Type Isomorphisms for Multiplicative-Additive Linear Logic

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 a...

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Vydáno v:Logical methods in computer science Ročník 21, Issue 4; číslo 4
Hlavní autoři: Di Guardia, Rémi, Laurent, Olivier
Médium: Journal Article
Jazyk:angličtina
Vydáno: Logical Methods in Computer Science Association 21.11.2025
Témata:
Computer Science
Logic in Computer Science
Proof-nets
Type Isomorphisms
Multiplicative-Additive fragment
Linear Logic
Star-autonomous categories with finite products
Sequent calculus
ISSN:1860-5974, 1860-5974
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Shrnutí: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.
ISSN:1860-5974
1860-5974
DOI:10.46298/lmcs-21(4:24)2025