The HoTT Game

The Homotopy Type Theory (HoTT) Game is a project written by mathematicians for mathematicians interested in HoTT and no experience in proof verification, with the aim of introducing Cubical Agda as a tool for trying out mathematics in HoTT. This page will help you get the Game working for you.

Installing Agda and the Cubical Agda library

Our Game is in Agda, which can be installed following instructions on their site. It is recommended that you use Agda in the text editor emacs, in particular Doom Emacs, if you can't be bothered to do a bunch of configuration.

Once you have Emacs and Agda, get the Cubical Library (version 0.3) and make sure Agda knows where your cubical library is by following instructions on the library management page. In short: locate (or create) your libraries file and add a line

the-directory/cubical.agda-lib

to it, where the-directory is the location of cubical.agda-lib on your computer.

Get the HoTT Game by cloning this repository into a folder and then making sure that Agda knows where the HoTT Game is by adding a line

the-directory/HoTTGameLib.agda

to your libraries file as above.

Try opening Trinitarianism/Quest0.agda in Emacs and do Ctrl-c Ctrl-l. Some text should be highlighted, and any ? should turn into { }.

Where to start?

You can start with 0Trinitarianism if you are interested in how logic, type theory and category theory come together as different ways to view the same thing. If you are more interested in homotopy theory, try 1FundamentalGroup where we show that the fundamental group of S¹ is ℤ.

How to start?

To start with 1FundamentalGroup (for example), find the GitHub page 1FundamentalGroup/Quest0Part0.md and follow the instructions there, then trying the following files in the same directory. Open up the corresponding .agda file in emacs to follow along with the instructions in the quests.

Emacs issues

If you can't figure out emacs or forget some command, then try consulting our guide for basic Emacs commands.