Designs with Angelic Nondeterminism

Hoare and He's Unifying Theories of Programming (UTP) are a predicative relational framework for the definition and combination of refinement languages for a variety of programming paradigms. Previous work has defined a theory for angelic nondeterminism in the UTP; this is basically an encoding of binary multirelations in a predicative model. In the UTP a theory of designs (pre and postcondition pairs) provides, not only a model of terminating programs, but also a stepping stone to define a theory for state-rich reactive processes. In this paper, we cast the angelic nondeterminism theory of the UTP as a theory of designs with the long-term objective of providing a model for well established refinement process algebras like Communicating Sequential Processes (CSP) and Circus.