Type Theory with Explicit Universe Polymorphism
Paper in 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

University of Bergen

Thierry Coquand

University of Gothenburg

Peter Dybjer

Chalmers, Computer Science and Engineering (Chalmers), 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,

Subject Categories

Computer and Information Science



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