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

Pre-proceedings paper presented at the 28th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt am Main, Germany, 4-6 September 2018 (arXiv:1808.03326)