mathlib4

Mathlib is a user maintained library for the Lean theorem prover. It contains both programming infrastructure and mathematics, as well as tactics that use the former and allow to develop the latter.

Installation

You can find detailed instructions to install Lean, mathlib, and supporting tools on our website. Alternatively, click on one of the buttons below to open a GitHub Codespace or a Gitpod workspace containing the project.

Using mathlib4 as a dependency

Please refer to https://github.com/leanprover-community/mathlib4/wiki/Using-mathlib4-as-a-dependency

Experimenting

Got everything installed? Why not start with the tutorial project?

For more pointers, see Learning Lean.

Documentation

Besides the installation guides above and Lean's general documentation, the documentation of mathlib consists of:

• The mathlib4 docs: documentation generated automatically from the source .lean files.
• A description of currently covered theories, as well as an overview for mathematicians.
• Some extra Lean documentation not specific to mathlib (see "Miscellaneous topics")
• Documentation for people who would like to contribute to mathlib

Much of the discussion surrounding mathlib occurs in a Zulip chat room, and you are welcome to join, or read along without signing up. Questions from users at all levels of expertise are welcome! We also provide an archive of the public discussions, which is useful for quick reference.

Contributing

The complete documentation for contributing to mathlib is located on the community guide contribute to mathlib

The process is different from other projects where one should not fork the repository. Instead write permission for non-master branches should be requested on Zulip by introducing yourself, providing your GitHub handle and what contribution you are planning on doing. You may want to subscribe to the mathlib4 stream

• To obtain precompiled olean files, run lake exe cache get. (Skipping this step means the next step will be very slow.)

• To build mathlib4 run lake build.

• To build and run all tests, run lake test.

• You can use lake build Mathlib.Import.Path to build a particular file, e.g. lake build Mathlib.Algebra.Group.Defs.

• If you added a new file, run the following command to update Mathlib.lean

  lake exe mk_all

Guidelines

Mathlib has the following guidelines and conventions that must be followed

• The style guide
• A guide on the naming convention
• The documentation style

Downloading cached build files

You can run lake exe cache get to download cached build files that are computed by mathlib4's automated workflow.

If something goes mysteriously wrong, you can try one of lake clean or rm -rf .lake before trying lake exe cache get again. In some circumstances you might try lake exe cache get! which re-downloads cached build files even if they are available locally.

Call lake exe cache to see its help menu.

Building HTML documentation

The mathlib4_docs repository is responsible for generating and publishing the mathlib4 docs.

That repo can be used to build the docs locally:

git clone https://github.com/leanprover-community/mathlib4_docs.git
cd mathlib4_docs
cp ../mathlib4/lean-toolchain .
lake exe cache get
lake build Mathlib:docs

The last step may take a while (>20 minutes). The HTML files can then be found in .lake/build/doc.

Transitioning from Lean 3

For users familiar with Lean 3 who want to get up to speed in Lean 4 and migrate their existing Lean 3 code we have:

• A survival guide for Lean 3 users
• Instructions to run mathport on a project other than mathlib. mathport is the tool the community used to port the entirety of mathlib from Lean 3 to Lean 4.

Dependencies

If you are a mathlib contributor and want to update dependencies, use lake update, or lake update batteries aesop (or similar) to update a subset of the dependencies. This will update the lake-manifest.json file correctly. You will need to make a PR after committing the changes to this file.

Please do not run lake update -Kdoc=on as previously advised, as the documentation related dependencies should only be included when CI is building documentation.

Maintainers:

For a list containing more detailed information, see https://leanprover-community.github.io/teams/maintainers.html

• Anne Baanen (@Vierkantor): algebra, number theory, tactics
• Matthew Robert Ballard (@mattrobball): algebra, algebraic geometry, category theory, performance
• Reid Barton (@rwbarton): category theory, topology
• Riccardo Brasca (@riccardobrasca): algebra, number theory, algebraic geometry, category theory
• Kevin Buzzard (@kbuzzard): algebra, number theory, algebraic geometry, category theory
• Mario Carneiro (@digama0): lean formalization, tactics, type theory, proof engineering
• Bryan Gin-ge Chen (@bryangingechen): documentation, infrastructure
• Johan Commelin (@jcommelin): algebra, number theory, category theory, algebraic geometry
• Anatole Dedecker (@ADedecker): topology, functional analysis, calculus
• Rémy Degenne (@RemyDegenne): probability, measure theory, analysis
• Floris van Doorn (@fpvandoorn): measure theory, model theory, tactics
• Frédéric Dupuis (@dupuisf): linear algebra, functional analysis
• Gabriel Ebner (@gebner): tactics, infrastructure, core, formal languages
• Sébastien Gouëzel (@sgouezel): topology, calculus, geometry, analysis, measure theory
• Markus Himmel (@TwoFX): category theory
• Yury G. Kudryashov (@urkud): analysis, topology, measure theory
• Robert Y. Lewis (@robertylewis): tactics, documentation
• Jireh Loreaux (@j-loreaux): analysis, topology, operator algebras
• Heather Macbeth (@hrmacbeth): geometry, analysis
• Patrick Massot (@patrickmassot): documentation, topology, geometry
• Bhavik Mehta (@b-mehta): category theory, combinatorics
• Kyle Miller (@kmill): combinatorics, tactics, metaprogramming
• Kim Morrison (@kim-em): category theory, tactics
• Oliver Nash (@ocfnash): algebra, geometry, topology
• Joël Riou (@joelriou): category theory, homology, algebraic geometry
• Damiano Testa (@adomani): algebra, algebraic geometry, number theory, tactics
• Adam Topaz (@adamtopaz): algebra, category theory, algebraic geometry
• Eric Wieser (@eric-wieser): algebra, infrastructure

Past maintainers:

• Jeremy Avigad (@avigad): analysis
• Johannes Hölzl (@johoelzl): measure theory, topology
• Simon Hudon (@cipher1024): tactics
• Chris Hughes (@ChrisHughes24): algebra