Work

Type Isomorphisms for Multiplicative-Additive Linear Logic

Year: 2025

Type: article

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.

Source: Logical Methods in Computer Science

DOI: 10.46298/lmcs-21(4:24)2025

Authors: Rémi Di Guardia, Olivier Laurent

Institutions: Lyon 1 Université, École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Laboratoire de l'Informatique du Parallélisme

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Awards: Dynamic Versatile Semantics, Quantitative Reasoning Methods for Probabilistic Logics, PROJET AVENIR LYON SAINT-ETIENNE, Community of mathematics and fundamental computer science in Lyon, Reasoning with Circular proofs for Programming