Lean4Agent: Formal Modeling and Verification for Agent Workflow and Trajectory

Computer Science > Artificial Intelligence [Submitted on 2 Jun 2026] Lean4Agent: Formal Modeling and Verification for Agent Workflow and Trajectory Ruida Wang, Jerry Huang, Pengcheng Wang, Xuanqing Liu, Luyang Kong, Tong Zhang 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 Focus to learn more Submission history From: Ruida Wang [view email] [v1] Tue, 2 Jun 2026 18:46:50 UTC (542 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-06 Change to browse by: cs cs.LG cs.LO cs.SE References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)