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-Ro...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2022-11-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/6743/pdf |
| Summary: | 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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| ISSN: | 1860-5974 |