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Journal Articles Logical Methods in Computer Science Year : 2022

Algebraic coherent confluence and higher globular Kleene algebras

Abstract

We extend the formalisation of confluence results in Kleene algebras to a formalisation of coherent confluence proofs. For this, we introduce the structure of higher globular Kleene algebra, a higher-dimensional generalisation of modal and concurrent Kleene algebra. We calculate a coherent Church-Rosser theorem and a coherent Newman’s lemma in higher Kleene algebras by equational reasoning. We instantiate these results in the context of higher rewriting systems modelled by polygraphs.
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Dates and versions

hal-03161580 , version 1 (07-03-2021)
hal-03161580 , version 2 (08-07-2023)

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Cameron Calk, Eric Goubault, Philippe Malbos, Georg Struth. Algebraic coherent confluence and higher globular Kleene algebras. Logical Methods in Computer Science, 2022, 18 (4), ⟨10.46298/lmcs-18(4:9)2022⟩. ⟨hal-03161580v2⟩
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