A calculus of constructions with explicit subtyping

Ali Assaf (1, 2)

1 DEDUCTEAM - Deduction modulo, interopérabilité et démonstration automatique
2 X - École polytechnique

The calculus of constructions can be extended with an infinite hierarchy of universes and cumulative subtyping. In this hierarchy, each universe is contained in a higher universe. Subtyping is usually left implicit in the typing rules. We present an alternative version of the calculus of constructions where subtyping is explicit. This new system avoids problems related to coercions and dependent types by using the Tarski style of universes and by introducing additional equations to reflect equality.

Mots clés: calculus of constructions; type theory; universes; cumulativity; subtyping; explicit coercions

Domaines: Informatique [cs]

Ali Assaf. A calculus of constructions with explicit subtyping. 2014. ⟨hal-01097401v1⟩