Type Theory with Explicit Universe Polymorphism (revised and extended version)
Type Theory with Explicit Universe Polymorphism (revised and extended version)
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.
This paper was presented at Types'2022 and appeared in the post-proceedings published by LIPIcs. This version adds a correction in Appendix C. Otherwise the paper is as the one published by LIPIcs
- University of Birmingham United Kingdom
- Chalmers University of Technology Sweden
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, 03B38, F.4.1, Logic in Computer Science (cs.LO)
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, 03B38, F.4.1, Logic in Computer Science (cs.LO)
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