Towards a Coq-verified Chain of Esterel Semantics

TL;DR

This paper develops a Coq-based formal framework for Esterel semantics, introducing a new microstep semantics and proving their equivalence and refinement, enhancing the reliability of Esterel compiler semantics.

Contribution

It introduces a novel microstep semantics for Esterel and provides formal proofs of equivalence and refinement with existing semantics using Coq.

Findings

Formalized Esterel semantics in Coq

Proved equivalence between CBS and CSS semantics

Established refinement of CSS by microstep semantics

Abstract

This paper focuses on formally specifying and verifying the chain of formal semantics of the Esterel synchronous programming language using the Coq proof assistant. In particular, in addition to the standard logical (LBS) semantics, constructive semantics (CBS) and constructive state semantics (CSS), we introduce a novel microstep semantics that gets rid of the Must/Can potential function pair of the constructive semantics and can be viewed as an abstract version of Esterel's circuit semantics used by compilers to generate software code and hardware designs. Excluding the loop construct from Esterel, the paper also provides formal proofs in Coq of the equivalence between the CBS and CSS semantics and of the refinement of the CSS by the microstep semantics.