Homotopy canonicity for cubical type theory
Paper i 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.

Författare

Thierry Coquand

Logik och Typer

Simon Huber

Chalmers, Data- och informationsteknik, Datavetenskap

Christian Sattler

Logik och Typer

Leibniz International Proceedings in Informatics, LIPIcs

18688969 (ISSN)

Vol. 131 11:1-11:23

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

Algebra och logik

Datavetenskap (datalogi)

DOI

10.4230/LIPIcs.FSCD.2019.11

Mer information

Skapat

2023-11-15