Agent-Assisted Lean Formalization Engine: A New Paradigm for AI-Assisted Mathematical Theorem Proving

This article introduces the Agent-Assisted Lean Formalization Engine project, which realizes the automatic formalization process of mathematical theorems by building a multi-agent collaborative workflow, combining large language models (LLMs) with the Lean4 theorem prover. Its core is a closed-loop mechanism of generation-verification-correction, aiming to lower the barrier to formalized mathematics, accelerate the machine verification of mathematical knowledge, and open up new paths for AI-assisted mathematical research.

Formal verification of mathematical theorems is an important direction in the intersection of computer science and mathematics. Lean4 has become a mainstream tool due to its powerful type system and metaprogramming capabilities. However, manually converting natural language proofs into Lean code is time-consuming and has a high barrier (requiring professional knowledge and being error-prone), which limits the popularization of formalized mathematics. The Agent-Assisted Lean project attempts to automate this process through agent workflows, providing new ideas to solve this dilemma.

The project adopts a multi-agent collaborative architecture with a four-stage workflow: 1. Theorem understanding and decomposition: Parse natural language propositions, identify key concepts, assumptions, and conclusions, and split complex tasks into subtasks; 2. Lean code generation: Map mathematical concepts to Lean syntax, generate type definitions, proof scripts, etc., with emphasis on standards and annotations; 3. Type checking and error fixing: Use the Lean type checker to verify code and correct errors through closed-loop feedback; 4. Proof optimization and refactoring: Simplify structure, eliminate redundancy, and improve code conciseness and readability.

The project's technology stack includes a flexible agent framework (supporting the combination of LLMs and tool components) and well-designed prompt engineering; it integrates Lean4 through the Language Server Protocol (LSP) to achieve real-time type checking feedback; it provides rich examples (from simple algebraic identities to complex analysis theorems) to verify the system's effectiveness and provide references for users.

1. Education field: As an intelligent tutor, interactively display the formalization process to accelerate Lean learning; 2. Research assistance: Help mathematicians quickly generate initial proof drafts and improve the efficiency of formalized research; 3. Large-scale projects: Undertake routine work, allowing experts to focus on core theorems and promote the progress of large-scale formalization projects (such as library construction).

Current challenges: LLMs have limitations in handling highly abstract mathematical concepts, and generated code requires manual correction; the rapid development of the Lean4 ecosystem needs continuous follow-up. Future directions: Support more proof strategies and tool integrations; improve the ability to handle complex mathematical structures; establish a formal code quality evaluation system; integrate mathematical knowledge bases to assist in proving new theorems.

The Agent-Assisted Lean Formalization Engine combines LLM language understanding with Lean4 formal verification capabilities, lowering the barrier to formalized mathematics and accelerating the machine verification of mathematical knowledge. It is a model of collaboration between human wisdom and machine capabilities. We look forward to more mathematical results being strictly formalized and verified in the future, pushing the inheritance and verification of mathematical knowledge into a new stage.