Building Formally Verified Software with AI Agents

Summary & Methodology Analysis

AI agents are increasingly deployed for writing code, but existing benchmarks typically focus on individual functions or evaluate proof generation using provided implementations. This leaves a gap regarding whether agents can handle coherent implementation and proof choices across real multi-module codebases. To answer this, the paper introduces a framework and benchmark evaluation for agents. The methodology relies on a structured sequence of steps executed by agents and supporting tools. First, an agent discovers, selects, and plans by listing all available declarations from the source repository, identifying which ones to include, computing their dependencies, and committing to specific Lean signatures and a module layout. Next, an executor agent translates per-module definitions in dependency order, followed by curator review. Specifications are drafted in natural language and formalised in Lean for Track 2 non-formal repositories. The system then runs automated structure and build checks alongside LLM-judged semantic reviews of specification intent and idiomatic Lean usage. Finally, benchmark evaluation is executed on agents in either proof-only mode or code-and-proof mode with full tool access. Regarding empirical performance, GPT-5.5 (xhigh) passes 87.3% of specifications in code-and-proof and 85.8% in proof-only. However, ten instances resist all eight configurations across both modes.