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arXiv · 2405.17109

Left-Linear Completion with AC Axioms

Johannes Niederhauser·Nao Hirokawa·Aart Middeldorp
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Abstract

We revisit completion modulo equational theories for left-linear term rewrite systems where unification modulo the theory is avoided and the normal rewrite relation can be used in order to decide validity questions. To that end, we give a new correctness proof for finite runs and establish a simulation result between the two inference systems known from the literature. Given a concrete reduction order, novel canonicity results show that the resulting complete systems are unique up to the representation of their rules' right-hand sides. Furthermore, we show how left-linear AC completion can be simulated by general AC completion. In particular, this result allows us to switch from the former to the latter at any point during a completion process.

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Johannes Niederhauser, Nao Hirokawa, Aart Middeldorp. 2024-05-27. Left-Linear Completion with AC Axioms. https://doi.org/10.46298/lmcs-21(2%3A10)2025

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