Automatic Goal Clone Detection in Rocq (2504.19129v1)

Abstract: Proof engineering in Rocq is a labor-intensive process, and as proof developments grow in size, redundancy and maintainability become challenges. One such redundancy is goal cloning, i.e., proving {\alpha}-equivalent goals multiple times, leading to wasted effort and bloated proof scripts. In this paper, we introduce clone-finder, a novel technique for detecting goal clones in Rocq proofs. By leveraging the formal notion of {\alpha}-equivalence for Gallina terms, clone-finder systematically identifies duplicated proof goals across large Rocq codebases. We evaluate clone-finder on 40 real-world Rocq projects from the CoqGym dataset. Our results reveal that each project contains an average of 27.73 instances of goal clone. We observed that the clones can be categorized as either exact goal duplication, generalization, or {\alpha}-equivalent goals with different proofs, each signifying varying levels duplicate effort. Our findings highlight significant untapped potential for proof reuse in Rocq-based formal verification projects, paving the way for future improvements in automated proof engineering.