Cubical Type Theory
Cubical type theory is a flavor of dependent type theory in which maps out of an interval primitive is used to define cubical path types, rather ...
Cubical Type Theory: a constructive interpretation of the univalence ...
This paper presents a type theory in which it is possible to directly manipulate n-dimensional cubes (points, lines, squares, cubes, etc.)
What's the point of cubical type theory? - MathOverflow
The rough point of cubical type theory is that it is computable: the univalence axiom failed to compute in other, earlier, approaches. Not to ...
Cubical Type Theory - amelia.how
The main idea of cubical type theory is the type of paths, so let's talk about that at length. Paths Even in boring old Martin-Löf type theory, as soon as we ...
Cubical type theory for dummies - Discover gists · GitHub
I'm going to take a shot to explain it informally in the format of Q&As. I prefer using syntax or terminologies that fit better rather than the more standard ...
Wrapping My Head Around Cubical Path Types - Shea Levy
Cubical type theory is a computational interpretation of Voevodsky's homotopy type theory based on a cubical set model.
A hands-on introduction to cubicaltt - Homotopy Type Theory
Cubical Type Theory has a model in cubical sets with lots of structure (symmetries, connections, diagonals) and is hence consistent. Furthermore ...
Towards a cubical type theory without an interval∗ - Ambrus Kaposi
Homotopy Type Theory [17] introduces the univalence axiom, which basically identifies propositional equality with equivalence of types1. We can understand the ...
Newest 'cubical-type-theory' Questions
Questions tagged [cubical-type-theory]. Ask Question. Cubical type theory is a version of homotopy type theory in which univalence is not just an axiom but a ...
Cartesian Cubical Computational Type Theory: Constructive ...
a type (and equality of members in a type). Intensional type theories—including homotopy type theory and the cubical type theory of Cohen et al. [17] ...
Naive cubical type theory - PhilSci-Archive
Since cubical type theory comes in many different forms, depending on the structure one imposes on the cube category it is based on, we should emphasize that.
Cubical Type Theory: A Constructive Interpretation of the Univalence ...
based on an interpretation of dependent type theory in a cubical set model. This enables new ways to reason about identity types, for instance, function ...
A tutorial on implementing De Morgan cubical type theory - arXiv
This tutorial explains (one way) how to implement De Morgan cubical type theory to people who know how to implement a dependent type theory.
Experimental implementation of Cubical Type Theory - GitHub
Cubical Type Theory. Experimental implementation of Cubical Type Theory in which the user can directly manipulate n-dimensional cubes. The language extends type ...
Naive cubical type theory - PhilArchive
Now, considering that cubical type theory comes in many different forms, depending on the structure one imposes on the cube category the framework is built on, ...
On Higher Inductive Types in Cubical Type Theory
Abstract. Cubical type theory provides a constructive justification to certain aspects of homotopy type theory such as Voevodsky's univalence axiom. This makes ...
Syntax and Models of Cartesian Cubical Type Theory
(Bezem and Coquand, 2015), Bezem et al. (2014, 2018) gave a constructive model of univalent type theory in cubical sets, which are presheaves over the free ...
Cubical Type Theory: a constructive interpretation of the univalence ...
based on an interpretation of dependent type theory in a cubical set model. This enables new ways to reason about identity types, for instance, function ...
Glue types in cubical type theory - Mathematics Stack Exchange
The main obstacle for me is the distinction of Path, Id and Glue types. I can sort of wrap my head around Path and Id, but I can't come up with a way to think ...
Maximilian Doré: Automating Reasoning in Cubical Type Theory
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