Pré-Publication, Document De Travail Année : 2024

Type Isomorphisms for Multiplicative-Additive Linear Logic

Résumé

We characterize type isomorphisms in the multiplicative-additive fragment of linear logic (MALL), and thus in *-autonomous categories with finite products, extending a result for the multiplicative fragment by Balat and Di Cosmo. This yields a much richer equational theory involving distributivity and cancellation laws. The unit-free case is obtained by relying on the proof-net syntax introduced by Hughes and Van Glabbeek. We use the sequent calculus to extend our results to full MALL, including all units, thanks to a study of cut-elimination and rule commutations.

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Dates et versions

hal-04460547 , version 1 (15-02-2024)
hal-04460547 , version 2 (16-09-2025)
hal-04460547 , version 3 (24-11-2025)

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  • HAL Id : hal-04460547 , version 2

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Rémi Di Guardia, Olivier Laurent. Type Isomorphisms for Multiplicative-Additive Linear Logic. 2025. ⟨hal-04460547v2⟩
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