Trocq: Proof Transfer for Free, Beyond Equivalence and Univalence
This article presents Trocq , a new proof transfer framework for dependent type theory. Trocq is based on a novel formulation of type equivalence, used to generalize the univalent parametricity translation. This framework takes care of avoiding dependency on the axiom of univalence when possible, and may be used with more relations than just equivalences. We have implemented a corresponding plugin for the Rocq/Coq interactive theorem prover, in the Coq-Elpi meta-language.
Authors
- Assia Mahboubi (ORCID: https://orcid.org/0000-0002-0312-5461)
- Enzo Crance (ORCID: https://orcid.org/0000-0002-0498-0910)
- Cyril Cohen (ORCID: https://orcid.org/0000-0003-3540-1050)
Institutions
- École Centrale de Nantes (FR)
- Université Claude Bernard Lyon 1 (FR)
- École Normale Supérieure de Lyon (FR)
- Centre National de la Recherche Scientifique (FR)
- Mitsubishi Electric (France) (FR)
- Laboratoire des Sciences du Numérique de Nantes (FR)
- Vrije Universiteit Amsterdam (NL)
- Nantes Université (FR)
Publication Details
- Journal
- ACM Transactions on Programming Languages and Systems
- Published
- 2025-05-26
- DOI
- https://doi.org/10.1145/3737283
- Primary Topic
- Logic, programming, and type systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00