A Refinement Calculus for Logic Programs

TL;DR

This paper introduces a refinement calculus for logic programs that integrates executable and specification constructs, providing a formal framework for stepwise development and correctness assurance.

Contribution

It develops a wide-spectrum logic programming language with a declarative semantics and refinement laws, enabling systematic derivation of logic programs from specifications.

Findings

Defines a declarative semantics based on executions

Introduces correctness-preserving refinement laws

Illustrates the calculus with example derivations

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.