The Timed Predicative Calculus as a Framework for Comparative Semantics

Predicates are used in a variety of formal specification languages, though a predicate does not always mean the same thing in each approach. For example, the predicate false in Z means the same thing as true in the predicative calculus of Hehner. In this paper, we compare the specification languages Z, Morgan’s Refinement Calculus, and Parnas’s Limited Domain relations, using the timed predicative calculus (TP) of Hehner as an underlying framework. In particular, we show that TP is more expressive than the other languages. We also show that refinement in TP is strictly weaker than the refinement relations associated with the other languages. As a result, refinement laws from the other languages can be reused in TP. We conject that the simplicity of TP makes it a good candidate as a specification language and program development method for the refinement of procedural specifications, as well as real-time object oriented specifications. ∗Email: {jonathan, paige}@cs.yorku.ca. Supported by a grant from NSERC.