Cartesian closed 2-categories and permutation equivalence in higher-order rewriting

Tom Hirschowitz

doi:10.2168/LMCS-9(3:10)2013

Tom Hirschowitz - Cartesian closed 2-categories and permutation equivalence in higher-order rewriting

lmcs:1132 - Logical Methods in Computer Science, September 4, 2013, Volume 9, Issue 3 - https://doi.org/10.2168/LMCS-9(3:10)2013

Cartesian closed 2-categories and permutation equivalence in higher-order rewritingArticle

Authors: Tom Hirschowitz

We propose a semantics for permutation equivalence in higher-order rewriting.
This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.

https://doi.org/10.2168/LMCS-9(3:10)2013

Source: arXiv.org:1307.6318

Volume: Volume 9, Issue 3

Published on: September 4, 2013

Imported on: October 5, 2010

Keywords: Computer Science - Logic in Computer Science, Computer Science - Programming Languages, Mathematics - Category Theory

Licence: arXiv.org - Non-exclusive license to distribute

Funding:

Source : OpenAIRE Graph

Realizability for classical logic, concurrency, references and rewriting; Funder: French National Research Agency (ANR); Code: ANR-11-BS02-0010
Formal Verification of Distributed Components; Funder: French National Research Agency (ANR); Code: ANR-10-BLAN-0305

Classifications

Mathematics Subject Classification 2020¹

Sources:

[1] zbMATH Open.

Bibliographic References

10 Documents citing this article

Hugo Paquet;Philip Saville, 2023, Effectful Semantics in 2-Dimensional Categories: Premonoidal and Freyd Bicategories, Electronic Proceedings in Theoretical Computer Science, 397, pp. 190-209, 10.4204/eptcs.397.12, https://doi.org/10.4204/eptcs.397.12.

Vincent van Oostrom, 2023, On Causal Equivalence by Tracing in String Rewriting, Electronic Proceedings in Theoretical Computer Science, 377, pp. 27-43, 10.4204/eptcs.377.2, https://doi.org/10.4204/eptcs.377.2.

Marcelo Fiore;Philip Saville, 2021, Coherence for bicategorical cartesian closed structure, Apollo, 31, 7, pp. 822-849, 10.1017/s0960129521000281, https://doi.org/10.17863/cam.76328.

André Hirschowitz;Tom Hirschowitz;Ambroise Lafont, 2020, Modules over Monads and Operational Semantics, Leibniz-Zentrum für Informatik (Schloss Dagstuhl), 10.4230/lipics.fscd.2020.12, https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.12.

Marcelo Fiore;Philip Saville, 2020, Coherence and normalisation-by-evaluation for bicategorical cartesian closed structure, Apollo (University of Cambridge), pp. 425-439, 10.1145/3373718.3394769, https://www.repository.cam.ac.uk/handle/1810/310417.

Marcelo Fiore;Philip Saville, 2020, Relative Full Completeness for Bicategorical Cartesian Closed Structure, Lecture notes in computer science, pp. 277-298, 10.1007/978-3-030-45231-5_15, https://doi.org/10.1007/978-3-030-45231-5_15.

Benedikt Ahrens;André Hirschowitz;Ambroise Lafont;Marco Maggesi, 2019, Reduction monads and their signatures, Proceedings of the ACM on Programming Languages, 4, POPL, pp. 1-29, 10.1145/3371099, https://doi.org/10.1145/3371099.

Marcelo Fiore;Philip Saville, 2019, A type theory for cartesian closed bicategories (Extended Abstract), Edinburgh Research Explorer (University of Edinburgh), pp. 1-13, 10.1109/lics.2019.8785708.

Damiano Mazza;Luc Pellissier;Pierre Vial, 2017, Polyadic approximations, fibrations and intersection types, Proceedings of the ACM on Programming Languages, 2, POPL, pp. 1-28, 10.1145/3158094, https://doi.org/10.1145/3158094.

BENEDIKT AHRENS;BENEDIKT AHRENS, 2014, Modules over relative monads for syntax and semantics, arXiv (Cornell University), 26, 1, pp. 3-37, 10.1017/s0960129514000103, http://arxiv.org/abs/1107.5252.

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