We present a model of type theory with dependent product, sum, and identity, in cubical sets. We describe a universe and explain how to transform an equivalence between two types into an equality. We also explain how to model propositional truncation and the circle. While not expressed internally in type theory, the model is expressed in a constructive metalogic. Thus it is a step towards a computational interpretation of Voevodsky\u27s Univalence Axiom
This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. ...
This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. ...
This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. ...
We present a model of type theory with dependent product, sum, and identity, in cubical sets. We des...
We present a model of type theory with dependent product, sum, and identity, in cubical sets. We des...
The interpretation of types in intensional Martin-Löf type theory as spaces and their equalities as ...
This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional c...
International audienceThis paper presents a type theory in which it is possible to directly manipula...
In this paper we provide a syntax for the cubical set model of type theory [3]. We start by defining...
Following the cubical set model of type theory which validates the univalence axiom, cubical type th...
We present a new constructive model of univalent type theory based on cubical sets. Unlike prior wor...
Following the cubical set model of type theory which validates the univalence axiom, cubical type th...
Following the cubical set model of type theory which validates the univalence axiom, cubical type th...
Following the cubical set model of type theory which validates the univalence axiom, cubical type th...
We construct a model of cubical type theory with a univalent and impredicative universe in a categor...
This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. ...
This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. ...
This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. ...
We present a model of type theory with dependent product, sum, and identity, in cubical sets. We des...
We present a model of type theory with dependent product, sum, and identity, in cubical sets. We des...
The interpretation of types in intensional Martin-Löf type theory as spaces and their equalities as ...
This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional c...
International audienceThis paper presents a type theory in which it is possible to directly manipula...
In this paper we provide a syntax for the cubical set model of type theory [3]. We start by defining...
Following the cubical set model of type theory which validates the univalence axiom, cubical type th...
We present a new constructive model of univalent type theory based on cubical sets. Unlike prior wor...
Following the cubical set model of type theory which validates the univalence axiom, cubical type th...
Following the cubical set model of type theory which validates the univalence axiom, cubical type th...
Following the cubical set model of type theory which validates the univalence axiom, cubical type th...
We construct a model of cubical type theory with a univalent and impredicative universe in a categor...
This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. ...
This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. ...
This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. ...