代数相干合流与高球状Kleene代数

Log. Methods Comput. Sci. Pub Date : 2020-06-29 DOI:10.46298/lmcs-18(4:9)2022

Cameron Calk, É. Goubault, P. Malbos, G. Struth

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引用次数: 2

摘要

将Kleene代数中合流结果的形式化推广到相干合流证明的形式化。为此，我们引入了高球Kleene代数的结构，它是模态Kleene代数和并发Kleene代数的高维推广。用方程推理的方法计算了高等Kleene代数中的一个相干church - rosser定理和一个相干Newman引理。我们在由测谎仪建模的高级重写系统的背景下实例化这些结果。

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Algebraic coherent confluence and higher globular Kleene algebras

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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Log. Methods Comput. Sci.

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