ILC: A Foundation for Automated Reasoning About Pointer Programs

Abstract

This paper shows how to use Girard's intuitionistic linear logic extended with a classical sublogic to reason about pointer programs. More specifically, first, the paper defines the proof theory for ILC (Intuitionistic Linear logic with Constraints) and shows it is well-defined via a proof of cut elimination. Second, inspired by prior work of O'Hearn, Reynolds, and Yang, the paper explains how to interpret linear logical formulas as descriptions of a program store. Third, this paper defines a simple imperative programming language with mutable references and arrays and gives verification condition generation rules that produce assertions in ILC. Finally, we identify a fragment of ILC, ILC−−, that is both decidable and closed under generation of verification conditions. Since verification condition generation is syntax-directed, we obtain a decidable procedure for checking properties of pointer programs.