A Coq Library for Verification of Concurrent Programs

Abstract

Thanks to recent advances, modern proof assistants now enable verification of realistic sequential programs. However, regarding the concurrency paradigm, previous work essentially focused on formalization of abstract systems, such as pure concurrent calculi, which are too minimal to be realistic. In this paper, we propose a library that enables verification of realistic concurrent programs in the Coq proof assistant. Our approach is based on an extension of the π-calculus whose encoding enables such programs to be modeled conveniently. This encoding is coupled with a specification language akin to spatial logics, including in particular a notion of fairness, which is important to write satisfactory specifications for realistic concurrent programs. In order to facilitate formal proof, we propose a collection of lemmas that can be reused in the context of different verifications. Among these lemmas, the most effective for simplifying the proof task take advantage of confluence properties. In order to evaluate feasibility of verification of concurrent programs using this library, we perform verification for a non-trivial application.