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arXiv · 2402.11987

Type Isomorphisms for Multiplicative-Additive Linear Logic

Rémi Di Guardia·Olivier Laurent
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Abstract

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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Rémi Di Guardia, Olivier Laurent. 2024-02-19. Type Isomorphisms for Multiplicative-Additive Linear Logic. https://doi.org/10.46298/lmcs-21(4%3A24)2025

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