Type Theory with Explicit Universe Polymorphism
Paper i proceeding, 2023

The aim of this paper is to refine and extend proposals by Sozeau and Tabareau and by Voevodsky for universe polymorphism in type theory. In those systems judgments can depend on explicit constraints between universe levels. We here present a system where we also have products indexed by universe levels and by constraints. Our theory has judgments for internal universe levels, built up from level variables by a successor operation and a binary supremum operation, and also judgments for equality of universe levels.

constraint-indexed products

type theory

universes in type theory

level-indexed products

universe polymorphism


M. Bezem

Universitetet i Bergen

Thierry Coquand

Göteborgs universitet

Peter Dybjer

Chalmers, Data- och informationsteknik, Computing Science

Martín Hötzel Escardó

University of Birmingham

Leibniz International Proceedings in Informatics, LIPIcs

18688969 (ISSN)

Vol. 269 13
9783959772853 (ISBN)

28th International Conference on Types for Proofs and Programs, TYPES 2022
Nantes, France,


Data- och informationsvetenskap



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