{"id":24518195,"url":"https://github.com/pyzh/cubical","last_synced_at":"2026-02-25T00:35:30.697Z","repository":{"id":196578063,"uuid":"164675984","full_name":"pyzh/cubical","owner":"pyzh","description":"Groupoid Infinity cubical base library for cubicaltt","archived":false,"fork":false,"pushed_at":"2019-01-03T14:31:34.000Z","size":172,"stargazers_count":0,"open_issues_count":0,"forks_count":1,"subscribers_count":2,"default_branch":"master","last_synced_at":"2025-03-15T11:12:02.241Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":"https://groupoid.space/mltt/types/","language":null,"has_issues":false,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":"groupoid/CCHM","license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/pyzh.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null}},"created_at":"2019-01-08T15:18:24.000Z","updated_at":"2019-01-08T15:18:27.000Z","dependencies_parsed_at":"2023-09-26T08:18:58.007Z","dependency_job_id":null,"html_url":"https://github.com/pyzh/cubical","commit_stats":null,"previous_names":["pyzh/cubical"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/pyzh/cubical","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/pyzh%2Fcubical","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/pyzh%2Fcubical/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/pyzh%2Fcubical/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/pyzh%2Fcubical/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/pyzh","download_url":"https://codeload.github.com/pyzh/cubical/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/pyzh%2Fcubical/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":29806664,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-02-24T22:43:48.403Z","status":"ssl_error","status_checked_at":"2026-02-24T22:43:18.536Z","response_time":75,"last_error":"SSL_connect returned=1 errno=0 peeraddr=140.82.121.5:443 state=error: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2025-01-22T01:40:37.278Z","updated_at":"2026-02-25T00:35:30.681Z","avatar_url":"https://github.com/pyzh.png","language":null,"funding_links":[],"categories":[],"sub_categories":[],"readme":"[![Build Status](https://travis-ci.org/groupoid/cubical.svg?branch=master)](https://travis-ci.org/groupoid/cubical)\n\nGroupoid Infinity\n=================\n\nThe Groupoid Infinity Cubical Base Library is dedicated to [cubical](https://github.com/mortberg/cubicaltt)-compatible\ntypecheckers based on homotopy interval \u003cb\u003e[0,1]\u003c/b\u003e and MLTT as a core. The base library is founded\non top of 5 core modules: \u003cb\u003eproto\u003c/b\u003e (composition, id, const), \u003cb\u003epath\u003c/b\u003e (subst, trans, cong, refl, singl, sym),\n\u003cb\u003epropset\u003c/b\u003e (isContr, isProp, isSet), \u003cb\u003eequiv\u003c/b\u003e (fiber, eqiuv) and \u003cb\u003eiso\u003c/b\u003e (lemIso, isoPath).\nThis machinery is enough to prove univalence axiom.\n\n(i) The library has rich recursion scheme primitives in lambek module, while very basic nat, list, stream\nfunctionality. (ii) The very basic theorems are given in pi, iso_pi, sigma, iso_sigma, retract modules.\n(iii) The library has category theory theorems from HoTT book in cat, fun and category modules.\n(iv) The library also includes some impredicative categorical encoding sketches in coproduct_set.\nlambek also includes inductive semantics modeled with cata/ana recursion and fixpoint adjoints in/out.\n\nThis library is best to read with HoTT book at http://groupoid.space/mltt/types/\n\n![depgr](https://github.com/groupoid/cubical/blob/master/doc/img/base.png?raw=true)\n\n* [bool](http://groupoid.space/mltt/types/#bool) — Boolean\n* [control](http://groupoid.space/mltt/types/#control) — Control Free/CoFree, fix, pure/applicative typeclasses)\n* [eq](http://groupoid.space/mltt/types/#eq) — Runtime equality typeclass\n* [functor](http://groupoid.space/mltt/types/#functor) — Runtime Functor typeclass\n* [either](http://groupoid.space/mltt/types/#either) — Runtime Either\n* [maybe](http://groupoid.space/mltt/types/#either) — Runtime Maybe\n* [nat](http://groupoid.space/mltt/types/#nat) — Runtime Nat\n* [list](http://groupoid.space/mltt/types/#list) — Runtime List\n* [stream](http://groupoid.space/mltt/types/#stream) — Runtime Stream\n* [vector](http://groupoid.space/mltt/types/#vector) — Runtime Vector\n* [function](http://groupoid.space/mltt/types/#function) — Runtime Function\n* [equiv](http://groupoid.space/mltt/types/#equiv) — Core Equivalence\n* [propset](http://groupoid.space/mltt/types/#propset) — Core isContr isProp isSet isGroupoid\n* [path](http://groupoid.space/mltt/types/#path) — Core Path Type\n* [proto](http://groupoid.space/mltt/types/#proto) — Core Proto File\n* [iso](http://groupoid.space/mltt/iso) — Core Iso\n* [iso_pi](http://groupoid.space/mltt/iso.pi) — Iso Pi Theorems\n* [iso_sigma](http://groupoid.space/mltt/iso.sigma) — Iso Sigma Theorems\n* [pi](http://groupoid.space/mltt/types/#pi) — Pi\n* [sigma](http://groupoid.space/mltt/types/#pi) — Sigma\n* [lambek](http://groupoid.space/mltt/iso.sigma) — Inductive Models\n* [cat](http://groupoid.space/mltt/types/#cat) — HoTT Category\n* [univ](http://groupoid.space/mltt/univ) — HoTT Univalence\n* [circle](http://groupoid.space/mltt/types/#circle) — HoTT Circle\n* [retract](http://groupoid.space/mltt/types/#retract) — HoTT Retract\n* [fun](http://groupoid.space/mltt/types/#fun) — HoTT Categorical Functor\n\nAuthor\n------\n\n* Maxim Sokhatsky\n\nCredits\n-------\n\n* Eugene Smolanka\n* Andy Melnikov\n* Denis Stoyanov\n* Dmitry Astapov\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fpyzh%2Fcubical","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fpyzh%2Fcubical","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fpyzh%2Fcubical/lists"}