New results on rewrite-based satisfiability procedures

Abstract

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T . If a sound and complete inference system for first-order logic is guaranteed to terminate on T -satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T -satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.

Combinable Extensions of Abelian Groups

“…That restriction is justified by technical reasons: an important issue would be to discard it, enlarging in this way the applicability of our results. As a second direction we foresee, it would be interesting to find general methods to ensure the termination of the calculus by developing, for instance, an automatic meta-saturation method [16], or by considering a variable-inactivity condition [1]. Finally, it would be interesting to study how our calculus can be integrated into Satisfiability Modulo Theories solvers, by exploiting for instance the general framework developed in [4].…”

“…Nowadays, there is a growing interest in applying theorem provers to construct decision procedures for theories of interest in verification [2,1,8,4]. The problem of incorporating some reasoning modulo arithmetic properties inside theorem provers is particularly challenging.…”

A Write-Based Solver for SAT Modulo the Theory of Arrays

“…• storecomm (2030 benchs), storeinv (172 benchs) and swap (1368 benchs): benchmarks from the paper [14] encoding simple properties about arrays. They do not contain any arithmetic.…”

Extensional Crisis and Proving Identity

“…It is partially motivated by program analysis, since collection types are first-class types in many programming languages and nearly every programming languages has collection libraries. While there has been a considerable amount of work on deciding universal theories of collection types, including using superposition provers [2] and decidability or undecidability of their extensions [9,13], our work is different since we consider collections in first-order logic with quantifiers. As many others, we are trying to bridge the gap between quantifier and theory reasoning, but in a way that is friendly to existing architectures of first-order theorem provers.…”

“…As many others, we are trying to bridge the gap between quantifier and theory reasoning, but in a way that is friendly to existing architectures of first-order theorem provers. Unlike [2], we impose no additional constraints on the used simplification ordering and can deal with arbitrary axioms on top of array axioms.…”