Displayed Monoidal Categories for the Semantics of Linear Logic

Benedikt Ahrens, Ralph Matthes, Niels Van Der Weide, Kobe Wullaert

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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Abstract

We present a formalization of different categorical structures used to interpret linear logic. Our formalization takes place in UniMath, a library of univalent mathematics based on the Coq proof assistant. All the categorical structures we formalize are based on monoidal categories. As such, one of our contributions is a practical, usable library of formalized results on monoidal categories. Monoidal categories carry a lot of structure, and instances of monoidal categories are often built from complicated mathematical objects. This can cause challenges of scalability, regarding both the vast amount of data to be managed by the user of the library, as well as the time the proof assistant spends on checking code. To enable scalability, and to avoid duplication of computer code in the formalization, we develop "displayed monoidal categories". These gadgets allow for the modular construction of complicated monoidal categories by building them in layers; we demonstrate their use in many examples. Specifically, we define linear-non-linear categories and construct instances of them via Lafont categories and linear categories.

Original languageEnglish
Title of host publicationCPP 2024 - Proceedings of the 13th ACM SIGPLAN International Conference on Certified Programs and Proofs
EditorsAmin Timany, Dmitriy Traytel, Brigitte Pientka, Sandrine Blazy
Place of PublicationNew York, NY, USA
PublisherAssociation for Computing Machinery (ACM)
Pages260-273
Number of pages14
ISBN (Print)979-8-4007-0488-8
DOIs
Publication statusPublished - 2024
Event13th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2024, in affiliation with the annual Symposium on Principles of Programming, Languages, ,POPL 2024 - London, United Kingdom
Duration: 15 Jan 202416 Jan 2024

Conference

Conference13th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2024, in affiliation with the annual Symposium on Principles of Programming, Languages, ,POPL 2024
Country/TerritoryUnited Kingdom
CityLondon
Period15/01/2416/01/24

Keywords

  • categorical semantics
  • Coq
  • linear logic
  • monoidal categories
  • UniMath

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