🤖 AI Summary
This work presents the first successful application of a large language model—specifically, Claude Opus 4.6—as an AI-powered programming assistant to automatically generate and verify a semantic-preserving proof for the Administrative Normal Form (ANF) transformation in the CertiCoq compiler, entirely without manual proof coding. Guided by human oversight and built upon the Rocq proof language, the approach adapts and transfers techniques from an existing continuation-passing style (CPS) transformation proof. Within approximately 96 hours, the system produced 7,800 lines of machine-checkable proof code, surpassing the previous CPS proof of 5,300 lines and substantially reducing development time. This result demonstrates the feasibility and significant potential of large language models in formal verification.
📝 Abstract
We report on using an agentic coding assistant (Claude Code, powered by Claude Opus 4.6) to mechanize a substantial Rocq correctness proof from scratch, with human guidance but without human proof writing. The proof establishes semantic preservation for the administrative normal form (ANF) transformation in the CertiCoq verified compiler for Rocq. The closely related continuation-passing style (CPS) transformation in CertiCoq was previously proved correct by human experts over several months. We use this proof as a template and instruct the LLM to adapt the proof technique to the ANF setting, which differs in important technical ways. The resulting ANF proof comprises approximately 7,800 lines of Rocq (larger than the 5,300-line CPS proof) and was developed in approximately 96 hours. We describe the proof technique and report on the experience of developing it with an LLM, discussing both the strengths and limitations of the approach and its implications for verified compiler construction.