Specification statements and refinement

We discuss the development of executable programs from state-based specifications written in the language of first-order predicate calculus. Notable examples of such specifications are those written using the techniques Z and VDM; but our interest is in the rigorous derivation of the algorithms from which they deliberately abstract. This is, of course, the role of a development method. Here we propose a development method based on specification statements with which specifications are embedded in programs—standing in for developments “yet to be done.” We show that specification statements allow description, development, and execution to be carried out within a single language: programs/specifications become hybrid constructions in which both predicates and directly executable operations can appear. The use of a single language—embracing both high- and low-level constructs—has a very considerable influence on the development style, and it is that influence we discuss: the specification statement is described, its associated calculus of refinement is given, and the use of that calculus is illustrated.