Expression Refinement Explained

This paper describes a calculus for the stepwise and piecewise refinement of expressions. It provides a means for the derivation of executable expressions from initial specifications. We take the view that a refinement calculus consists of: a specification language, which usually includes constructs which are non-executable, but is a “superlanguage” of a programming language; a refinement relation between specifications, which possesses particular properties necessary for the refinement of specifications in a stepwise and piecewise manner; and a set of laws determining how such refinements may proceed. A specification language of expressions is described, which includes constructs for reasoning about undefined terms and non-deterministic expressions, as well as improper expressions. Examples are used to illustrate how and why each type of expression might arise. An outline is given of how refinement of specifications might proceed, and a refinement relation is defined using six axioms.