Cameron Calk ; Eric Goubault ; Philippe Malbos ; Georg Struth - Algebraic coherent confluence and higher globular Kleene algebras

lmcs:6743 - Logical Methods in Computer Science, November 28, 2022, Volume 18, Issue 4 - https://doi.org/10.46298/lmcs-18(4:9)2022
Algebraic coherent confluence and higher globular Kleene algebrasArticle

Authors: Cameron Calk ; Eric Goubault ; Philippe Malbos ; Georg Struth

    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.


    Volume: Volume 18, Issue 4
    Published on: November 28, 2022
    Accepted on: July 20, 2022
    Submitted on: August 29, 2020
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Category Theory

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