Generalised Reactive Processes in Isabelle/UTP

Hoare and He’s UTP theory of reactive processes provides a unifying foundation for the semantics of process calculi and reactive programming. A reactive process is a form of UTP relation which can refer to both state variables and also a trace history of events. In their original presentation, a trace was modelled solely by a discrete sequence of events. Here, we generalise the trace model using “trace algebra”, which characterises traces abstractly using cancellative monoids, and thus enables application of the theory to a wider family of computational models, including hybrid computation. We recast the reactive healthiness conditions in this setting, and prove all the associated distributivity laws. We tackle parallel composition of reactive processes using the “parallel-by-merge” scheme from UTP. We also identify the associated theory of “reactive relations”, and use it to define generic reactive laws, a Hoare logic, and a weakest precondition calculus.