Specifying computations using hyper transition systems

Abstract

We study hyper transition systems as a formalism to give semantics to specification languages which support both unbounded angelic and unbounded demonic non-determinism as well as recursion. Hyper transition are a generalization of transition systems and are suited for the specification of computations by means of properties that atomic steps in a computation have to satisfy. As an application we use a hyper transition system to give an operational semantics to the language of Back's refinement calculus. This operational semantics abstracts from the internal configurations and we prove it to be equivalent to the standard weakest precondition semantics. Finally, we propose a refinement relation that preserves the atomic step of a computation and generalizes the simulation relation on ordinary transition systems. This can be used to augment specification languages with a form of concurrency.