Lean4Agent: Formal Modeling and Verification for Agent Workflow and Trajectory

Large language model (LLM) agents are increasingly entrusted with natural-language workflow instructions (e.g., retail-payment policies) that specify not only what outcome to achieve, but also which steps, branches, and tool interactions are permitted. When these instructions are supplied as prompt context, however, the model retains control over both procedure selection and step execution. As interactions accumulate, an agent can skip required steps, take unsupported branches, or execute a valid step with unsupported arguments or effects--a failure mode we call workflow misalignment. In this work, we propose COVENANT, a compiler-and-interpreter architecture for workflow-aligned agent execution. Our key insight is to treat workflow instructions as source programs rather than prompts. COVENANT converts the instructions into a workflow abstract syntax tree (WAST) and lowers it to a workflow control-flow graph (WCFG). At runtime, a controller interprets the WCFG one node at a time, checks each proposal against requirements extracted from the instructions before committing controller state or advancing the graph, and returns diagnostic feedback for repair. To evaluate COVENANT, we use 120 cases from three existing benchmarks, spanning seven workflow scenarios. Compared with state-of-the-art LLM agents, COVENANT improves benchmark success from 50.00% to 83.33% and reduces the workflow-misalignment failure rate from 42.50% to 15.83% (62.75% relative). These results show that COVENANT substantially mitigates workflow misalignment, moving LLM-agent alignment beyond isolated prompt following toward reliable execution of complex and multi-step workflows.

Formal verification offers a path to provably correct software, but writing verified code remains expensive enough that the technique is rarely used in production. Recent large language models can accelerate this work, and recent benchmarks measure their ability to translate specifications into code and machine-checked proofs of correctness. This thesis evaluates the state of such LLM-driven verified-code generation ("vericoding") in Lean and develops search-based methods for improving verification performance. We first reproduce a subset of the vericoding-benchmark Lean leaderboard on a current cross-vendor model pool, finding that non-reasoning performance remains roughly steady on US closed-source models while open-weight models have slightly improved. We update the iterative methodology of vericoding-benchmark with an agentic loop equipped with mathlib search, finding that model performance greatly improves and scales with agent budget. GPT-5.4 nearly saturates the benchmark at 95.0% on 423 specs with $K=50$ LLM calls. We then design two agent-directed tree-search formulations: a state-based orchestrator that branches on partial-proof states, and a context-based orchestrator that branches on full subagent contexts. Compared against the agent baseline, the context-based design solves a wider range of intermediate-difficulty specs at lower token cost, while the agent baseline retains an advantage on the hardest specs, where uninterrupted iteration matters most. We conclude that search structure has selective advantages over a strong agent baseline, and that more challenging benchmarks drawn from modern code are important to measure and drive further progress in automated formal verification. Code available upon request by contacting the author at leoy@mit.edu.

Agentic systems driven by large language models (LLMs) are increasingly deployed in real-world workflows where they act on persistent operational data. Before deployment, these systems need to be verified against business requirements that govern workflow execution and data evolution. However, existing approaches do not provide such system-level guarantees, as they mainly constrain or analyse behaviour at the agent's interface level. We study here the verification of agentic systems comprising a single LLM and a tool orchestration harness over relational operational data. We formalise them as Stateful Tool-Enabled Agentic Deployments (STEADs), give their semantics, define the problem of verifying them against First-Order Computation Tree Logic (FO-CTL) specifications, and show that it is undecidable. We identify sufficient conditions for exact preservation of FO-CTL specifications under a finite-domain restriction, over which verification is PSPACE-complete. The key requirement is that renaming opaque identifiers in the data must correspondingly rename the selected tool calls. We show that LLM-driven agents can violate this condition and introduce a canonical deployment wrapper that guarantees it for arbitrary base agents while preserving already-equivariant behaviour. We prove that computing canonical representations required by this construction is graph-isomorphism-hard. Finally, we illustrate our framework on an LLM agent orchestrating a case-management workflow.