Compiler-Guided Adaptive Proof Search with Cross-Model Synergy on Context-Dependent Theorem Proving
arXiv:2608.18084v1 Announce Type: new Abstract: Theorem proving in real-world Lean 4 projects is challenging because proofs often depend on project-specific context. While iterative refinement can use compiler errors to repair failed proofs, reusing failed attempts requires careful search control: some proofs provide better starting points than others, and later revisions may degrade a partially correct proof. We propose a compiler-guided proof search framework that balances exploration and exploitation. It explores diverse starting points through dual-model generation and stagnation-triggered resampling, while exploiting promising proof states through current-best refinement guided by compiler-grounded pairwise comparison. Experiments on seven real-world Lean 4 projects from miniCTX-v2 show that our method achieves a better effectiveness--efficiency tradeoff than pass@k baselines. Within the pass@32 budget, our method improves average pass rate by 12.8 percentage points while reducing LLM calls by 21.9%.
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[Submitted on 4 Jun 2026]
Title:Compiler-Guided Adaptive Proof Search with Cross-Model Synergy on Context-Dependent Theorem Proving
View a PDF of the paper titled Compiler-Guided Adaptive Proof Search with Cross-Model Synergy on Context-Dependent Theorem Proving, by Zhuo Liu and 2 other authors
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Abstract:Theorem proving in real-world Lean 4 projects is challenging because proofs often depend on project-specific context. While iterative refinement can use compiler errors to repair failed proofs, reusing failed attempts requires careful search control: some proofs provide better starting points than others, and later revisions may degrade a partially correct proof. We propose a compiler-guided proof search framework that balances exploration and exploitation. It explores diverse starting points through dual-model generation and stagnation-triggered resampling, while exploiting promising proof states through current-best refinement guided by compiler-grounded pairwise comparison. Experiments on seven real-world Lean 4 projects from miniCTX-v2 show that our method achieves a better effectiveness--efficiency tradeoff than pass@k baselines. Within the pass@32 budget, our method improves average pass rate by 12.8 percentage points while reducing LLM calls by 21.9%.
Comments: 16 pages
Subjects:
Computation and Language (cs.CL); Programming Languages (cs.PL)
Cite as: arXiv:2608.18084 [cs.CL]
(or arXiv:2608.18084v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2608.18084
arXiv-issued DOI via DataCite
Submission history
From: Zhuo Liu [view email] [v1] Thu, 4 Jun 2026 11:21:04 UTC (494 KB)
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