A Predicate Transformer Semantics for a Concurrent Language of Refinement

Circus is a combination of Z and CSP; its chief distinguishing feature is the inclusion of the ideas of the refinement calculus. Our main objective is the definition of refinement methods for concurrent programs. The original semantic model for Circus is Hoare and He’s unifying theories of programming. In this paper, we present an equivalent semantics based on predicate transformers. With this new model, we provide a more adequate basis for the formalisation of refinement and verificationcondition generation rules. Furthermore, this new framework makes it possible to include logical variables and angelic nondeterminism in Circus. The consistency of the relational and predicate transformer models gives us confidence in their accuracy.