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Type Isomorphisms for Multiplicative-Additive Linear Logic

Authors Rémi Di Guardia, Olivier Laurent

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Author Details

Rémi Di Guardia
  • Univ Lyon, EnsL, UCBL, CNRS, LIP, F-69342, LYON Cedex 07, France
Olivier Laurent
  • Univ Lyon, EnsL, UCBL, CNRS, LIP, F-69342, LYON Cedex 07, France

Funding

This work was performed within the framework of the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007), and supported by the projects DyVerSe (ANR-19-CE48-0010), QuaReMe (ANR-20-CE48-0005) and ReCiProg (ANR-21-CE48-0019), all operated by the French National Research Agency (ANR). This work was also supported by the IRN Linear Logic.

Cite AsGet BibTex

Rémi Di Guardia and Olivier Laurent. Type Isomorphisms for Multiplicative-Additive Linear Logic. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 26:1-26:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.FSCD.2023.26

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).

Subject Classification

ACM Subject Classification
  • Theory of computation → Linear logic
Keywords
  • Linear Logic
  • Type Isomorphisms
  • Multiplicative-Additive fragment
  • Proof nets
  • Sequent calculus
  • Star-autonomous categories with finite products

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References

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