Type Isomorphisms for Multiplicative-Additive Linear Logic
Logic in Computer Science
2025-11-26 v4
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.
Keywords
Cite
@article{arxiv.2402.11987,
title = {Type Isomorphisms for Multiplicative-Additive Linear Logic},
author = {Rémi Di Guardia and Olivier Laurent},
journal= {arXiv preprint arXiv:2402.11987},
year = {2025}
}