{"id":19489334,"url":"https://github.com/redprl/agda-mugen","last_synced_at":"2026-02-01T00:07:42.247Z","repository":{"id":58397755,"uuid":"531362499","full_name":"RedPRL/agda-mugen","owner":"RedPRL","description":"A formalization of the theory behind the mugen library","archived":false,"fork":false,"pushed_at":"2024-06-24T01:56:08.000Z","size":454,"stargazers_count":19,"open_issues_count":5,"forks_count":1,"subscribers_count":4,"default_branch":"main","last_synced_at":"2025-06-13T05:43:30.057Z","etag":null,"topics":[],"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/RedPRL.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":"2022-09-01T04:29:04.000Z","updated_at":"2025-01-22T15:02:43.000Z","dependencies_parsed_at":"2024-05-27T18:32:04.553Z","dependency_job_id":null,"html_url":"https://github.com/RedPRL/agda-mugen","commit_stats":null,"previous_names":[],"tags_count":2,"template":false,"template_full_name":null,"purl":"pkg:github/RedPRL/agda-mugen","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/RedPRL%2Fagda-mugen","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/RedPRL%2Fagda-mugen/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/RedPRL%2Fagda-mugen/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/RedPRL%2Fagda-mugen/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/RedPRL","download_url":"https://codeload.github.com/RedPRL/agda-mugen/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/RedPRL%2Fagda-mugen/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":28961232,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-01-31T23:03:11.038Z","status":"ssl_error","status_checked_at":"2026-01-31T22:56:44.691Z","response_time":128,"last_error":"SSL_connect returned=1 errno=0 peeraddr=140.82.121.6:443 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":"2024-11-10T21:08:08.236Z","updated_at":"2026-02-01T00:07:42.229Z","avatar_url":"https://github.com/RedPRL.png","language":"Agda","readme":"\u003c!--- vim: set nowrap: ---\u003e\n\n# ♾ mugen 無限 in Agda\n\nThis is a formalization of the displacement algebras, their properties, and part of meta-theoretic analysis found in our POPL 2023 paper [“An Order-Theoretic Analysis of Universe Polymorphism”.](https://favonia.org/files/mugen.pdf) The accompanying OCaml implementation is at \u003chttps://github.com/RedPRL/mugen/\u003e.\n\n🚧 This repository is under major rewrites and cleanups. See version 0.1.0 for the code that matches the POPL 2023 paper.\n\n## Mechanized Results\n\n### Displacement Algebras\n\n🚧 The links are currently broken.\n\n| Displacements                         | Paper Section    | Agda Module                                                                    | OCaml Module(s)                                                                                                                                                     |\n| :------------------------------------ | :--------------- | :----------------------------------------------------------------------------- | :------------------------------------------------------------------------------------------------------------------------------------------------------------------ |\n| Natural numbers                       | 3.3.1            | [Nat](src/Mugen/Algebra/Displacement/Instances/Nat.agda)                       | [Nat](https://redprl.org/mugen/mugen/Mugen/Shift/Nat) and [Nat](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/Nat)                                             |\n| Integers                              | 3.3.1            | [Int](src/Mugen/Algebra/Displacement/Instances/Int.agda)                       | [Int](https://redprl.org/mugen/mugen/Mugen/Shift/Int) and [Int](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/Int)                                             |\n| Non-positive integers                 | 3.3.1            | [NonPositive](src/Mugen/Algebra/Displacement/Instances/NonPositive.agda)       | [NonPositive](https://redprl.org/mugen/mugen/Mugen/Shift/NonPositive) and [NonPositive](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/NonPositive)             |\n| Constant displacements                | 3.3.2            | [Constant](src/Mugen/Algebra/Displacement/Instances/Constant.agda)             | [Constant](https://redprl.org/mugen/mugen/Mugen/Shift/Constant)                                                                                                     |\n| Binary products                       | 3.3.3            | [Product](src/Mugen/Algebra/Displacement/Instances/Product.agda)               | [Product](https://redprl.org/mugen/mugen/Mugen/Shift/Product) and [Product](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/Product)                             |\n| Lexicographic binary products         | 3.3.4            | [Lexicographic](src/Mugen/Algebra/Displacement/Instances/Lexicographic.agda)   | [Lexicographic](https://redprl.org/mugen/mugen/Mugen/Shift/Lexicographic) and [Lexicographic](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/Lexicographic)     |\n| Indexed products                      | 3.3.5            | [IndexedProduct](src/Mugen/Algebra/Displacement/Instances/IndexedProduct.agda) | _(not implementable)_                                                                                                                                               |\n| Nearly constant infinite products     | 3.3.5            | [NearlyConstant](src/Mugen/Algebra/Displacement/Instances/NearlyConstant.agda) | [NearlyConstant](https://redprl.org/mugen/mugen/Mugen/Shift/NearlyConstant) and [NearlyConstant](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/NearlyConstant) |\n| Infinite products with finite support | 3.3.5            | [FiniteSupport](src/Mugen/Algebra/Displacement/Instances/FiniteSupport.agda)   | [FiniteSupport](https://redprl.org/mugen/mugen/Mugen/Shift/FiniteSupport) and [FiniteSupport](https://redprl.org/mugen/mugen/Mugen/ShiftWithJoin/FiniteSupport)     |\n| Prefix order                          | 3.3.6            | [Prefix](src/Mugen/Algebra/Displacement/Instances/Prefix.agda)                 | [Prefix](https://redprl.org/mugen/mugen/Mugen/Shift/Prefix)                                                                                                         |\n| Fractal displacements                 | 3.3.7            | [Fractal](src/Mugen/Algebra/Displacement/Instances/Fractal.agda)               | [Fractal](https://redprl.org/mugen/mugen/Mugen/Shift/Fractal)                                                                                                       |\n| Opposite displacements                | 3.3.8            | [Opposite](src/Mugen/Algebra/Displacement/Instances/Opposite.agda)             | [Opposite](https://redprl.org/mugen/mugen/Mugen/Shift/Opposite)                                                                                                     |\n| Weird fractal displacements           | 3.3.9 (JFP only) | [WeirdFractal](src/Mugen/Algebra/Displacement/Instances/WeirdFractal.agda)     | [Fractal](https://redprl.org/mugen/mugen/Mugen/Shift/Fractal)                                                                                                       |\n| Endomorphisms                         | 3.4 (Lemma 3.7)  | [Endomorphism](src/Mugen/Algebra/Displacement/Instances/Endomorphism.agda)     | _(not implementable)_                                                                                                                                               |\n\n### Other Theorems\n\n| Theorems                              | Paper Section      | Agda Module                                                                                      |\n| :------------------------------------ | :----------------- | :----------------------------------------------------------------------------------------------- |\n| Traditional level polymorphism        | 2.2                | [Traditional](./src/Mugen/Cat/HierarchyTheory/Traditional.agda)                                  |\n| Validity of McBride monads            | 3.1                | [McBride](./src/Mugen/Cat/HierarchyTheory/McBride.agda)                                          |\n| Embedding of endomorphisms            | 3.4 (Lemma 3.8)    | [EndomorphismEmbedding](./src/Mugen/Cat/HierarchyTheory/Universality/EndomorphismEmbedding.agda) |\n| Embedding of small hierarchy theories | 3.4 (Lemma 3.9)    | [SubcategoryEmbedding](./src/Mugen/Cat/HierarchyTheory/Universality/SubcategoryEmbedding.agda)   |\n| Universality of McBride monads        | 3.4 (Theorem 3.10) | [Universality](./src/Mugen/Cat/HierarchyTheory/Universality.agda)                                |\n\n## Building\n\nRun the following command to check formalization.\n\n```sh\ndocker build -t agda-mugen:edge .\ndocker run agda-mugen:edge\n```\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fredprl%2Fagda-mugen","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fredprl%2Fagda-mugen","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fredprl%2Fagda-mugen/lists"}