Towards Modularly Comparing Programs using Automated Theorem Provers

In this paper, we present a general framework for modularly comparing two (imperative) programs that can leverage single-program verifiers based on automated theorem provers. We formalize (i) it mutual summaries for comparing the summaries of two programs, and (ii) it relative termination to describe conditions under which two programs relatively terminate. The two rules together allow for checking correctness of interprocedural transformations. We also provide a general framework for dealing with unstructured control flow (including loops) in this framework. We demonstrate the usefulness and limitations of the framework for verifying equivalence, compiler optimizations, and interprocedural transformations.