kcsongor / cubical

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.

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.

For an introduction to Cubical Agda and this library see this blog post. Note that many files and results have moved compared to state of the library described in the blog post.

Maintainers

• Anders Mörtberg

• Andrea Vezzosi