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

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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)


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
  • Linear Logic
  • Type Isomorphisms
  • Multiplicative-Additive fragment
  • Proof nets
  • Sequent calculus
  • Star-autonomous categories with finite products


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