@TECHREPORT{Denney98atheory, author = {Ewen W. K. C. Denney}, title = {A Theory of Program Refinement}, institution = {}, year = {1998} }

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Abstract

We give a canonical program refinement calculus based on the lambda calculus and classical first-order predicate logic, and study its proof theory and semantics. The intention is to construct a metalanguage for refinement in which basic principles of program development can be studied. The idea is that it should be possible to induce a refinement calculus in a generic manner from a programming language and a program logic. For concreteness, we adopt the simply-typed lambda calculus augmented with primitive recursion as a paradigmatic typed functional programming language, and use classical first-order logic as a simple program logic. A key feature is the construction of the refinement calculus in a modular fashion, as the combination of two orthogonal extensions to the underlying programming language (in this case, the simply-typed lambda calculus). The crucial observation is that a refinement calculus is given by extending a programming language to allow indeterminate expressions (or ‘stubs’) involving the construction ‘some program x such that P ’. Factoring this into ‘some x...’