Correct Transformation of Rewrite Systems for Implementation Purposes

Abstract

We propose the notion of a correct transformation of one rewrite system into another. If such a transformation is correct, then the normal forms of a term in the original rewrite system can be obtained by computing the normal forms of the interpretation of this term in the transformed rewrite system. We show for several transformations from the literature that they are correct, most notably for the notion of simulation from Kamperman and Walters.