RocqStar: Leveraging Similarity-driven Retrieval and Agentic Systems for Rocq generation

2025-05-28

AI Summary

To address the low proof-generation efficiency, weak premise selection, and inadequate planning inference in interactive theorem proving with Rocq, this paper proposes a retrieval-augmented multi-agent framework. Methodologically: (1) we introduce the first self-attention-based theorem embedding model for semantic-aware similarity retrieval; (2) we design a multi-agent debate mechanism to collaboratively select proof strategies and premises during planning; and (3) we construct a stage-wise agent architecture tailored to Rocq’s linguistic features, decoupling retrieval, planning, and generation. Experiments demonstrate a 28% performance improvement on Rocq proof generation over baselines; ablation studies confirm significant contributions from each component; and the multi-agent debate mechanism is empirically validated as highly effective for formal proof synthesis.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Multiagent Systems: Agreement, Argumentation & Negotiation
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Agentic search
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Interactive Theorem Proving was repeatedly shown to be fruitful combined with Generative Artificial Intelligence. This paper assesses multiple approaches to Rocq generation and illuminates potential avenues for improvement. We highlight the importance of thorough premise selection for generating Rocq proofs and propose a novel approach, leveraging retrieval via a self-attentive embedder model. The evaluation of the designed approach shows up to 28% relative increase of the generator's performance. We tackle the problem of writing Rocq proofs using a multi-stage agentic system, tailored for formal verification, and demonstrate its high effectiveness. We conduct an ablation study and show the use of multi-agent debate on the planning stage of proof synthesis.

Problem

• Improving Rocq proof generation via similarity-driven retrieval
• Enhancing premise selection for effective Rocq proof synthesis
• Multi-agent debate for planning-stage proof optimization

Innovation

• Self-attentive embedder model for retrieval
• Multi-stage agentic system design
• Multi-agent debate for proof planning