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 $varphi$ which are intended to hold in the *canonical model* of such a theory, which is often incomputable. Recently, we have shown that properties $varphi$ expressed as the existential closure of a boolean combination of atoms can be *disproved* by just finding a model of $S$ and the *negation* $negvarphi$ of $varphi$. 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 emph{arbitrary} properties, expressed as sentences without any special restriction. Consequently, one can prove a program property $varphi$ by just *finding a model* of an appropriate theory (including $S$ and possibly something else) and an appropriate first-order formula related to $varphi$. Beyond its possible theoretical interest, we show that our results can also be of practical use in several respects.