Verification of forward simulations with thread-local, step-local proof obligations

Abstract

This paper presents a proof technique for proving refinements for general state-based models of concurrent systems that reduces proving forward simulations to thread-local, step-local proof obligations. The approach has been implemented in our theorem prover KIV, which translates imperative programs to a set of transition rules and generates proof obligations accordingly. Instances of this proof technique should also be applicable to systems specified with ASM rules, B events, or Z operations. To exemplify the proof methodology, we demonstrate it with two case studies. The first verifies linearizability of a lock-free implementation of concurrent hash sets by showing that it refines an abstract concurrent system with atomic operations. The second applies the proof technique to the verification of opacity of Transactional Mutex Locks (TML), a Software Transactional Memory algorithm. Compared to the standard approach of proving a forward simulation directly, both case studies show a significant reduction in proof effort.