License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2023.26
URN: urn:nbn:de:0030-drops-180103
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18010/
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Di Guardia, Rémi ; Laurent, Olivier

Type Isomorphisms for Multiplicative-Additive Linear Logic

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LIPIcs-FSCD-2023-26.pdf (0.8 MB)

Abstract

We characterize type isomorphisms in the multiplicative-additive fragment of linear logic (MALL), and thus for ⋆-autonomous categories with finite products, extending a result for the multiplicative fragment by Balat and Di Cosmo [Vincent Balat and Roberto Di Cosmo, 1999]. This yields a much richer equational theory involving distributivity and annihilation laws. The unit-free case is obtained by relying on the proof-net syntax introduced by Hughes and Van Glabbeek [Dominic Hughes and Rob van Glabbeek, 2005]. We then use the sequent calculus to extend our results to full MALL (including all units).

BibTeX - Entry

@InProceedings{diguardia_et_al:LIPIcs.FSCD.2023.26,
  author =	{Di Guardia, R\'{e}mi and Laurent, Olivier},
  title =	{{Type Isomorphisms for Multiplicative-Additive Linear Logic}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{26:1--26:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18010},
  URN =		{urn:nbn:de:0030-drops-180103},
  doi =		{10.4230/LIPIcs.FSCD.2023.26},
  annote =	{Keywords: Linear Logic, Type Isomorphisms, Multiplicative-Additive fragment, Proof nets, Sequent calculus, Star-autonomous categories with finite products}
}

Keywords: Linear Logic, Type Isomorphisms, Multiplicative-Additive fragment, Proof nets, Sequent calculus, Star-autonomous categories with finite products
Collection: 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)
Issue Date: 2023
Date of publication: 28.06.2023

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