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Constructive HoTT

A note about various constructive interpretations of HoTT, including the Path type, HITs and the univalence principle (instead of axiom, because it's no longer an axiom!).

Build

To build a preprint PDF, you'll need TeXLive, a python package Pygments, the most recent version of Agda and its cubical library.

Installing Pygments:

pip install Pygments

or:

pip3 install Pygments

Installing TeXLive && Pygments on NixOS:

nix-env -iA nixos.python37Packages.pygments nixos.texlive.combined.scheme-full

Installing Agda requires an extra step if you're on a non-English version of Windows:

CHCP 65001

then you follow the instructions here. Unfortunately, this project cannot be built on Windows. To build this note on Windows, you'll need to port Makefile to Windows, and I don't have time to do so.

After all dependencies are installed, run this to compile the PDF:

make main

Any sort of contribution is welcomed.

TODOs

  • Univalence
  • xtt
  • The rest of this list