knrafto / cubical

An experimental library for Cubical Agda

An experimental library for Cubical Agda

This library compiles with the master branch of the development version of Agda. For detailed install instructions see the INSTALL file.

If you want to use Agda 2.6.0.1 instead of the latest development version, you can check out the tag v0.1 of this library.

If you want to use Agda 2.6.1 instead of the latest development version, you can check out the tag v0.2 of this library.

For an introduction to Cubical Agda, see Cubical Agda: a dependently typed programming language with univalence and higher inductive types by Andrea Vezzosi, Anders Mörtberg, and Andreas Abel.

For an introduction to this library, see this blog post. Note that many files and results have moved since this blog post was written.

The type theory that Cubical Agda implements is a variation of the cubical type theory of:

Cubical Type Theory: a constructive interpretation of the univalence axiom - Cyril Cohen, Thierry Coquand, Simon Huber, Anders Mörtberg.

The key difference is that the Kan composition operations are decomposed into homogeneous composition and generalized transport as in:

On Higher Inductive Types in Cubical Type Theory - Thierry Coquand, Simon Huber, Anders Mörtberg.

This makes it possible to directly represent higher inductive types.

Maintainers

• Anders Mörtberg

• Andrea Vezzosi