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A Refinement Calculus for Logic Programs

Ian Hayes·Robert Colvin·David Hemer·Paul Strooper·Ray Nickson
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Abstract

Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic programming language, including executable constructs such as sequential conjunction, disjunction, and existential quantification, as well as specification constructs such as general predicates, assumptions and universal quantification. A declarative semantics is defined for this wide-spectrum language based on executions. Executions are partial functions from states to states, where a state is represented as a set of bindings. The semantics is used to define the meaning of programs and specifications, including parameters and recursion. To complete the calculus, a notion of correctness-preserving refinement over programs in the wide-spectrum language is defined and refinement laws for developing programs are introduced. The refinement calculus is illustrated using example derivations and prototype tool support is discussed.

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Ian Hayes, Robert Colvin, David Hemer, Paul Strooper, Ray Nickson. 2002-02-04. A Refinement Calculus for Logic Programs. https://arxiv.org/abs/cs/0202002

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