{"id":13992916,"url":"https://github.com/forked-from-1kasper/ground_zero","last_synced_at":"2025-02-24T18:55:20.766Z","repository":{"id":37477712,"uuid":"472351480","full_name":"forked-from-1kasper/ground_zero","owner":"forked-from-1kasper","description":"Ground Zero: Lean 4 HoTT Library","archived":false,"fork":false,"pushed_at":"2024-12-10T11:38:15.000Z","size":3739,"stargazers_count":49,"open_issues_count":0,"forks_count":1,"subscribers_count":3,"default_branch":"master","last_synced_at":"2025-01-07T08:26:16.642Z","etag":null,"topics":["ctt","cubical-type-theory","homotopy-type-theory","hott","lean","lean4","leanprover","math"],"latest_commit_sha":null,"homepage":"","language":"Lean","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/forked-from-1kasper.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2022-03-21T13:32:56.000Z","updated_at":"2025-01-06T14:05:11.000Z","dependencies_parsed_at":"2023-01-31T10:30:46.909Z","dependency_job_id":"4260d1ed-4825-4bd3-a428-dbe5517e74aa","html_url":"https://github.com/forked-from-1kasper/ground_zero","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/forked-from-1kasper%2Fground_zero","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/forked-from-1kasper%2Fground_zero/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/forked-from-1kasper%2Fground_zero/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/forked-from-1kasper%2Fground_zero/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/forked-from-1kasper","download_url":"https://codeload.github.com/forked-from-1kasper/ground_zero/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":240540552,"owners_count":19817791,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","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":["ctt","cubical-type-theory","homotopy-type-theory","hott","lean","lean4","leanprover","math"],"created_at":"2024-08-09T14:02:10.521Z","updated_at":"2025-02-24T18:55:20.747Z","avatar_url":"https://github.com/forked-from-1kasper.png","language":"Lean","funding_links":[],"categories":["Lean"],"sub_categories":[],"readme":"# Ground Zero\n\nThis is an attempt to develop Homotopy Type Theory in [Lean 4](https://github.com/leanprover/lean4/).\n\nAs in [gebner/hott3](https://github.com/gebner/hott3), no modifications to the Lean kernel are made, because library uses [large eliminator checker](https://github.com/forked-from-1kasper/ground_zero/blob/master/GroundZero/Meta/HottTheory.lean) ported [from Lean 3](https://github.com/gebner/hott3/blob/master/src/hott/init/meta/support.lean). So stuff like this will print an error:\n\n```lean\nhott example {α : Type u} {a b : α} (p q : a = b) : p = q :=\nbegin cases p; cases q; apply Id.refl end\n```\n\n## HITs\n\n[Most HITs in the library](https://github.com/forked-from-1kasper/lean/tree/master/ground_zero/HITs) constructed using [quotients](https://leanprover.github.io/theorem_proving_in_lean/axioms_and_computation.html#quotients). Quotients in Lean have good computational properties (`Quot.ind` computes), so we can define HITs with them without any other changes in Lean’s kernel.\n\nThere are:\n\n* [Interval](https://github.com/forked-from-1kasper/ground_zero/blob/master/GroundZero/HITs/Interval.lean) $I$.\n* [Pushout](https://github.com/forked-from-1kasper/ground_zero/blob/master/GroundZero/HITs/Pushout.lean) $\\alpha \\sqcup^\\sigma \\beta $.\n* [Homotopical reals](https://github.com/forked-from-1kasper/ground_zero/blob/master/GroundZero/HITs/Reals.lean) $R$.\n* (Sequential) [colimit](https://github.com/forked-from-1kasper/ground_zero/blob/master/GroundZero/HITs/Colimit.lean).\n* [Generalized circle](https://github.com/forked-from-1kasper/ground_zero/blob/master/GroundZero/HITs/Generalized.lean) $\\{\\alpha\\}$.\n* [Propositional truncation](https://github.com/forked-from-1kasper/ground_zero/blob/master/GroundZero/HITs/Merely.lean) as a colimit of a following sequence:\n  $` \\alpha \\rightarrow \\{\\alpha\\} \\rightarrow \\{\\{\\alpha\\}\\} \\rightarrow \\ldots `$\n* [Suspension](https://github.com/forked-from-1kasper/ground_zero/blob/master/GroundZero/HITs/Suspension.lean) $\\Sigma \\alpha$ is defined as the pushout of the span $\\mathbf{1} \\leftarrow \\alpha \\rightarrow \\mathbf{1}$.\n* [Circle](https://github.com/forked-from-1kasper/ground_zero/blob/master/GroundZero/HITs/Circle.lean) $S^1$ is the suspension of the bool $\\mathbf{2}$.\n* Sphere $S^2$ is the suspension of the circle $S^1$.\n* [Join](https://github.com/forked-from-1kasper/ground_zero/blob/master/GroundZero/HITs/Join.lean) $\\alpha \\ast \\beta$.\n\nThere are also HITs that cannot be constructed this way. These HITs are defined using standard trick with [private structures](https://github.com/forked-from-1kasper/ground_zero/blob/master/GroundZero/HITs/Trunc.lean).\n\n## Dependency map\n\n![dependency map](pictures/dependency-map.svg \"dependency map\")\n\n\n## License\n\nCopyright © 2018–2024 Siegmentation Fault \u0026lt;siegmentationfault@yandex.ru\u0026gt;\n\nLicensed under the Apache License, Version 2.0 (the “License”);\nyou may not use this project except in compliance with the License.\nYou may obtain a copy of the License at\n\nhttp://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an “AS IS” BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fforked-from-1kasper%2Fground_zero","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fforked-from-1kasper%2Fground_zero","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fforked-from-1kasper%2Fground_zero/lists"}