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All Your Base Are Belong to Us: Sort Polymorphism for Proof Assistants

Josselin Poiret, Gaëtan Gilbert, Kenji Maillard, Pierre-Marie Pédrot, Matthieu Sozeau, Nicolas Tabareau, Éric Tanter

Proof assistants based on dependent type theory, such as Coq, Lean and Agda, use different universes to classify types, typically combining a predicative hierarchy of universes for computationally-relevant types, and an impredicative universe of proof-irrelevant propositions. In …