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.

Computational Semantics of Cartesian Cubical Type Theory - KiltHub

Computational Semantics of Cartesian Cubical Type Theory.

Computational semantics of Cartesian cubical type theory

I Define programming language and operational semantics. I Define a notion of equality at each type. I Check this is compatible with desired ...

Computational Semantics of Cartesian Cubical Type Theory

In the past decade, type theories have also attracted the attention of mathematicians due to surprising connections with homotopy theory; the study of these ...

Computational Semantics of Cartesian Cubical Type Theory

I describe Cartesian cubical type theory (× 2) and present its computational semantics. Published at POPL 2017 [A., Harper, Wilson] and CSL 2018 ...

Cartesian Cubical Computational Type Theory: Constructive ...

Our type theory is defined by a semantics in cubical partial equivalence relations, and is the first two-level type theory to satisfy the canonicity property: ...

Carlo Angiuli, Computational semantics of Cartesian cubical type ...

Homotopy Type Theory Electronic Seminar Talks, 2018-03-15 Dependent types are simultaneously a theory of constructive mathematics and a ...

Cartesian Cubical Computational Type Theory - PKC

The theory is defined by a semantics in cubical partial equivalence relations, and is the first two-level type theory to satisfy the canonicity property: all ...

Cartesian Cubical Computational Type Theory - Favonia

Cartesian cubical + computational. Dependent types. Univalent Kan ... Computational Semantics. Transition system for closed terms. (λa.M)N ...

cubical type theory in nLab

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.

Cartesian Cubical Computational Type Theory - Semantic Scholar

A dependent type theory organized around a Cartesian notion of cubes, supporting both fibrant and non-fibrant types, and is the first two-level type theory ...

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 ...

Cartesian Cubical Computational Type Theory - EasyChair

Our type theory is defined by a semantics in cubical partial equivalence relations, and is the first two-level type theory to satisfy the canonicity property: ...

Cartesian Cubical Computational Type Theory - Favonia

Cartesian cubical + computational. Dependent types. Univalent Kan ... Computational semantics: values. (⟨x⟩M)@r ↦ M⟨r/x⟩ coex. A. [r ...

Cubical Computational Type Theory - Zulip Chat Archive

(Cartesian) Cubical Computational Type Theory is a logical framework. You'd need an implementation of it to do everyday computing. Given such an ...

Cartesian Cubical Computational Type Theory - DROPS

Our type theory is defined by a semantics in cubical partial equivalence relations, and is the first two-level type theory to satisfy the canonicity property: ...

Cartesian cubical computational type theory - YouTube

... type-theoretic semantics with all the features but instead based on Cartesian cubes. In addition to using a different cubical structure, our ...

[1712.01800] Computational Higher Type Theory III - arXiv

Abstract:This is the third in a series of papers extending Martin-Löf's meaning explanations of dependent type theory to a Cartesian cubical ...

Cartesian cubical computational type theory: Constructive reasoning ...

Our type theory is defined by a semantics in cubical partial equivalence relations, and is the first two-level type theory to satisfy the ...

Yet Another Cartesian Cubical Type Theory

Computational Higher Type Theory III: Univalent Universes and Exact Equality. (Angiuli, Favonia, Harper - AFH). Cartesian Cubical Type Theory.