Papers › The Marriage of Univalence and Parametricity
The Marriage of Univalence and Parametricity
Nicolas Tabareau, Éric Tanter, Matthieu Sozeau
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Reasoning modulo equivalences is natural for everyone, including mathematicians. Unfortunately, in proof assistants based on type theory, equality is appallingly syntactic and, as a result, exploiting equivalences is cumbersome at best. Parametricity and univalence are two major concepts that have been explored to transport programs and proofs across type equivalences, but they fall short of achieving seamless, automatic transport. This work first clarifies the limitations of these two concepts in isolation, and then devises a fruitful marriage between both. The resulting concept, univalent parametricity, is an heterogeneous extension of parametricity strengthened with univalence that fully realizes programming and proving modulo equivalences. In addition to the theory of univalent parametricity, we present a lightweight framework implemented in Coq that allows the user to transparently transfer definitions and theorems for a type to an equivalent one, as if they were equal. For instance, this makes it possible to conveniently switch between an easy-to-reason-about representation and a computationally-efficient representation, as soon as they are proven equivalent. The combination of parametricity and univalence supports transport \`a la carte: basic univalent transport, which stems from a type equivalence, can be complemented with additional proofs of equivalences between functions over these types, in order to be able to lift more programs and proofs, as well as to yield more efficient terms. We illustrate the use of univalent parametricity on several examples, including a recent integration of native integers in Coq.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections