{"id":13993123,"url":"https://github.com/bryangingechen/lean-matroids","last_synced_at":"2025-10-26T16:59:48.717Z","repository":{"id":55577672,"uuid":"149715612","full_name":"bryangingechen/lean-matroids","owner":"bryangingechen","description":"matroids in lean","archived":false,"fork":false,"pushed_at":"2020-12-21T03:51:54.000Z","size":60,"stargazers_count":5,"open_issues_count":1,"forks_count":1,"subscribers_count":2,"default_branch":"master","last_synced_at":"2025-07-22T17:46:13.403Z","etag":null,"topics":["formal-mathematics","formal-proofs","lean","matroids","theorem-proving"],"latest_commit_sha":null,"homepage":null,"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/bryangingechen.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}},"created_at":"2018-09-21T05:45:25.000Z","updated_at":"2025-01-22T20:34:12.000Z","dependencies_parsed_at":"2022-08-15T03:31:00.336Z","dependency_job_id":null,"html_url":"https://github.com/bryangingechen/lean-matroids","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/bryangingechen/lean-matroids","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bryangingechen%2Flean-matroids","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bryangingechen%2Flean-matroids/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bryangingechen%2Flean-matroids/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bryangingechen%2Flean-matroids/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/bryangingechen","download_url":"https://codeload.github.com/bryangingechen/lean-matroids/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/bryangingechen%2Flean-matroids/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":281139039,"owners_count":26450140,"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","status":"online","status_checked_at":"2025-10-26T02:00:06.575Z","response_time":61,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"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":["formal-mathematics","formal-proofs","lean","matroids","theorem-proving"],"created_at":"2024-08-09T14:02:14.452Z","updated_at":"2025-10-26T16:59:48.676Z","avatar_url":"https://github.com/bryangingechen.png","language":"Lean","funding_links":[],"categories":["Lean"],"sub_categories":[],"readme":"# lean-matroids\n\nA formalization of [matroids](https://en.wikipedia.org/wiki/Matroid) in [Lean](https://leanprover.github.io), so far following the (beginning of the) first chapter of *Matroid Theory*, by James Oxley. These files depend on and are inspired by the Lean [mathlib](https://github.com/leanprover/mathlib), and maybe someday some of this will make it in there as well.\n\nCurrently [`matroid.lean`](src/matroid.lean) contains:\n* structures implementing the following formulations of matroids:\n  * independent sets\n  * circuits\n  * bases\n  * rank functions (only partially done)\n* proofs that the circuit / basis formulations are equivalent to the independent set formulation, via explicit conversion functions\n* proofs that the conversion functions are mutually inverse\n\nAnother file [`matroidexamples.lean`](src/matroidexamples.lean) contains:\n* the independent set definitions of:\n  * the loopy matroid (all subsets dependent)\n  * the free matroid (all subsets independent)\n  * the uniform matroid\n* various explicit example computations involving the basis and circuit lemmas and functions defined in [`matroid.lean`](src/matroid.lean).\n\n### Acknowledgements\n\nThanks to the denizens of the [Lean Zulip chat](https://leanprover.zulipchat.com) for patiently answering questions and providing proofs, several of which have been copied into this repository.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fbryangingechen%2Flean-matroids","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fbryangingechen%2Flean-matroids","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fbryangingechen%2Flean-matroids/lists"}