{"id":13829715,"url":"https://github.com/agda/cubical","last_synced_at":"2026-02-03T09:34:47.255Z","repository":{"id":33370960,"uuid":"153086880","full_name":"agda/cubical","owner":"agda","description":"An experimental library for Cubical 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standard library for Cubical Agda\n===================================\n\nThe source code has a glorious clickable [rendered version](https://agda.github.io/cubical/Cubical.Everything.html).\n\nThere is also a [discord server](https://discord.gg/yjTKHzepMx), shared with [agda-unimath](https://unimath.github.io/agda-unimath/) and the [1lab](https://1lab.dev/).\n\nCompiling, using and installing\n-------------------------------\nThis library checks with [Agda](https://github.com/agda/agda/) version indicated in the table below.\nFor detailed install instructions see the\n[INSTALL](https://github.com/agda/cubical/blob/master/INSTALL.md)\nfile.\nIf you want to use some specific release of Agda,\nthe following table lists which releases of Agda are known to work with which release of this library.\nMost likely, a lot more combinations work as well.\nAgda versions as written below, correspond to tags.\n\n| cubical library version | Agda versions                  |\n|-------------------------|--------------------------------|\n| current master          | `v2.8.0`                       |\n| `v0.9`                  | `v2.8.0`                       |\n| `v0.8`                  | `v2.6.4.1` `v2.7.0.1`          |\n| `v0.7`                  | `v2.6.4` `v2.6.4.1`            |\n| `v0.6`                  | `v2.6.4`                       |\n| `v0.5`                  | `v2.6.3` `v2.6.4`              |\n| `v0.4`                  | `v2.6.2.2`                     |\n| `v0.3`                  | `v2.6.2`                       |\n| `v0.2`                  | `v2.6.1.3`                     |\n| `v0.1`                  | `v2.6.0.1`                     |\n\nFor example, if you have Agda 2.6.2.2, you can switch to version 0.4 of the cubical library with\n```\ngit checkout v0.4\n```\n\nLearning materials\n------------------\n* Introductory material from the HoTTest summer school:\n  [literate agda files](https://github.com/martinescardo/HoTTEST-Summer-School/tree/main/Agda/Cubical)\n  [recordings on youtube](https://www.youtube.com/channel/UC-9jDbJ-HegCFuWuam1SfvQ)\n\n* For an introduction to this library, see this [blog\n  post](https://homotopytypetheory.org/2018/12/06/cubical-agda/). Note that many\n  files and results have moved since this blog post was written.\n\n* For some introductory lecture notes see the material for the Cubical Agda course\n  of the [EPIT 2021 spring school](https://github.com/HoTT/EPIT-2020/blob/main/04-cubical-type-theory/).\n\n\nTheoretical background\n----------------------\nFor a paper with details about Cubical Agda, see [Cubical Agda: a dependently typed\nprogramming language with univalence and higher inductive\ntypes](https://dl.acm.org/doi/10.1145/3341691) by Andrea Vezzosi, Anders\nMörtberg, and Andreas Abel.\n\nThe type theory that Cubical Agda implements is a variation of the\ncubical type theory of:\n\n[Cubical Type Theory: a constructive interpretation of the univalence\naxiom](https://arxiv.org/abs/1611.02108) - Cyril Cohen, Thierry\nCoquand, Simon Huber, Anders Mörtberg.\n\n\nThe key difference is that the Kan composition operations are\ndecomposed into homogeneous composition and generalized transport as\nin:\n\n[On Higher Inductive Types in Cubical Type\nTheory](https://arxiv.org/abs/1802.01170) - Thierry Coquand, Simon\nHuber, Anders Mörtberg.\n\nThis makes it possible to directly represent higher inductive types.\n\n\nReviewing of [pull requests](https://github.com/agda/cubical/pulls?q=is%3Apr+is%3Aopen+draft%3Afalse)\n--------------------------\nIf you switch your draft pull request (PR) to 'ready to merge',\nor directly create an open PR,\nwe should request a review, by one of the reviewers below.\nIf that doesn't happen, you can also request a reviewer yourself (for reviewer expertise see below),\nto make us aware of the open PR. Feel free to use Discord to get in touch with a reviewer in case reviewing is taking a very long time.\n\n| Reviewer                                                           | github handle                                 | Area of expertise                          |\n|--------------------------------------------------------------------|-----------------------------------------------|--------------------------------------------|\n| [Anders Mörtberg](https://staff.math.su.se/anders.mortberg/)       | [mortberg](https://github.com/mortberg)       | *Most topics*                              |\n| [Evan Cavallo](https://ecavallo.net/)                              | [ecavallo](https://github.com/ecavallo)       | *Most topics*                              |\n| [Felix Cherubini](https://felix-cherubini.de)                      | [felixwellen](https://github.com/felixwellen) | *Mainly algebra related topics*            |\n| [Max Zeuner](https://www.su.se/english/profiles/maze1512-1.450461) | [mzeuner](https://github.com/mzeuner)         | *Algebra related topics*                   |\n| [Axel Ljungström](https://aljungstrom.github.io)                   | [aljungstrom](https://github.com/aljungstrom) | *Synthetic homotopy theory and cohomology* |\n| [Max New](http://maxsnew.com)                                      | [maxsnew](https://github.com/maxsnew)         | *Category theory*                          |\n| [Andrea Vezzosi](http://saizan.github.io/)                         | [Saizan](https://github.com/Saizan)           | *Inactive*                                 |\n\n[Overview](https://github.com/agda/cubical/pulls?q=is%3Apr+is%3Aopen+sort%3Aupdated-asc+draft%3Afalse) of the current open PRs, descending time since last action.\n","funding_links":[],"categories":["Agda"],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fagda%2Fcubical","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fagda%2Fcubical","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fagda%2Fcubical/lists"}