Homotopy canonicity for cubical type theory
Paper in proceeding, 2019

Cubical type theory provides a constructive justification of homotopy type theory. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices. We present in this article two canonicity results, both proved by a sconing argument: a homotopy canonicity result, every natural number is path equal to a numeral, even if we take away the equations defining the lifting operation on the type structure, and a canonicity result, which uses these equations in a crucial way. Both proofs are done internally in a presheaf model.

Author

Thierry Coquand

Logic and Types

Simon Huber

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Christian Sattler

Logic and Types

Leibniz International Proceedings in Informatics, LIPIcs

18688969 (ISSN)

Vol. 131 11:1-11:23

4th International Conference on Formal Structures for Computation and Deduction
, ,

Subject Categories

Algebra and Logic

Computer Science

DOI

10.4230/LIPIcs.FSCD.2019.11

More information

Created

11/15/2023