Parallel Closure Theorem for Left-Linear Nominal Rewriting Systems
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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.
We are grateful to the anonymous referees for valuable comments. This research was supported by JSPS KAKENHI Grant Numbers 15K00003 and 16K00091.
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