Proofs Promptly: An Experience Report on Proof-Oriented Programming with AI Agents
The widespread adoption of AI-assisted coding is directly proportional to an increase in software bugs; can AI-assisted formal verification help reduce bugs at a comparable scale? In this experience report we give an anecdotal account of AI agents, equipped with a CLI and a proof assistant, producing thousands of lines of machine-checked code. We detail our experience across different proof-engineering tasks: implementing verified data structures for a standard library, translating unverified code into a formal language while inferring its specification, and porting and refactoring existing proofs to new frameworks. We present the techniques that made agentic proof-oriented programming (PoP) effective—or ineffective—and characterize the role of the human expert, whose contribution reduces to providing natural-language problem descriptions, reviewing auto-generated specifications, and occasionally supplying a key invariant. Our findings suggest that this division of labor can provide unprecedented leverage to a human expert in the loop and that agentic PoP has crossed the threshold of practical usefulness.