Parallel Closure Theorem for Left-Linear Nominal Rewriting Systems

Abstract

Nominal rewriting has been introduced as an extension of first-order term rewriting by a binding mechanism based on the nominal approach. In this paper, we extend Huet’s parallel closure theorem and its generalisation on confluence of left-linear term rewriting systems to the case of nominal rewriting. The proof of the theorem follows a previous inductive confluence proof for orthogonal uniform nominal rewriting systems, but the presence of critical pairs requires a much more delicate argument. The results include confluence of left-linear uniform nominal rewriting systems that are not \(\alpha \)-stable and thus are not represented by any systems in traditional higher-order rewriting frameworks.