A calculus for Esterel: if can, can. if no can, no can.

Abstract

The language Esterel has found success in many safety-critical applications, such as fly-by-wire systems and nuclear power plant control software. Its imperative style is natural to programmers building such systems and its precise semantics makes it work well for reasoning about programs. Existing semantics of Esterel generally fall into two categories: translation to Boolean circuits, or operational semantics that give a procedure for running a whole program. In contrast, equational theories enable reasoning about program behavior via equational rewrites at the source level. Such theories form the basis for proofs of transformations inside compilers or for program refactorings, and defining program evaluation syntactically. This paper presents the first such equational calculus for Esterel. It also illustrates the calculus's usefulness with a series of example equivalences and discuss how it enabled us to find bugs in Esterel implementations.

A Dynamic Logic for Verification of Synchronous Models based on Theorem Proving

“…Similar to the type-theory approach [41], instead of directly using SAT/SMT solving, SDL provides compositional rules for decomposing SPs according to their syntactic structures, so as to divide a big verification problem into small SMT-solving problems in derivation processes. [42] proposed an equation theory for pure Esterel. There, term rewrite rules were built for describing the constructive semantics of Esterel so that two different Esterel programs can be formally compared and their equivalences can be formally reasoned about.…”

“…Compared to [42,43], the verification of SDL is not solely based on term rewriting, but also based on a Hoare-style program verification [17] process. Instead of verifying by checking the equivalences or refinement relations between two programs, we reason about the satisfaction relation between a program and a logic formula, in a form [p]φ or [p] φ.…”

“…Instead of verifying by checking the equivalences or refinement relations between two programs, we reason about the satisfaction relation between a program and a logic formula, in a form [p]φ or [p] φ. In SPs, the rewrite rules built in Table 2 for reducing parallel SPs play a similar role as the rewrite rules defined in [42,43] for symbolically executing parallel Esterel programs. The synchronous effects used to capture the behaviours of Esterel programs in [43] was similar to the form of SPs.…”

A fault-tolerant programming model for distributed interactive applications

“…Functional reactive programming (FRP) originally considers systems with continuous time [Elliott and Hudak 1997] but has inspired many languages that like F R handle discrete changes [Cooper and Krishnamurthi 2006;Czaplicki and Chong 2013;Kamina and Aotani 2018]. Florence et al [2019] provide a calculus for Esterel ś a synchronous programming language conceptually similar to discrete FRP, but with very different syntax. DREAM Salvaneschi 2014, 2018] analyze consistency levels of different propagation algorithms based on a formal model of FRP like propagation of events in a distributed system.…”