用大模型生成证明草图,融合整体推理与细粒度推导,提升形式化证明效率。
HybridProver: Augmenting Theorem Proving with LLM-Driven Proof Synthesis and Refinement
- 以证明草图为中间表示,融合整体证明生成与逐步策略推导
- 在miniF2F上达到73.8%成功率,超越此前最佳的61.9%
- 轻量级7B模型即可高效生成Isabelle/HOL证明,适合资源受限场景
形式化方法通过严格的数学验证保障关键系统的可靠性,但因手动构造证明耗时费力而应用受限。大语言模型(LLMs)的进展为自动化定理证明带来新机遇。现有方法主要分为两类:逐步策略生成和整体证明合成。二者各有优势,但多被孤立使用。本文提出HybridProver,一种统一框架,通过证明草图作为中间表示,整合整体证明合成与基于策略的生成。该设计支持部分正确证明结构的复用,同时兼顾高层规划与细粒度推理。我们在Isabelle/HOL中实现HybridProver,并在优化后的Isabelle数据集上对两个7B规模的LLM进行后训练。在miniF2F Isabelle基准测试中,成功率达到73.8%,优于先前最优结果(61.9%),表明轻量模型结合本方法可有效生成Isabelle/HOL证明,无需依赖超大规模模型。消融实验进一步分析了数据质量、训练配置与采样策略对证明生成的影响。
原文摘要 · Abstract (English)
Formal methods play a crucial role in ensuring the reliability of critical systems through rigorous mathematical verification. However, their adoption remains limited due to the labor-intensive nature of manual proof construction. Recent advances in large language models (LLMs) have opened new opportunities for automated theorem proving. Two main paradigms have emerged: stepwise tactic-based generation and whole-proof synthesis. While both approaches have complementary strengths, existing work largely treats them in isolation. In this work, we propose HybridProver, a unified framework that integrates whole-proof synthesis and tactic-based generation through proof sketches as an intermediate representation. This design enables the reuse of partially correct proof structures while effectively combining high-level planning with fine-grained reasoning. We implement HybridProver in Isabelle/HOL and post-train two 7B-scale LLMs on our optimized Isabelle datasets. Experiments on the miniF2F Isabelle benchmark achieved a 73.8% success rate and improved upon the previous state of the art (61.9%), demonstrating that lightweight models, when combined with our approach, can effectively generate Isabelle/HOL proofs without relying on very large LLMs. Ablation studies further analyze the impact of dataset quality, training configurations, and sampling strategies on proof generation.
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