Lean4Agent: Formal Modeling and Verification for Agent Workflow and Trajectory
This paper proposes Lean4Agent, the first framework that uses Lean4, a dependent-type formal language, to model and verify LLM agent behavior. It includes FormalAgentLib for verification and LeanEvolve for workflow revision. Experiments show verification-passing workflows outperform failing ones by 11.94%, and LeanEvolve further improves SWE performance by 7.47%.
[2606.06523] Lean4Agent: Formal Modeling and Verification for Agent Workflow and Trajectory
[Submitted on 2 Jun 2026]
Title:Lean4Agent: Formal Modeling and Verification for Agent Workflow and Trajectory
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Abstract:Equipping Large Language Models (LLMs) to execute reliable multi-step workflows has become a central challenge in artificial intelligence. Despite recent advances in LLMs' agentic capabilities, most agent systems still lack formal methods for specifying, verifying, and debugging their workflow and execution trajectories. This challenge mirrors a long-standing problem in mathematics, where the ambiguity of natural languages (NLs) motivates the development of formal languages (FLs). Inspired by this paradigm, we propose Lean4Agent, to the best of our knowledge, the first framework that uses Lean4, a dependent-type FL to model and verify agent behavior. Lean4Agent launches FormalAgentLib, an extensible Lean4 library for formally modeling and verifying agent workflows' semantic consistency under explicit assumptions, and enabling localization of execution-time failures revealed by trajectories. Building on FormalAgentLib, we further develop LeanEvolve, which applies results in FormalAgentLib to revise workflows to enhance its capability. Extensive experiments on a hard problem subset of SWE-Bench-Verified and a subset of ELAIP-Bench across 5 leading LLMs indicate that the verification-passing workflows outperform the failing ones by an average of 11.94%, and LeanEvolve further improves SWE performance by 7.47% on average. Furthermore, Lean4Agent establishes a foundation for a new field of using expressive dependent-type FL to formally model and verify agent behavior.
Subjects:
Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Logic in Computer Science (cs.LO); Software Engineering (cs.SE)
Cite as: arXiv:2606.06523 [cs.AI]
(or arXiv:2606.06523v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2606.06523
arXiv-issued DOI via DataCite
Submission history
From: Ruida Wang [view email] [v1] Tue, 2 Jun 2026 18:46:50 UTC (542 KB)
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