Calculating modules in contextual logic program refinement

TL;DR

This paper extends the refinement calculus for logic programs by developing methods to calculate implementation modules from specification modules, incorporating contextual and module refinement in a unified framework.

Contribution

It introduces a generalized approach for module refinement and provides a method to derive implementation modules from specifications within the refinement calculus.

Findings

Extended and unified framework for contextual and module refinement

Method for calculating implementation modules from specification modules

Generalization of earlier refinement techniques

Abstract

The refinement calculus for logic programs is a framework for deriving logic programs from specifications. It is based on a wide-spectrum language that can express both specifications and code, and a refinement relation that models the notion of correct implementation. In this paper we extend and generalise earlier work on contextual refinement. Contextual refinement simplifies the refinement process by abstractly capturing the context of a subcomponent of a program, which typically includes information about the values of the free variables. This paper also extends and generalises module refinement. A module is a collection of procedures that operate on a common data type; module refinement between a specification module A and an implementation module C allows calls to the procedures of A to be systematically replaced with calls to the corresponding procedures of C. Based on the conditions for module refinement, we present a method for calculating an implementation module from a specification module. Both contextual and module refinement within the refinement calculus have been generalised from earlier work and the results are presented in a unified framework.