Confluence and Commutation for Nominal Rewriting Systems with Atom-Variables

Abstract

Nominal rewriting was introduced as an extension of first-order term rewriting by a binding mechanism based on the nominal approach. Recently, a new format of nominal rewriting has been introduced where rewrite rules are defined with atom-variables rather than atoms. In this paper, we investigate the difference between the new format and the original nominal rewriting, and prove confluence and commutation for some classes of rewriting systems whose rewrite rules have no proper overlaps which are computed using nominal unification with atom-variables. The properties we prove are expected to be used in a form of program transformation that is realised as an equivalence transformation of rewriting systems.