Cubical Computational Type Theory and RedPRL

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Cartesian Cubical Computational Type Theory

We present a dependent type theory organized around a Cartesian notion of cubes (with faces, degeneracies, and diagonals), supporting both fibrant and non-fibrant types. The fibrant fragment includes Voevodsky’s univalence axiom and a circle type, while the non-fibrant fragment includes exact (strict) equality types satisfying equality reflection. Our type theory is defined by a semantics in cu...

متن کامل

Higher Inductive Types in Cubical Computational Type Theory

In homotopy type theory (HoTT), higher inductive types provide a means of defining and reasoning about higher-dimensional objects such as circles and tori. The formulation of a schema for such types remains a matter of current research. We investigate the question in the context of cubical type theory, where the homotopical structure implicit in HoTT is made explicit in the judgmental apparatus...

متن کامل

Cartesian Cubical Type Theory

We present a cubical type theory based on the Cartesian cube category (faces, degeneracies, symmetries, diagonals, but no connections or reversal) with univalent universes, each containing Π, Σ, path, identity, natural number, boolean, pushout, and glue (equivalence extension) types. The type theory includes a syntactic description of a uniform Kan operation, along with judgemental equality rul...

متن کامل

Cubical Type Theory

() : ∆→ () σ : ∆→ Γ ∆ ` u : Aσ (σ, x = u) : ∆→ Γ, x : A σ : ∆→ Γ ∆ ` φ : I (σ, i = φ) : ∆→ Γ, i : I σ : ∆→ Γ Γ ` A ∆ ` Aσ σ : ∆→ Γ Γ ` t : A ∆ ` tσ : Aσ We can define 1Γ : Γ→ Γ by induction on Γ and then if Γ ` u : A we write (x = u) : Γ→ Γ, x : A for 1Γ, x = u. If we have further Γ, x : A ` t : B we may write t(u) and B(u) respectively instead of t(x = u) and B(x = u). Similarly if Γ ` φ : I w...

متن کامل

Computational Higher Type Theory II: Dependent Cubical Realizability

This is the second in a series of papers extending Martin-Löf’smeaning explanation of dependent type theory to account for higher-dimensional types. We build on the cubical realizability framework for simple types developed in Part I, and extend it to a meaning explanation of dependent higher-dimensional type theory. This extension requires generalizing the computational Kan condition given in ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science

سال: 2018

ISSN: 2075-2180

DOI: 10.4204/eptcs.274.0.1