A unifying cartesian cubical type theory

A unified approach to type theory through a refined 2-calculus

Barendregt's cube, for example, is an attempt to unify various type systems and his associated logic cube is an attempt to find ... Cartesian product Hx : A.B..

What is the most intuitive dependent type theory I could learn? - Reddit

For non-dependent languages of the Barendregt cube, there is some truth to the type hierarchy because you still have a clear staging of ...

A Cubical Language for Bishop Sets - Daniel Gratzer

We present XTT, a version of Cartesian cubical type theory specialized for. Bishop sets `a la Coquand, in which every type enjoys a definitional ...

Cubical Homotopy Theory - Personal pages

These elementary constructions unify many basic concepts and endow the category of topological spaces with a sophis- ticated way to “add ...

Homotopy Type Theory: Unified Foundations of Mathematics and ...

Euclidean geometry has a model in the cartesian ... to the globular syntax of type theory, or to revise the syntax of type theory to be cubical.

Intuitionistic Type Theory - Stanford Encyclopedia of Philosophy

It is a full-scale system which aims to play a similar role for constructive mathematics as Zermelo-Fraenkel Set Theory does for classical ...

Fox cartesian structure for Gray monoidal double categories

Talk at Applied Category Theory 2023 This talk presents some results from the article, Cartesian Gray-Monoidal Double Categories.

From Set Theory to Type Theory | The n-Category Café

For instance, the rule for forming cartesian product types essentially says that the elements of A × B A\times B are, by definition, pairs ( a , ...

Unifying Cubical and Multimodal Type Theory - TYPES 2022

General modal type theory. Parameterised by a mode theory: A mode theory specifies the modal situation. A mode theory is a 2-category.

Rafaël Bocquet, Strict Rezk completions of models of HoTT and ...

Homotopy Type Theory Electronic Seminar Talks, 2024-02-29 https ... cartesian cubical sets.

Cartesian Cubical Computational Type Theory - EasyChair

We present a dependent type theory organized around a Cartesian notion of cubes (with faces, degeneracies, and diagonals), supporting both fibrant and non- ...

Cubical — Agda 2.6.3 documentation

The Cubical mode extends Agda with a variety of features from Cubical Type Theory. In particular, computational univalence and higher inductive types.

Cartesian cubical computational type theory: Constructive reasoning ...

We present a dependent type theory organized around a Cartesian notion of cubes (with faces, degeneracies, and diagonals), supporting both ...

Terrence Howard is Legitimately Insane - YouTube

At least a hundred of you asked for it, so here it is. Terrence Howard has been acting like a complete lunatic for years now, ...