A Case Study on the Effectiveness of LLMs in Verification with Proof Assistants (2508.18587v1)

Abstract: LLMs can potentially help with verification using proof assistants by automating proofs. However, it is unclear how effective LLMs are in this task. In this paper, we perform a case study based on two mature Rocq projects: the hs-to-coq tool and Verdi. We evaluate the effectiveness of LLMs in generating proofs by both quantitative and qualitative analysis. Our study finds that: (1) external dependencies and context in the same source file can significantly help proof generation; (2) LLMs perform great on small proofs but can also generate large proofs; (3) LLMs perform differently on different verification projects; and (4) LLMs can generate concise and smart proofs, apply classical techniques to new definitions, but can also make odd mistakes.