Proving Program Properties as First-Order Satisfiability

Abstract

Program semantics can often be expressed as a (many-sorted) first-order theory S, and program properties as sentences ϕ which are intended to hold in the canonical model of such a theory, which is often incomputable. Recently, we have shown that properties ϕ expressed as the existential closure of a boolean combination of atoms can be disproved by just finding a model of S and the negation ¬ϕ of ϕ. Furthermore, this idea works quite well in practice due to the existence of powerful tools for the automatic generation of models for (many-sorted) first-order theories. In this paper we extend our previous results to arbitrary properties, expressed as sentences without any special restriction. Consequently, one can prove a program property ϕ by just finding a model of an appropriate theory (including S and possibly something else) and an appropriate first-order formula related to ϕ. Beyond its possible theoretical interest, we show that our results can also be of practical use in several respects.

Proving semantic properties as first-order satisfiability

“…6 In particular, Sections 3, 4, and 5.2 are completely new. Also, whilst examples in [34] centered the attention in rewriting-based systems, in this paper we show the generality of our approach by also considering examples from relational and deductive databases, logic programming, etc.…”

“…This paper is an extended and completely revised version of [34]. 6 In particular, Sections 3, 4, and 5.2 are completely new.…”