Total Correctness by Local Improvement in Program Transformation

Abstract

The goal of program transformation is to improve efficiency while preserving meaning. One of the best known transformation techniques is Burstall and Darlington's unfold-fold method. Unfortunately the unfold-fold method itself guarantees neither improvement in efficiency nor total-correctness. The correctness problem for unfold-fold is an instance of a strictly more general problem: transformation by locally equivalence-preserving steps does not necessarily preserve (global) equivalence.