The Lean mathematical library, mathlib, is a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant.
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. This project is very active, with many contributors and daily activity.
This is free and open source software.
Website: leanprover-community.github.io
Support: GitHub Code Repository
Developer: Many contributors
License: Apache License 2.0
mathlib4 is written in Lean. Lean is a functional programming language that makes it easy to write correct and maintainable code. You can also use Lean as an interactive theorem prover. Lean programming primarily involves defining types and functions. This allows your focus to remain on the problem domain and manipulating its data, rather than the details of programming.
A proof assistant is a piece of software that provides a language for defining objects, specifying properties of these objects, and proving that these specifications hold. The system checks that these proofs are correct down to their logical foundation.
These tools are often used to verify the correctness of programs. But they can also be used for abstract mathematics, which is something of interest to the mathlib community. In a formalization, all definitions are precisely specified and all proofs are virtually guaranteed to be correct.
Related Software
| Proof Assistants | |
|---|---|
| Rocq Prover | Formal proof management system |
| Isabelle | Generic proof assistant; express mathematical formulas in a formal language |
| Lean | Programming language and theorem prover |
| Agda | Interactive system for writing and checking proofs |
| F* | Functional language for verified programs with dependent refinement types |
| HOL4 | Interactive higher-order logic environment for rigorous theorem development |
| Aya | Dependently typed language for formalisation and certified programming |
| Lambdapi | Logical framework for defining and checking expressive type systems |
| HOL Light | Lightweight higher-order logic system with a small trusted kernel |
| PVS | Specification and verification suite for analysing complex systems |
| LISA | Scala-based platform for formal mathematics and automated reasoning |
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