{"id":13836560,"url":"https://github.com/math-comp/analysis","last_synced_at":"2025-05-16T14:08:34.807Z","repository":{"id":37396595,"uuid":"112471761","full_name":"math-comp/analysis","owner":"math-comp","description":"Mathematical Components compliant Analysis 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Theory and Mathematics"],"readme":"\u003c!---\nThis file was generated from `meta.yml`, please do not edit manually.\nFollow the instructions on https://github.com/coq-community/templates to regenerate.\n---\u003e\n# Analysis library compatible with Mathematical Components\n\n[![Nix CI][nix-action-shield]][nix-action-link]\n[![Chat][chat-shield]][chat-link]\n\n[nix-action-shield]: https://github.com/math-comp/analysis/actions/workflows/nix-action-master.yml/badge.svg?branch=master\n[nix-action-link]: https://github.com/math-comp/analysis/actions?query=branch%3Amaster+event%3Apush\n\n[chat-shield]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg\n[chat-link]: https://coq.zulipchat.com/login/#narrow/stream/237666-math-comp-analysis\n\nThis repository contains a real analysis library for the Coq proof-assistant.\nIt is based on the [Mathematical Components](https://math-comp.github.io/) library.\n\nIn terms of [opam](https://opam.ocaml.org/doc/Install.html), it comes as the following packages:\n- `coq-mathcomp-classical`: a layer for classical reasoning\n- `coq-mathcomp-reals`: real numbers for MathComp\n- `coq-mathcomp-reals-stdlib`: compatibility with the real numbers of the Coq standard library\n- `coq-mathcomp-analysis-stdlib`: compatibility with the Coq standard library (topology only)\n- `coq-mathcomp-analysis`: theories for real analysis\n- `coq-mathcomp-experimental-reals`: sequences of real numbers and distributions (experimental)\n\n## Meta\n\n- Author(s):\n  - Reynald Affeldt (initial)\n  - Alessandro Bruni\n  - Yves Bertot\n  - Cyril Cohen (initial)\n  - Marie Kerjean\n  - Assia Mahboubi (initial)\n  - Damien Rouhling (initial)\n  - Pierre Roux\n  - Kazuhiko Sakaguchi\n  - Zachary Stone\n  - Pierre-Yves Strub (initial)\n  - Laurent Théry\n- License: [CeCILL-C](LICENSE)\n- Compatible Coq versions: Coq 8.19 to 8.20 (or dev)\n- Additional dependencies:\n  - [MathComp ssreflect 2.1.0 or later](https://math-comp.github.io)\n  - [MathComp fingroup 2.1.0 or later](https://math-comp.github.io)\n  - [MathComp algebra 2.1.0 or later](https://math-comp.github.io)\n  - [MathComp solvable 2.1.0 or later](https://math-comp.github.io)\n  - [MathComp field 2.1.0 or later](https://math-comp.github.io)\n  - [MathComp finmap 2.0.0](https://github.com/math-comp/finmap)\n  - [MathComp bigenough 1.0.0](https://github.com/math-comp/bigenough)\n  - [Hierarchy Builder 1.4.0 or later](https://github.com/math-comp/hierarchy-builder)\n- Coq namespace: `mathcomp.analysis`\n\n## Building and installation instructions\n\nThe easiest way to install the latest released version of MathComp-Analysis library is\nvia the [opam](https://opam.ocaml.org/doc/Install.html) package manager:\n\n```shell\nopam repo add coq-released https://coq.inria.fr/opam/released\nopam install coq-mathcomp-analysis\n```\nNote that the packages `coq-mathcomp-classical` and `coq-mathcomp-reals` will be installed as dependencies.\n\n### Manual installation\n\nTo build and install manually, make sure that the dependencies are met and do:\n\n``` shell\ngit clone https://github.com/math-comp/analysis.git\ncd analysis\nmake   # or make -j \u003cnumber-of-cores-on-your-machine\u003e \nmake install\n```\n\n## About the stability of this library\n\nChanges are documented systematically in [CHANGELOG.md](CHANGELOG.md) and\n[CHANGELOG_UNRELEASED.md](CHANGELOG_UNRELEASED.md).\n\nWe bump the minor part of the version number for breaking changes.\n\nWe use deprecation warnings to help transitioning to new versions.\n\nWe try to preserve backward compatibility as best as we can.\n\n## Documentation\n\nEach file is documented in its header in ASCII.\n\n[HTML rendering of the source code](https://math-comp.github.io/analysis/htmldoc_1_9_0/index.html) (using a fork of [`coq2html`](https://github.com/xavierleroy/coq2html)).\nIt includes inheritance diagrams for the mathematical structures that MathComp-Analysis adds on top of MathComp's ones.\n\nOverview presentations:\n- [Classical Analysis with Coq](https://perso.crans.org/cohen/CoqWS2018.pdf) (2018)\n- [A selection of links to well-known lemmas](https://github.com/math-comp/analysis/wiki/What's-where%3F)\n- [An Introduction to MathComp-Analysis](https://staff.aist.go.jp/reynald.affeldt/documents/karate-coq.pdf) (2024)\n\nPublications about MathComp-Analysis:\n- [Formalization Techniques for Asymptotic Reasoning in Classical Analysis](https://jfr.unibo.it/article/view/8124) (2018) doi:[10.6092/issn.1972-5787/8124](https://doi.org/10.6092/issn.1972-5787/8124)\n- [Formalisation Tools for Classical Analysis](http://www-sop.inria.fr/members/Damien.Rouhling/data/phd/thesis.pdf) (2019)\n- [Competing inheritance paths in dependent type theory---a case study in functional analysis](https://hal.inria.fr/hal-02463336) (2020) doi:[10.1007/978-3-030-51054-1_1](https://doi.org/10.1007/978-3-030-51054-1_1)\n- [Measure Construction by Extension in Dependent Type Theory with Application to Integration](https://arxiv.org/pdf/2209.02345.pdf) (2023) doi:[10.1007/s10817-023-09671-5](https://doi.org/10.1007/s10817-023-09671-5)\n- [The Radon-Nikodým Theorem and the Lebesgue-Stieltjes Measure in Coq](https://www.jstage.jst.go.jp/article/jssst/41/2/41_2_41/_pdf/-char/en) (2024) doi:[10.11309/jssst.41.2_41](https://doi.org/10.11309/jssst.41.2_41)\n- [A Comprehensive Overview of the Lebesgue Differentiation Theorem in Coq](https://drops.dagstuhl.de/storage/00lipics/lipics-vol309-itp2024/LIPIcs.ITP.2024.5/LIPIcs.ITP.2024.5.pdf) (2024) doi:[10.4230/LIPIcs.ITP.2024.5](https://doi.org/10.4230/LIPIcs.ITP.2024.5)\n\nOther work using MathComp-Analysis:\n- [A Formal Classical Proof of Hahn-Banach in Coq](https://lipn.univ-paris13.fr/~kerjean/slides/slidesTYPES19.pdf) (2019)\n- [Semantics of Probabilistic Programs using s-Finite Kernels in Coq](https://hal.inria.fr/hal-03917948/document) (2023)\n- [CoqQ: Foundational Verification of Quantum Programs](https://arxiv.org/pdf/2207.11350.pdf) (2023)\n- [Experimenting with an intrinsically-typed probabilistic programming language in Coq](https://staff.aist.go.jp/reynald.affeldt/documents/syntax-aplas2023.pdf) (2023)\n- [Taming Differentiable Logics with Coq Formalisation](https://drops.dagstuhl.de/storage/00lipics/lipics-vol309-itp2024/LIPIcs.ITP.2024.4/LIPIcs.ITP.2024.4.pdf) (2024)\n\n## Development information\n\n[Detailed requirements and installation procedure](INSTALL.md)\n\n[Developping with nix](https://github.com/math-comp/math-comp/wiki/Using-nix)\n\n[Contributing](CONTRIBUTING.md)\n\n## Previous work reused at the time of the first releases\n\nThis library was inspired by the [Coquelicot library](http://coquelicot.saclay.inria.fr/)\nby Sylvie Boldo, Catherine Lelay, and Guillaume Melquiond.\nIn the first releases, `topology.v` and `normedtype.v` contained a reimplementation of the file\n`Hierarchy.v` from the library Coquelicot.\n\nThe instantiation of the mathematical structures of the Mathematical Components library\nwith the real numbers of the standard Coq library used a well-known file (`Rstruct.v`)\nfrom the [CoqApprox library](http://tamadi.gforge.inria.fr/CoqApprox/) (with\nmodifications by various authors).\n\nThe proof of Zorn's Lemma in `classical_sets.v` (NB: new filename) was a reimplementation\nof the one by Daniel Schepler (https://github.com/coq-community/zorns-lemma) but it has been rewritten for version 1.3.0;\nwe also originally took inspiration from Schepler's work on topology (https://github.com/coq-community/topology) for parts\nof `topology.v`.\n\n[ORIGINAL_FILES.md](ORIGINAL_FILES.md) gives more details about the\nfiles in the first releases.\n\n## Acknowledgments\n\nMany thanks to [various contributors](https://github.com/math-comp/analysis/graphs/contributors)\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmath-comp%2Fanalysis","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmath-comp%2Fanalysis","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmath-comp%2Fanalysis/lists"}