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Notes on Homotopy Type Theory in Agda
https://github.com/lemastero/agda-hott

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Notes on Homotopy Type Theory in Agda

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# Agda HoTT

Notes in Agda about
* [Homotopy Type Theory](https://homotopytypetheory.org/book/) (based on
* [Introduction to Univalent Foundations of Mathematics with Agda](https://www.cs.bham.ac.uk/~mhe/HoTT-UF-in-Agda-Lecture-Notes/) by Martín Hötzel Escardó, ([arxiv 1911.00580](https://arxiv.org/abs/1911.00580)),
* [Introduction to Homotopy Type Theory](https://arxiv.org/abs/2212.11082) by Egbert Rijke,
* [HoTTEST Summer School 2022](https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest_summer_school_2022.html) ([Agda](https://martinescardo.github.io/HoTTEST-Summer-School/)), ([lectures & exercises](https://github.com/martinescardo/HoTTEST-Summer-School/tree/main/HoTT)), ([videos](https://www.youtube.com/user/jdchristensen123)), ([GH](https://github.com/martinescardo/HoTTEST-Summer-School)),
* [Homotopy type theory](https://github.com/andrejbauer/homotopy-type-theory-course) by Andrej Bauer ([videos](https://www.youtube.com/watch?v=FBjz8mFXH7M&list=PL-47DDuiZOMCRDiXDZ1fI0TFLQgQqOdDa)),
* [Math 721: Homotopy Type Theory](https://github.com/emilyriehl/721) by Emily Riehl
* [Category Theory](https://ncatlab.org/nlab/show/category+theory) (based on
* CS410 Advanced Functional Programming at the University of Strathclyde by Conor McBride ([videos](https://www.youtube.com/playlist?list=PLqggUNm8QSqmeTg5n37oxBif-PInUfTJ2)), ([GH repo with code](https://github.com/pigworker/CS410-17)), ([lecture notes](https://github.com/pigworker/CS410-15/blob/master/CS410-notes.pdf)), ([GH 2018](https://github.com/pigworker/CS410-18)),
* [agda-categories](https://github.com/agda/agda-categories))
* Functional Programming (abstractions from category theory used in Haskell, Scala, PureScript, Idris)

Abstractions in FP can be seen as continuation of [scala_typeclassopedia](https://github.com/lemastero/scala_typeclassopedia) - this time in Agda :)

[src/FP/zio-prelude](src/FP/zio-prelude) aims at formally verifying encoding from Scala library [zio-prelude](https://zio.dev/zio-prelude/) (that improve usual encoding of FP abstractions e.g. by adding Zivariant, introducing novel definitions like ZRerf that is a generalization of optics).

Category theory definitions are strict - use equality (agda-categories are parametrized by equivalence relation).

## Getting Agda

[Official install instructions](https://agda.readthedocs.io/en/latest/getting-started/installation.html)

### for Nix

If you are nix user you can get shell with recent Agda by running:

```sh
nix develop
```