Fusion and simultaneous execution in the refinement calculus

Abstract

In the refinement calculus, program statements are modelled as predicate transformers. A product operator for predicate transformers was introduced by Martin [18] and Naumann [25] using category theoretic considerations. In this paper, we look more closely at the refinement-oriented properties of this operator and at its applications. We also generalise the definition of the product operator to form what we call a fusion operator. Together, the fusion and product operators provide us with algebraic ways of composing program statements in the refinement calculus in order to model effects such as conjunction of specifications, simultaneous execution, and embedding of smaller programs into larger contexts.