Our experimental evaluation supports the conclusión that, for inferring set-sharing, as it was the case for inferring pair-sharing, precisión losses are limited, while useful efficieney gains are obtained. We also derive useful conclusions regarding the interactions between thresholds, precisión, efficieney and cost of widening. At the limit, the clique-set representation allowed analyzing some programs that exceeded memory capacity using classical sharing representations

Optimality in Goal-Dependent Analysis of Sharing

In the context of abstract interpretation based static analysis, we cope with the problem of correctness and optimality for logic program analysis. We propose a new framework equipped with a denotational, goal-dependent semantics which refines many goal-driven frameworks appeared in the literature. The key point is the introduction of two specialized concrete operators for forward and backward unification. We prove that our goal-dependent semantics is correct w.r.t. computed answers and we provide the best correct approximations of all the operators involved in the semantics for set-sharing analysis. We show that the precision of the overall analysis is strictly improved and that, in some cases, we gain precision w.r.t. more complex domains involving linearity and freeness information

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, 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