A unifying cartesian cubical type theory

A unifying cartesian cubical type theory - Google Groups

We can also illustrate what the pushout product with a cofibration looks like, using the boundary inclusion 2 -> I as an example: The codomain is the product T ...

a unifying cartesian cubical type theory - Semantic Scholar

This note presents a univalent type theory based on cartesian cubical sets. The difference from earlier work on similar models is that it depends neither on ...

A Unifying Cartesian Cubical Set Model

Univalent Type Theory has a constructive model in cartesian Kan cubical sets (“ABCFHL model”). A. Mörtberg. Introduction. August 21, 2019. 6 / ...

A Unifying Cartesian Cubical Set Model - GitHub Pages

working on computational cartesian cubical type theory. This then led to: Theorem (Angiuli, Brunerie, Coquand, Favonia, Harper, Licata, 2017).

cubical type theory in nLab

If you add only diagonals, then you have the 'cartesian cube category'. This was used as a basis for a cubical type theory by Angiuli, Brunerie, ...

Syntax and Models of Cartesian Cubical Type Theory

Cubical type theories are a family of formal systems for Homotopy Type Theory/Univalent. Foundations (Voevodsky, 2006; The Univalent Foundations Program, ...

mortberg/gen-cart: A Unifying Cartesian Cubical Set Model - GitHub

Agda code for a Cartesian cubical set model of univalent type theory based on a weakened version of ABCFHL fibrations. This generalizes the construction in ...

Syntax and models of Cartesian cubical type theory | Cambridge Core

We present a cubical type theory based on the Cartesian cube category (faces, degeneracies, symmetries, diagonals, but no connections or reversal) with ...

Unifying Cubical Models of Univalent Type Theory - Evan Cavallo

Cartesian cubical sets are hence better-suited as a basis for cubical type theory, and they are known to support higher inductive types. However, constructing ...

Unifying cubical and multimodal type theory - arXiv

Definition 4.1. A cosmos is a pseudofunctor F : M. Cat that takes objects to locally cartesian closed categories and morphisms to right adjoints. We denote the ...

[PDF] Unifying Cubical Models of Univalent Type Theory | Semantic ...

Log. Methods Comput. Sci. 2022. TLDR. XTT, a version of Cartesian cubical type theory specialized ...

Computational Semantics of Cartesian Cubical Type Theory

Dependent type theories are a family of logical systems that serve as expressive functional programming languages and as the basis of many proof assistants.

Unifying Cubical Models of Homotopy Type Theory

Univalent Type Theory has a constructive model in cartesian Kan cubical sets (“ABCFHL model”). A. Mörtberg. Introduction. October 23, 2019. 10 / ...

Anders Mörtberg, Unifying cubical models of homotopy type theory

... cubical models. The crucial idea of this generalization is to weaken the notion of fibration from the cartesian cubical set model so that it ...

Unifying Cubical Models of Univalent Type Theory - DROPS

By applying the construction in the presence of diagonal cofibrations or connections and reversals, we recover the existing cartesian and De ...

[2101.11479] Normalization for Cubical Type Theory - arXiv

Abstract:We prove normalization for (univalent, Cartesian) cubical type theory, closing the last major open problem in the syntactic metatheory ...

Newest 'cubical-type-theory' Questions

Cubical type theory is a version of homotopy type theory in which univalence is not just an axiom but a theorem, hence, since this is constructive, ...

Unifying Cubical Models of Univalent Type Theory - DiVA portal

By applying the construction in the presence of diagonal cofibrations or connections and reversals, we recover the existing cartesian and De Morgan cubical set ...

RedPRL/redtt: "Between the darkness and the dawn, a red cube rises!"

redtt is a core language for cartesian cubical type theory with extension types. We plan to build an extensible interactive proof assistant around it.

Unifying Cubical Models of Univalent Type Theory|INIS

By applying the construction in the presence of diagonal cofibrations or connections and reversals, we recover the existing cartesian and De Morgan cubical set ...