{"id":13829655,"url":"https://github.com/martinescardo/TypeTopology","last_synced_at":"2025-07-09T10:31:21.751Z","repository":{"id":37251656,"uuid":"120327357","full_name":"martinescardo/TypeTopology","owner":"martinescardo","description":"Logical manifestations of topological concepts, and other things, via the univalent point of view.","archived":false,"fork":false,"pushed_at":"2024-04-13T16:03:28.000Z","size":14903,"stargazers_count":211,"open_issues_count":20,"forks_count":39,"subscribers_count":14,"default_branch":"master","last_synced_at":"2024-04-14T12:04:07.984Z","etag":null,"topics":["agda","compact-type","constructive-mathematics","homotopy-type-theory","injective-type","ordinal","searchable-set","totally-separated-type","type-theory","univalent-foundations","univalent-mathematics"],"latest_commit_sha":null,"homepage":"","language":"Agda","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"gpl-3.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/martinescardo.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":"CONTRIBUTING.md","funding":null,"license":"LICENSE","code_of_conduct":"CODE-OF-CONDUCT.md","threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null}},"created_at":"2018-02-05T16:02:04.000Z","updated_at":"2024-04-15T16:05:07.202Z","dependencies_parsed_at":"2024-04-15T16:15:21.022Z","dependency_job_id":null,"html_url":"https://github.com/martinescardo/TypeTopology","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/martinescardo%2FTypeTopology","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/martinescardo%2FTypeTopology/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/martinescardo%2FTypeTopology/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/martinescardo%2FTypeTopology/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/martinescardo","download_url":"https://codeload.github.com/martinescardo/TypeTopology/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":225533017,"owners_count":17484179,"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":["agda","compact-type","constructive-mathematics","homotopy-type-theory","injective-type","ordinal","searchable-set","totally-separated-type","type-theory","univalent-foundations","univalent-mathematics"],"created_at":"2024-08-04T10:00:42.048Z","updated_at":"2025-07-09T10:31:21.739Z","avatar_url":"https://github.com/martinescardo.png","language":"Agda","funding_links":[],"categories":["Agda"],"sub_categories":[],"readme":"# Various new theorems in constructive univalent mathematics written in Agda\n\nThis development was started by Martin Escardo in 2010 as an `svn` project, and\ntransferred to `github` Monday 5th February 2018.\n\nIf you contribute, please add your full (legal or adopted) name and date\nat the place of contribution.\n\nAn [html rendering of the Agda\ncode](http://www.cs.bham.ac.uk/~mhe/TypeTopology/index.html) is hosted at\n[Martin Escardo](https://www.cs.bham.ac.uk/~mhe/index.html)'s institutional web\npage.\n\n## How to cite\n\nYou can use the following BibTeX entry to cite `TypeTopology`:\n\n```bibtex\n@misc{type-topology,\n  title    = {{TypeTopology}},\n  author   = {Escard\\'{o}, Mart\\'{i}n H. and {contributors}},\n  url      = {https://github.com/martinescardo/TypeTopology},\n  note     = {{Agda} development},\n}\n```\n\nIf you are citing only your own files, then create a different bibtex file with\nonly your name as author.\n\n## Root of the development\n\n * [source/index.lagda](source/index.lagda) (only `--safe` modules).\n * [source/AllModulesIndex.lagda](source/AllModulesIndex.lagda) (including\n   \"unsafe\" ones).\n * Each subdirectory in [source/](source/) has its own index file.\n\n## Current contributors in alphabetical order of first name\n\nPlease add yourself the first time you contribute.\n\n* Alice Laroche\n* Andrew Sneap\n* Andrew Swan\n* Ayberk Tosun\n* Brendan Hart\n* Bruno Paiva\n* Chuangjie Xu\n* Cory Knapp\n* Ettore Aldrovandi\n* Evan Cavallo\n* Fredrik Bakke\n* Fredrik Nordvall Forsberg\n* Ian Ray\n* Igor Arrieta (ii)\n* J.A. Carr\n* Jon Sterling\n* Kelton OBrien\n* Keri D'Angelo\n* Lane Biocini\n* Marc Bezem\n* Martin Escardo\n* Nicolai Kraus\n* Ohad Kammar\n* Paul Levy (i)\n* Paulo Oliva\n* Peter Dybjer\n* Simcha van Collem\n* Thierry Coquand\n* Todd Waugh Ambridge\n* Tom de Jong\n* Vincent Rahli\n\n(i) These authors didn't write any single line of Agda code here, but\nthey contributed to constructions, theorems and proofs via the hands\nof Martin Escardo.\n\n(ii) These authors didn't write single line of Agda code here, but they\ncontributed to constructions, theorems and proofs via the hands of Ayberk\nTosun.\n\n## Publications resulting from [`TypeTopology`]()\n\n1. Martín H. Escardó. *Infinite sets that satisfy the principle of\n   omniscience in any variety of constructive mathematics.* [The\n   Journal of Symbolic\n   Logic](https://www.cambridge.org/core/journals/journal-of-symbolic-logic),\n   Volume 78 , Issue 3 , 2013 , pp. 764 - 784.\n\n   https://doi.org/10.2178/jsl.7803040\n\n1. Martín H. Escardó. *Continuity of Gödel's system T functionals via\n   effectful forcing.* [Electronic Notes in Theoretical Computer\n   Science](https://www.sciencedirect.com/journal/electronic-notes-in-theoretical-computer-science),\n   Volume 298, 2013, Pages 119-141. [MFPS XXIX](https://www.cs.cornell.edu/Conferences/MFPS29/)\n\n   https://doi.org/10.1016/j.entcs.2013.09.010\n\n1. Nicolai Kraus, Martín H. Escardó, T. Coquand,\n   T. Altenkirch. *Generalizations of Hedberg's Theorem.* In: Hasegawa,\n   M. (eds) Typed Lambda Calculi and Applications. [TLCA\n   2013](https://www.kurims.kyoto-u.ac.jp/tlca2013/). Lecture Notes in\n   Computer Science, vol 7941. Springer.\n\n   https://doi.org/10.1007/978-3-642-38946-7_14\n\n1. Martín H. Escardó. *Constructive decidability of classical continuity.*\n   [Mathematical Structures in Computer Science][MSCS], Volume 25, Special\n   Issue 7: Computing with Infinite Data: Topological and Logical Foundations\n   Part 1, October 2015, pp. 1578 - 1589 DOI:\n\n   https://doi.org/10.1017/S096012951300042X\n\n1. Martín H. Escardó and Chuangjie Xu. *The inconsistency of a\n   Brouwerian continuity principle with the Curry-Howard\n   interpretation.* [13th International Conference on Typed Lambda\n   Calculi and Applications (TLCA 2015)](https://drops.dagstuhl.de/opus/portals/lipics/index.php?semnr=15006).\n\n   https://doi.org/10.4230/LIPIcs.TLCA.2015.153\n\n1. Martín H. Escardó and T. Streicher. *The intrinsic topology of\n   Martin-Löf universes.* [Annals of Pure and Applied\n   Logic](https://www.sciencedirect.com/journal/annals-of-pure-and-applied-logic),\n   Volume 167, Issue 9, 2016, Pages 794-805.\n\n   https://doi.org/10.1016/j.apal.2016.04.010\n\n1. Martín H. Escardó and Cory Knapp. *Partial elements and recursion via\n   dominances in univalent type theory.* [Leibniz International Proceedings in\n   Informatics\n   (LIPIcs)][LIPICS],\n   Proceedings of [CSL\n   2017](https://www.math-stockholm.se/konferenser-och-akti/logic-in-stockholm-2/26th-eacsl-annual-co/computer-science-logic-2017-august-20-24-1.717663).\n\n   https://doi.org/10.4230/LIPIcs.CSL.2017.21\n\n1. Nicolai Kraus, Martín H. Escardó, T. Coquand, T. Altenkirch. *Notions of\n   Anonymous Existence in Martin-Löf Type Theory.*  [Logical Methods in\n   Computer Science][LMCS], March 24, 2017, Volume 13, Issue 1.\n\n   https://doi.org/10.23638/LMCS-13(1:15)2017\n\n1. Tom de Jong. *The Scott model of PCF in univalent type\n   theory.* [Mathematical Structures in Computer\n   Science](https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science),\n   Volume 31, Issue 10 - Homotopy Type Theory 2019, July 2021.\n\n   https://doi.org/10.1017/S0960129521000153\n\n1. Martín H. Escardó. *The Cantor-Schröder-Bernstein Theorem for\n   ∞-groupoids.*  [Journal of Homotopy and Related\n   Structures](https://tcms.org.ge/Journals/JHRS/), 16(3), 363-366,\n   2021.\n\n   https://doi.org/10.1007/s40062-021-00284-6\n\n1. Martín H. Escardó.  *Injective types in univalent\n   mathematics.* [Mathematical Structures in Computer\n   Science](https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science),\n   Volume 31 , Issue 1 , 2021 , pp. 89 - 111.\n\n   https://doi.org/10.1017/S0960129520000225\n\n1. Tom de Jong and Martín H. Escardó. *Domain Theory in Constructive\n   and Predicative Univalent Foundations.* [Leibniz International\n   Proceedings in Informatics\n   (LIPIcs)](https://www.dagstuhl.de/en/publishing/series/details/LIPIcs),\n   Volume 183 - Proceedings of [CSL 2021][CSL21], January\n   2021.\n\n   https://doi.org/10.4230/LIPIcs.CSL.2021.28\n\n1. Dan R. Ghica and Todd Waugh Ambridge. *Global Optimisation with\n   Constructive Reals.*\n   [Logic in Computer Science (LICS)](https://dl.acm.org/conference/lics),\n   Proceedings of [LICS 2021][LICS21], June 2021.\n\n   https://doi.org/10.1109/LICS52264.2021.9470549\n\n1. Tom de Jong and Martín H. Escardó. *Predicative Aspects of Order\n   Theory in Univalent Foundations.* [Leibniz International Proceedings\n   in Informatics\n   (LIPIcs)](https://www.dagstuhl.de/en/publishing/series/details/LIPIcs),\n   Volume 195 - Proceedings of [FSCD 2021][FSCD21], July 2021.\n\n   https://doi.org/10.4230/LIPIcs.FSCD.2021.8\n\n1. Tom de Jong. *Domain Theory in Constructive and Predicative Univalent\n   Foundations*. PhD thesis. School of Computer Science, University of\n   Birmingham, UK. Submitted: 30 September 2022; accepted: 1 February 2023.\n\n   https://etheses.bham.ac.uk/id/eprint/13401/ \\\n   Updated versions: \\\n   https://arxiv.org/abs/2301.12405 \\\n   https://tdejong.com/writings/phd-thesis.pdf\n\n1. Ayberk Tosun and Martín H. Escardó. *Patch Locale of a Spectral\n   Locale in Univalent Type Theory.* [Electronic Notes in Theoretical\n   Informatics and Computer Science](https://entics.episciences.org/),\n   Volume 1 - Proceedings of [MFPS XXXVIII][MFPS38], February\n   2023.\n\n   https://doi.org/10.46298/entics.10808\n\n1. Tom de Jong, Nicolai Kraus, Fredrik Nordvall Forsberg and Chuangjie\n   Xu. *Set-Theoretic and Type-Theoretic Ordinals Coincide.*\n   [Logic in Computer Science (LICS)](https://dl.acm.org/conference/lics),\n   Proceedings of [LICS 2023][LICS23]. June 2023.\n\n   https://doi.org/10.1109/LICS56636.2023.10175762\n\n   Publicly available at https://arxiv.org/abs/2301.10696.\n\n1. Tom de Jong and Martín H. Escardó. *On Small Types in Univalent\n   Foundations.* [Logical Methods in Computer\n   Science](https://lmcs.episciences.org/), Volume 19, Issue 2, May\n   2023.\n\n   https://doi.org/10.46298/lmcs-19(2:8)2023\n\n1. Martín H. Escardó and Paulo Oliva. *Higher-order Games with\n   Dependent Types*.\n\n   [Theoretical Computer\n   Science](https://www.sciencedirect.com/journal/theoretical-computer-science),\n   Special issue \"Continuity, Computability, Constructivity: From\n   Logic to Algorithms\", dedicated to Ulrich Berger's 65th birthday,\n   volume 974, 29 September 2023, available online 2 August 2023.\n\n   https://doi.org/10.1016/j.tcs.2023.114111\n\n1. Todd Waugh Ambridge. *Exact Real Search: Formalised Optimisation and\n   Regression in Constructive Univalent Mathematics.* January 2024. University\n   of Birmingham. PhD thesis.\n\n   https://doi.org/10.48550/arXiv.2401.09270\n\n1. Igor Arrieta, Martín H. Escardó and Ayberk Tosun. *The Patch Topology in\n   Univalent Foundations*.\n\n   ArXiv preprint. Available online 5 February 2024.\n\n   https://arxiv.org/abs/2402.03134\n\n1. Tom de Jong. *Domain theory in univalent foundations I: Directed complete\n   posets and Scott's D∞*. July 2024.\n\n   https://doi.org/10.48550/arxiv.2407.06952\n\n1. Tom de Jong and Martín H. Escardó. *Domain theory in univalent\n   foundations II: Continuous and algebraic domains*. July 2024.\n\n   https://doi.org/10.48550/arxiv.2407.06956\n\n1. Tom de Jong, Nicolai Kraus, Fredrik Nordvall Forsberg and Chuangjie Xu.\n   *Ordinal Exponentiation in Homotopy Type Theory*. January 2025. Updated\n   May 2025. To appear at [LICS 2025][LICS25].\n\n   https://doi.org/10.48550/arxiv.2501.14542\n\n1. Martin H. Escardo, Bruno da Rocha Paiva, Vincent Rahli and Ayberk Tosun.\n   *Internal Effectful Forcing in System T*. To appear in [FSCD'2025](https://fscd2025.github.io/).\n\n   https://doi.org/10.48550/arXiv.2505.11055\n\n[CSL21]:  https://csl2021.fmf.uni-lj.si/\n[FSCD21]: https://fscd2021.dc.uba.ar/\n[LICS21]: https://easyconferences.eu/lics2021/\n[LICS23]: https://lics.siglog.org/lics23/\n[LICS25]: https://lics.siglog.org/lics25/\n[MFPS38]: https://www.cs.cornell.edu/mfps-2022/\n[LMCS]: https://lmcs.episciences.org/\n[MSCS]: https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science\n[LIPICS]: https://www.dagstuhl.de/en/publishing/series/details/LIPIcs\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmartinescardo%2FTypeTopology","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmartinescardo%2FTypeTopology","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmartinescardo%2FTypeTopology/lists"}