{"id":20606035,"url":"https://github.com/totbwf/agda-partial-setoid","last_synced_at":"2026-03-07T16:04:01.991Z","repository":{"id":87348549,"uuid":"197411564","full_name":"TOTBWF/agda-partial-setoid","owner":"TOTBWF","description":"An implementation of partial setiods in agda","archived":false,"fork":false,"pushed_at":"2019-07-21T21:18:08.000Z","size":20,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":2,"default_branch":"master","last_synced_at":"2025-03-06T17:16:08.448Z","etag":null,"topics":["agda","type-theory"],"latest_commit_sha":null,"homepage":null,"language":"Agda","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/TOTBWF.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,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2019-07-17T15:02:03.000Z","updated_at":"2019-10-28T21:13:27.000Z","dependencies_parsed_at":null,"dependency_job_id":"9f9c639d-4bc1-40fa-964c-9bc0527c69ae","html_url":"https://github.com/TOTBWF/agda-partial-setoid","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/TOTBWF/agda-partial-setoid","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/TOTBWF%2Fagda-partial-setoid","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/TOTBWF%2Fagda-partial-setoid/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/TOTBWF%2Fagda-partial-setoid/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/TOTBWF%2Fagda-partial-setoid/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/TOTBWF","download_url":"https://codeload.github.com/TOTBWF/agda-partial-setoid/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/TOTBWF%2Fagda-partial-setoid/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":30221193,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-03-07T14:02:48.375Z","status":"ssl_error","status_checked_at":"2026-03-07T14:02:43.192Z","response_time":53,"last_error":"SSL_read: 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":["agda","type-theory"],"created_at":"2024-11-16T09:32:10.244Z","updated_at":"2026-03-07T16:04:01.975Z","avatar_url":"https://github.com/TOTBWF.png","language":"Agda","funding_links":[],"categories":[],"sub_categories":[],"readme":"Partial Setoids in Agda\n=========================\n\nA setoid is some set (or type, in the case of agda), equipped with an\nequivalence relation. This is useful in agda, because it allows\nus to use a much more interesting notions of equality than\ndefinitional equality, and define things like quotients of types.\n\nPartial Setoids are a generalization of this concept.\nInstead of equipping our set/type with an equivalence relation,\nwe use a _partial_ equivalence relation (equivalence relation w/o reflexivity).\n\nWhereas Setoids let us enrich a type with extra equalities, Partial Setoids\nlet us take away equalities, opening the door for things like subsets of types.\n\nFor example, we define a \"subset\" of a type as follows. Let `S` be a Partial Setoid\nover some type `A` with a Partial Equivalence relationship `≈`. We say some `x : A`\nis a member of `S` (or `x ∈ S`) if we can prove that `x ≈ x`.\n\nThis library implements Partial Setoids in agda, and proves some interesting properties\nof otther structures using these definitions.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftotbwf%2Fagda-partial-setoid","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Ftotbwf%2Fagda-partial-setoid","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftotbwf%2Fagda-partial-setoid/lists"}