Equivalence Checking of Two Functional Programs Using Inductive Theorem Provers

Abstract

In this paper, we present a new method for generating inductive hypothesis for proving an equivalence between two imperative programs: one recursive and one iterative. The basic premise is to convert both programs in the form of term rewriting system that is acceptable to inductive theorem provers and to generate inductive generalization lemmas that such a theorem prover can discharge. As finding inductive generalizations automatically is an undecidable problem, we will focus on a certain class of recursive programs that cannot be handled by existing tools. We develop criteria under which we can prove the equivalence of two programs. A technique based on schematic programs for proving concrete ones is proposed.Schematic generalization lemmas are computed directly from given specifications.Concrete lemmas are obtained by instantiation of schematic generalization lemmas.The technique is applied prior to any proof attempt, then save time.Only the validity of the schematic generalization lemma is checked.