Mechanical Reasoning about Families of UTP Theories

In this paper we present a semantic embedding of Hoare and He's Unifying Theories of Programming (UTP) framework into the ProofPower-Z theorem prover; it concisely captures the notion of UTP theory, theory instantiation, and, additionally, type restrictions on the alphabet. We show how the encoding can be used to reason about UTP theories and their predicates, including models of particular specifications and programs. We support encoding and reasoning about combinations of elements of collections of theory instantiations, as typically found in UTP models of particular specifications and programs.