{"id":22162110,"url":"https://github.com/jaycech3n/isabelle-hott","last_synced_at":"2026-01-05T12:42:14.524Z","repository":{"id":162098905,"uuid":"134523964","full_name":"jaycech3n/Isabelle-HoTT","owner":"jaycech3n","description":"An experimental implementation of homotopy type theory in the interactive proof assistant Isabelle","archived":false,"fork":false,"pushed_at":"2022-11-30T12:22:25.000Z","size":415,"stargazers_count":34,"open_issues_count":2,"forks_count":3,"subscribers_count":6,"default_branch":"master","last_synced_at":"2025-01-29T20:48:48.051Z","etag":null,"topics":["homotopy-type-theory","interactive-theorem-proving","isabelle","type-theory"],"latest_commit_sha":null,"homepage":"","language":"Standard ML","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"other","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/jaycech3n.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":"2018-05-23T06:30:34.000Z","updated_at":"2024-04-24T17:43:51.000Z","dependencies_parsed_at":"2023-06-18T07:45:09.087Z","dependency_job_id":null,"html_url":"https://github.com/jaycech3n/Isabelle-HoTT","commit_stats":null,"previous_names":[],"tags_count":2,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/jaycech3n%2FIsabelle-HoTT","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/jaycech3n%2FIsabelle-HoTT/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/jaycech3n%2FIsabelle-HoTT/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/jaycech3n%2FIsabelle-HoTT/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/jaycech3n","download_url":"https://codeload.github.com/jaycech3n/Isabelle-HoTT/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":245300869,"owners_count":20593055,"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":["homotopy-type-theory","interactive-theorem-proving","isabelle","type-theory"],"created_at":"2024-12-02T04:19:12.430Z","updated_at":"2026-01-05T12:42:14.497Z","avatar_url":"https://github.com/jaycech3n.png","language":"Standard ML","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Isabelle/HoTT [![build](https://github.com/jaycech3n/Isabelle-HoTT/workflows/build/badge.svg)](https://github.com/jaycech3n/Isabelle-HoTT/actions?query=workflow%3Abuild)\n\nIsabelle/HoTT is an experimental implementation of [homotopy type theory](https://en.wikipedia.org/wiki/Homotopy_type_theory) in the [Isabelle](https://isabelle.in.tum.de/) interactive theorem prover.\nIt largely follows the development of the theory in the [Homotopy Type Theory book](https://homotopytypetheory.org/book/), but aims to be general enough to eventually support cubical and other kinds of homotopy type theories.\n\nWork is slowly ongoing to develop the logic into a fully-featured proof environment in which one can formulate and prove mathematical statements, in the style of the univalent foundations school.\nWhile Isabelle has provided support for object logics based on Martin-Löf type theory since the beginning, these have largely been ignored in favor of Isabelle/HOL.\nThus this project is also an experiment in creating a viable framework, based on dependent type theory, inside the simple type theoretic foundations of Isabelle/Pure.\n\n**Caveat prover**: *This project is under active experimentation and is not yet guaranteed fit for any particular purpose.*\n\n### References\n\n- *Homotopy Type Theory in Isabelle*. ITP 2021. DOI: [10.4230/LIPIcs.ITP.2021.12](https://drops.dagstuhl.de/opus/frontdoor.php?source_opus=13907)\n- *An Implementation of Homotopy Type Theory in Isabelle/Pure*. [arXiv:1911.00399 [cs.LO]](https://arxiv.org/abs/1911.00399)\n\n### Usage\n\nIsabelle/HoTT is compatible with Isabelle2021.\nTo use, add the Isabelle/HoTT folder path to `.isabelle/Isabelle2021/ROOTS` (on Mac/Linux/cygwin installations):\n\n```\n$ echo path/to/Isabelle/HoTT \u003e\u003e ~/.isabelle/Isabelle2021/ROOTS\n```\n\n### To-do list\n\nIn no particular order.\n\n- [ ] Dedicated type context data\n- [ ] Definitional unfolding, better simplification in the typechecker\n- [ ] Proper handling of universes\n- [ ] Recursive function definitions\n- [ ] Inductive type definitions\n- [ ] Higher inductive type definitions\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjaycech3n%2Fisabelle-hott","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fjaycech3n%2Fisabelle-hott","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjaycech3n%2Fisabelle-hott/lists"}