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README.md

An experimental library for Cubical Agda

This library compiles with the master branch of Agda. To install Agda in a cabal sandbox do:

git clone https://github.com/agda/agda
cd agda
cabal sandbox init
cabal install

The type theory that it 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.

The library is divided into:

  • Cubical/Core: minimal core library to get Cubical Agda up and running.

  • Cubical/Basics: basic theory (natural numbers, integers, basic results about equivalences...). This folder does not contain any HITs.

  • Cubical/HITs: various higher inductive types and results about them.

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