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

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

Xichen Tang

cs.LO Jan 28, 2025 · v1
meta-study tooling formalization verification
Read PDF arXiv abstract
TL;DR
Surveys the Lean 4 theorem prover's architecture, type system, metaprogramming, ecosystem, and applications in formal verification and mathematics.
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.
Problem

A comprehensive understanding of Lean 4 as both an interactive theorem prover and a functional programming language, including its ecosystem and comparative advantages, has not been consolidated in a single reference.

Approach

The survey examines Lean 4 architecture, its dependent type system, metaprogramming capabilities, and practical applications. It provides detailed comparisons with other proof assistants (Coq, Isabelle, Agda) and presents case studies in formal verification and mathematics, covering Lean 4 libraries, tools, and educational applications.

Results

The survey demonstrates Lean 4 advantages in proof automation, performance, and usability relative to other proof assistants. It documents the growing ecosystem including Mathlib, and identifies Lean 4 as having significant impact on formal methods and mathematical formalization.