Type Isomorphisms for Multiplicative-Additive Linear Logic
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911285364391936 |
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| author | Di Guardia, Rémi Laurent, Olivier |
| author_facet | Di Guardia, Rémi Laurent, Olivier |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Type Isomorphisms for Multiplicative-Additive Linear Logic Di Guardia, Rémi Laurent, Olivier Logic in Computer Science 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. |
| title | Type Isomorphisms for Multiplicative-Additive Linear Logic |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2402.11987 |