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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Published in:Logical methods in computer science Vol. 21, Issue 4; no. 4
Main Authors: Di Guardia, Rémi, Laurent, Olivier
Format: Journal Article
Language:English
Published: Logical Methods in Computer Science Association 21.11.2025
Subjects:
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
Online Access:Get full text
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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.
AbstractList 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.
Author Di Guardia, Rémi
Laurent, Olivier
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Issue 4
Keywords Proof-nets
Type Isomorphisms
Multiplicative-Additive fragment
Linear Logic
Star-autonomous categories with finite products
Sequent calculus
Language English
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Snippet We characterize type isomorphisms in the multiplicative-additive fragment of linear logic (MALL), and thus in *-autonomous categories with finite products,...
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Logic in Computer Science
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