Constraint-Based Program Reasoning with Heaps and Separation

TL;DR: A constraint language for finite partial maps a.k.a. heaps that incorporates the notion of separation from Separation Logic is introduced, using $\mathcal H$ to build an extension of Hoare Logic for reasoning over heap manipulating programs using constraint-based symbolic execution.

Abstract: This paper introduces a constraint language $\mathcal H$ for finite partial maps a.k.a. heaps that incorporates the notion of separation from Separation Logic. We use $\mathcal H$ to build an extension of Hoare Logic for reasoning over heap manipulating programs using constraint-based symbolic execution. We present a sound and complete algorithm for solving quantifier-free QF $\mathcal H$ -formulae based on heap element propagation. An implementation of the $\mathcal H$ -solver has been integrated into a Satisfiability Modulo Theories SMT framework. We experimentally evaluate the implementation against Verification Conditions VCs generated from symbolic execution of large heap manipulating programs. In particular, we mitigate the path explosion problem using subsumption via interpolation --- made possible by the constraint-based encoding.