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

TL;DR

This survey reviews Lean 4, highlighting its architecture, features, and applications in formal verification and mathematics, emphasizing its advantages in proof automation, performance, and usability.

Contribution

It provides a comprehensive analysis of Lean 4's architecture, capabilities, and ecosystem, comparing it with other proof assistants and showcasing recent developments.

Findings

Lean 4 offers superior proof automation and performance.

Its ecosystem includes extensive libraries and educational tools.

Lean 4 has a growing impact on formal methods and mathematical formalization.

Abstract

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.