Canonicity and homotopy canonicity for cubical type theory
-
Published:2022-02-03
Issue:
Volume:Volume 18, Issue 1
Page:
-
ISSN:1860-5974
-
Container-title:Logical Methods in Computer Science
-
language:en
-
Short-container-title:
Author:
Coquand Thierry,Huber Simon,Sattler Christian
Abstract
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.
Publisher
Centre pour la Communication Scientifique Directe (CCSD)
Subject
General Computer Science,Theoretical Computer Science
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献