Lean 4 is an open-source theorem prover and programming language developed by Microsoft Research and the Lean community. It combines powerful automation with expressive logic, allowing users to write and verify mathematical proofs as well as develop correct-by-construction software.

Pros

• Powerful theorem proving capabilities with a strong type system
• Supports both interactive and automated theorem proving
• Integrates well with software development practices
• Active and growing community with extensive documentation

Cons

• Steep learning curve for those new to formal verification
• Limited ecosystem compared to more established programming languages
• Performance can be slower compared to traditional programming languages
• May require significant effort to formalize complex mathematical concepts

Code Examples

1. Defining a simple function:

def add (a b : Nat) : Nat :=
  a + b

#eval add 3 5 -- Output: 8

2. Proving a simple theorem:

theorem add_comm (a b : Nat) : add a b = add b a := by
  simp [add]
  rw [Nat.add_comm]

3. Defining an inductive type:

inductive BinTree (α : Type)
  | leaf : BinTree α
  | node : BinTree α → α → BinTree α → BinTree α

def BinTree.size {α : Type} : BinTree α → Nat
  | leaf => 0
  | node l _ r => l.size + r.size + 1

Getting Started

1. Install Lean 4:

   curl https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh -sSf | sh
   

2. Create a new Lean project:

   mkdir my_project
   cd my_project
   lake init my_project
   

3. Open Main.lean in your preferred editor with Lean support (e.g., VS Code with the Lean 4 extension).

4. Start writing Lean code and theorems in Main.lean.