What is in lean?

Lean is a dependently typed programming language and theorem prover developed primarily at Microsoft Research. It is designed to bridge the gap between interactive theorem proving and programming. Lean aims to provide a foundation for both verified software and verified mathematics.

Key aspects of Lean include:

• Dependent Type Theory: Lean is based on a form of dependent type theory called the Calculus of Constructions. This allows types to depend on values, enabling very precise specification and verification.

• Interactive Theorem Proving: Lean is used interactively with an editor or IDE. Users write proof scripts and Lean checks their validity.

• Automation: Lean includes powerful automation tactics that can automatically solve many common proof obligations.

• Metaprogramming: Lean supports metaprogramming, which allows users to write programs that generate Lean code. This is useful for building custom tactics and automating complex reasoning.

• Formal Verification: Lean is used for formal verification of both software and hardware.

• Mathematical Libraries: The Lean community has developed extensive mathematical libraries that are used for formalizing mathematical theorems and proofs.

• Open Source: Lean is an open-source project.