Towards Static Analysis of Functional Programs Using Tree Automata Completion

Abstract

International audienceThis paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for com-puting or approximating the set of terms reachable by a rewriting rela-tion. The completion algorithm we focus on is parameterized by a set E of equations controlling the precision of the approximation and influenc-ing its termination. For completion to be used as a static analysis, the first step is to guarantee its termination. In this work, we thus give a sufficient condition on E and T (F) for completion algorithm to always terminate. In the particular setting of functional programs, this condi-tion can be relaxed into a condition on E and T (C) (terms built on the set of constructors) that is closer to what is done in the field of static analysis, where abstractions are performed on data

Pattern Eliminating Transformations

“…Thus, while providing sometimes a more precise characterization of the approximations of the normal forms, these techniques are constrained, in terms of termination, by some syntactical conditions. When testing 5 of our base case scenarios with two popular implementations, Timbuk3 [14] seems less powerful than our approach, while Timbuk4 [18] can check more systems but less eciently than our approach. For Timbuk3, the over-approximation strategies were to broad to check all considered examples.…”

“…While the work presented in this paper introduces an original approach to express and ensure a particular category of syntactical guarantees associated to program transformation, a number of dierent approaches presenting methods to obtain some guarantees for similar classes of functions exist in the literature. Tree automata completion Tree automata completion consists in techniques used to compute an approximation of the set of terms reachable by a rewriting relation [14]. Such techniques could, therefore, be applied to solve similar problems to the one presented in this paper.…”

Termination criteria for tree automata completion

“…This paper builds upon preliminary versions of two termination criteria defined in [8] and [9]. This is the result of a large research effort to make tree automata completion competitive with other program verification techniques.…”