Metavariables and Conditional Refinements in the Refinement Calculus

Abstract

We describe two techniques for the refinement calculus that facilitate goal-directed development. The techniques achieve this by allowing the deferring of decisions about the precise form of refinement steps, so high-level choices can be expressed as soon as those choices are appropriate. Metavariables are place-holders for components of partly developed programs that will be instantiated when they are suitably constrained by later refinements. The conditional refinements technique allows the development of alternative refinements of a specification, and the collection of those alternative refinements into a guarded command set.

We think that programmers developing programs using the refinement calculus make use of both of these techniques informally, but the written derivation does not usually reflect their use. We describe and illustrate a rigorous way to apply these techniques and record their use.