Univalence for free

Matthieu Sozeau (1, 2) , Nicolas Tabareau (3, 4)

1 PI.R2 - Design, study and implementation of languages for proofs and programs
2 PPS - Preuves, Programmes et Systèmes
3 ASCOLA - Aspect and composition languages
4 LINA - Laboratoire d'Informatique de Nantes Atlantique

We present an internalization of the 2-groupoid interpretation of the calculus of construction that allows to realize the univalence axiom, proof irrelevance and reasoning modulo. As an example, we show that in our setting, the type of Church integers is equal to the inductive type of natural numbers.

Domaines: Logique en informatique [cs.LO]; Catégories et ensembles [math.CT]

Matthieu Sozeau, Nicolas Tabareau. Univalence for free. 2013. ⟨hal-00786589v1⟩