Lean Theorem Prover and Programming Language

Lean is a functional programming language and automated theorem prover developed primarily by Leonardo de Moura at Microsoft Research (now Amazon) starting in 2013. Designed to bridge the gap between interactive theorem proving and practical programming, Lean has become one of the most popular proof assistants in mathematics. Key features: dependent type theory as the foundational logic, based on the Calculus of Inductive Constructions. Powerful elaborator and tactic framework for interactive proof development with both classic tactics and new term-mode proof construction. Metaprogramming framework allowing users to write custom tactics, automation, and extensions within the language itself. Mathlib community library containing over 1.5 million lines of formalized mathematics, covering analysis, algebra, topology, category theory, number theory, and more, representing one of the largest formal mathematics repositories in the world. Automated reasoning integration with SMT solvers for automated theorem proving. Efficient code generation compiling to C, enabling extracted programs to run with competitive performance. Universe polymorphism and quotient types for a smooth mathematical foundation. Type class inference for overloading and ad-hoc polymorphism. Support for classical and constructive mathematics through the law of excluded middle as an optional axiom. Lean 4 (current major version) is a full rewrite with a new elaborator, improved performance, and the ability to serve as a general-purpose programming language. Tight integration with VS Code for interactive development. Used for formalizing major mathematical results including the Liquid Tensor Experiment (Peter Scholze) and Polynomial Freiman-Ruzsa conjecture.