Lean4Agent: Formal Modeling and Verification for Agent Workflow and Trajectory

2026-06-02

AI Summary

This work addresses the limited reliability of multi-step tasks in existing large language model agents, which stems from the absence of formal specifications and verification mechanisms for workflows and execution traces. To bridge this gap, the authors propose Lean4Agent, a novel framework that introduces the dependently typed language Lean4 into agent behavior modeling. Central to this approach is FormalAgentLib, a library that formally encodes semantic consistency of workflows, coupled with LeanEvolve—a mechanism that automatically refines workflows based on formal verification outcomes. The framework enables precise failure localization in execution traces and supports automated workflow evolution. Evaluated on subsets of SWE-Bench-Verified and ELAIP-Bench, verified workflows consistently outperform unverified ones by 11.94% on average, while LeanEvolve further boosts SWE performance by 7.47%, establishing a new paradigm for integrating formal methods into agent systems.

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.

Problem

• agent workflow
• formal verification
• execution trajectory
• Large Language Models
• formal methods

Innovation

• formal verification
• dependent types
• agent workflow
• Lean4
• trajectory debugging