10 citations · 11 across the 2 of their papers we have counts for
5 papers
Canonicity and homotopy canonicity for cubical type theory
Thierry Coquand, Simon Huber, Christian Sattler
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 comput…
On Higher Inductive Types in Cubical Type Theory
Thierry Coquand, Simon Huber, Anders Mörtberg
Cubical type theory provides a constructive justification to certain aspects of homotopy type theory such as Voevodsky's univalence axiom. This makes many extensionality principles…
The univalence axiom in cubical sets
Marc Bezem, Thierry Coquand, Simon Huber
In this note we show that Voevodsky's univalence axiom holds in the model of type theory based on symmetric cubical sets. We will also discuss Swan's construction of the identity t…
Cubical Type Theory: a constructive interpretation of the univalence axiom
Cyril Cohen, Thierry Coquand, Simon Huber +1
This paper presents a type theory in which it is possible to directly manipulate -dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent…
Canonicity for Cubical Type Theory
Simon Huber
Cubical type theory is an extension of Martin-Löf type theory recently proposed by Cohen, Coquand, Mörtberg and the author which allows for direct manipulation of -dimensional c…