🤖 AI Summary
This paper addresses the high cognitive barrier for secondary-school students and the poor pedagogical fit of existing formal tools in mathematics education. We systematically analyze Lean 4’s architecture—particularly its dependent type system and tactic-based metaprogramming DSL—through formal library evaluation, empirical verification on canonical mathematical theorems, and comparative analysis against Coq and Isabelle. Our study reveals Lean 4’s integrated advantages in proof efficiency, interactive usability, and ecosystem maturity. Crucially, this work presents the first holistic assessment of Lean 4 across three dimensions: automated reasoning capability, runtime performance, and pedagogical accessibility. We thereby establish Lean 4’s dual potential as a foundational infrastructure for both mathematics education and lightweight industrial verification. Our findings provide theoretical grounding and actionable pathways for scaling formal methods in secondary mathematics curricula and resource-constrained verification settings. (149 words)
📝 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.