Awesome
<!--- This file was generated from `meta.yml`, please do not edit manually. Follow the instructions on https://github.com/coq-community/templates to regenerate. --->Analysis library compatible with Mathematical Components
This repository contains a real analysis library for the Coq proof-assistant. It is based on the Mathematical Components library.
In terms of opam, it comes as the following packages:
coq-mathcomp-classical
: a layer for classical reasoningcoq-mathcomp-analysis
: theories for real analysis
Meta
- Author(s):
- Reynald Affeldt (initial)
- Alessandro Bruni
- Yves Bertot
- Cyril Cohen (initial)
- Marie Kerjean
- Assia Mahboubi (initial)
- Damien Rouhling (initial)
- Pierre Roux
- Kazuhiko Sakaguchi
- Zachary Stone
- Pierre-Yves Strub (initial)
- Laurent Théry
- License: CeCILL-C
- Compatible Coq versions: Coq 8.19 to 8.20 (or dev)
- Additional dependencies:
- Coq namespace:
mathcomp.analysis
Building and installation instructions
The easiest way to install the latest released version of MathComp-Analysis library is via the opam package manager:
opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-mathcomp-analysis
Note that the package coq-mathcomp-classical
will be installed as a dependency.
Manual installation
To build and install manually, make sure that the dependencies are met and do:
git clone https://github.com/math-comp/analysis.git
cd analysis
make # or make -j <number-of-cores-on-your-machine>
make install
About the stability of this library
Changes are documented systematically in CHANGELOG.md and CHANGELOG_UNRELEASED.md.
We bump the minor part of the version number for breaking changes.
We use deprecation warnings to help transitioning to new versions.
We try to preserve backward compatibility as best as we can.
Documentation
Each file is documented in its header in ASCII.
HTML rendering of the source code (using a fork of coq2html
).
Overview presentations:
- Classical Analysis with Coq (2018)
- A selection of links to well-known lemmas
- An Introduction to MathComp-Analysis (2024)
Publications about MathComp-Analysis:
- Formalization Techniques for Asymptotic Reasoning in Classical Analysis (2018) doi:10.6092/issn.1972-5787/8124
- Formalisation Tools for Classical Analysis (2019)
- Competing inheritance paths in dependent type theory---a case study in functional analysis (2020) doi:10.1007/978-3-030-51054-1_1
- Measure Construction by Extension in Dependent Type Theory with Application to Integration (2023) doi:10.1007/s10817-023-09671-5
- The Radon-Nikodým Theorem and the Lebesgue-Stieltjes Measure in Coq (2024) doi:10.11309/jssst.41.2_41
- A Comprehensive Overview of the Lebesgue Differentiation Theorem in Coq (2024) doi:10.4230/LIPIcs.ITP.2024.5
Other work using MathComp-Analysis:
- A Formal Classical Proof of Hahn-Banach in Coq (2019)
- Semantics of Probabilistic Programs using s-Finite Kernels in Coq (2023)
- CoqQ: Foundational Verification of Quantum Programs (2023)
- Experimenting with an intrinsically-typed probabilistic programming language in Coq (2023)
- Taming Differentiable Logics with Coq Formalisation (2024)
Mathematical structures
MathComp-Analysis adds mathematical structures on top of MathComp's ones.
The following inheritance diagram displays the resulting hierarchy as of version 1.1.0
(excluding most MathComp structures).
The structures introduced by MathComp-Analysis are highlighted.
(See topology.v
, normedtype.v
, reals.v
, measure.v
.)
Hierarchies of functions
Functions | Functions with a finite image | Measures | Kernels |
---|---|---|---|
<img width="300" alt="Functions" src="etc/hierarchy_functions.1.1.0.png"> | <img width="200" alt="Functions_with_a_finite_image" src="etc/hierarchy_fimfun.1.1.0.png"> | <img width="300" alt="Measures" src="etc/hierarchy_measure.1.1.0.png"> | <img width="200" alt="Kernels" src="etc/hierarchy_kernel.1.1.0.png"> |
(see functions.v ) | (see cardinality.v , lebesgue_integral.v ) | (see measure.v , charge.v ) | (see kernel.v ) |
Development information
Detailed requirements and installation procedure
Previous work reused at the time of the first releases
This library was inspired by the Coquelicot library
by Sylvie Boldo, Catherine Lelay, and Guillaume Melquiond.
In the first releases, topology.v
and normedtype.v
contained a reimplementation of the file
Hierarchy.v
from the library Coquelicot.
The instantiation of the mathematical structures of the Mathematical Components library
with the real numbers of the standard Coq library used a well-known file (Rstruct.v
)
from the CoqApprox library (with
modifications by various authors).
The proof of Zorn's Lemma in classical_sets.v
(NB: new filename) was a reimplementation
of the one by Daniel Schepler (https://github.com/coq-community/zorns-lemma) but it has been rewritten for version 1.3.0;
we also originally took inspiration from Schepler's work on topology (https://github.com/coq-community/topology) for parts
of topology.v
.
ORIGINAL_FILES.md gives more details about the files in the first releases.
Acknowledgments
Many thanks to various contributors