Expanding Transformation: A Basis for Correctness Verification of Rewriting Rules

Abstract

Unfolding transformation has long been used for computation and program transformation both in functional programming and logic programming paradigms. In this paper, we clarify that an unfolding step can be regarded as the composition of two simpler operations, i.e., expanding transformation and unification, and show that expanding transformation, rather than unfolding transformation, is a suitable basis for verifying the correctness of rewriting rules by pattern manipulation, which in turn provides a basis for systematically generating rewriting rules from a given problem description. We verify the correctness of expanding transformation and demonstrate the correctness of a basic class of rewriting rules, called general rewriting rules, based on expanding transformation. Applying expanding transformation and its correctness result, we demonstrate correctness verification of a larger class of rewriting rules, called expanding-based rewriting rules, by transformation of clause patterns.