# A Comprehensive Survey of the Lean 4 Theorem Prover: Architecture, Applications, and Advances

arXiv: https://arxiv.org/abs/2501.18639 · HTML: https://mlsanity.com/paper/2501.18639/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2025.

## Built on by (most cited first, 2 of 2)

- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [SorryDB: Can AI Provers Complete Real-World Lean Theorems?](https://mlsanity.com/paper/2603.02668/) (2026)

## Abstract (arXiv)

This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in formal verification and mathematics. Through detailed comparisons with other proof assistants and extensive case studies, we demonstrate Lean 4's unique advantages in proof automation, performance, and usability. The paper also explores recent developments in its ecosystem, including libraries, tools, and educational applications, providing insights into its growing impact on formal methods and mathematical formalization.