{"id":18695056,"url":"https://github.com/rybla/lingua","last_synced_at":"2026-02-19T16:04:50.242Z","repository":{"id":81618213,"uuid":"317623811","full_name":"rybla/Lingua","owner":"rybla","description":"Implementations of and reasonings about a variety of simple functional languages, in Agda.","archived":false,"fork":false,"pushed_at":"2020-12-18T03:11:30.000Z","size":36,"stargazers_count":1,"open_issues_count":0,"forks_count":1,"subscribers_count":0,"default_branch":"master","last_synced_at":"2025-10-20T00:48:23.517Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":"","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/rybla.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}},"created_at":"2020-12-01T17:54:11.000Z","updated_at":"2020-12-18T03:11:32.000Z","dependencies_parsed_at":"2023-03-06T01:15:16.162Z","dependency_job_id":null,"html_url":"https://github.com/rybla/Lingua","commit_stats":null,"previous_names":["rybla/lingua"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/rybla/Lingua","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/rybla%2FLingua","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/rybla%2FLingua/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/rybla%2FLingua/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/rybla%2FLingua/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/rybla","download_url":"https://codeload.github.com/rybla/Lingua/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/rybla%2FLingua/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":29621903,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-02-19T13:04:20.082Z","status":"ssl_error","status_checked_at":"2026-02-19T13:03:33.775Z","response_time":117,"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":"2024-11-07T11:13:46.568Z","updated_at":"2026-02-19T16:04:45.234Z","avatar_url":"https://github.com/rybla.png","language":"Agda","funding_links":[],"categories":[],"sub_categories":[],"readme":"# README\n\nImplementations of and reasonings about the following languages:\n\n| name | description | common parlence | resources |\n| --- | --- | --- | --- |\n| [λ][λ] | simply-typed λ-calculus | STλC |\n| [λ2][λ2] | λ with type polymorphism | System F |\n| [λω][λω] | λ2 with type constructors | System Fω |\n| [λΠ][λΠ] | λ with dependent types | |\n| [λΠω][λΠω] | λΠ with type constructors | Calculus of Constructions | _Calculus of Constructions_ [[wiki](https://en.wikipedia.org/wiki/Calculus_of_constructions)]\n| [λS][λS] | λΠω with self types | System S | _Self Types for Dependently Typed Lambda Encodings_ [[paper](https://fermat.github.io/document/papers/rta-tlca.pdf)]\n| [λID][λID] | λΠω with inductive datatypes | Calculus of Inductive Constructions |\n| [λCD][λCD] | λΠω with coinductive datatypes | Calculus of Coinductive Constructions  |\n| [λPID][λPID] | predicative λΠω with inductive datatypes | Predicative Calculus of Coinductive Constructions |\n\n## λ\n\n**λ: Simply-typed λ-calculus.**\n\n`Language/Lambda/` contains an intrinsically-typed implementation. Based on [_Programming Language Foundations in Agda –– DeBruijn: Intrinsically-typed de Bruijn representation_](https://plfa.github.io/DeBruijn/).\n\n_Tasks._\n- [x] Grammar\n- [x] Typing\n- [x] Reducing\n- [ ] Examples\n  - [x] simples\n  - [ ] Church numerals\n\n\n## λ2\n\n**λ2: λ with type polymorphism (System F).**\n\n`Lambda/Lambda2/` contain an intrinsically-typed implementation. Based on [_System F in Agda for Fun and Profit_](https://github.com/input-output-hk/plutus/tree/master/papers/system-f-in-agda).\n\n_Tasks._\n- [ ] Kinding\n  - [ ] properties of `_≅ₛ_`\n  - [ ] properties of `rename-⊨`\n  - [ ] properties of `reflect`\n  - [ ] properties of `reify`\n  - [ ] interactions between `rename`, `substitute`, `extend`, `evaluate`, `reflect`, `reify`, and `_≅ₛ_`\n  - [ ] properties of `_≅ₛ_`\n  - [ ] properties of `_≅ₑ_`\n  - [ ] completeness\n  - [ ] stability\n  - [ ] interactions between `rename`, `substitute`, weakenings, and single substitutions\n- [x] Typing\n- [ ] Normal Typing\n  - [ ] normalization lemmas\n  - [ ] `normalize-Type` cases:\n    - [ ] ``` `fold```\n    - [ ] ``` `unfold```\n  - [ ] `progress` cases:\n    - [ ] ```_`∙♯_```\n    - [ ] ``` `unfold```\n- [ ] Type Erasure\n  - [ ] `erase-normalize-Type-≡`\n  - [ ] erase-substitution lemmas\n\n## λω\n\nTODO\n\n## λΠ\n\nTODO\n\n## λΠω\n\nTODO\n\n## λS\n\nTODO\n\n## λID\n\nTODO\n\n## λCID\n\nTODO\n\n## λPID\n\nTODO\n\n\n\u003c!--  --\u003e\n\n[λ]: #λ\n[λ2]: #λ2\n[λω]: #λω\n[λΠ]: #λΠ\n[λΠω]: #λΠω\n[λS]: #λS\n[λID]: #λID\n[λCD]: #λCD\n[λPID]: #λPID\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Frybla%2Flingua","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Frybla%2Flingua","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Frybla%2Flingua/lists"}