Compiler-Guided Adaptive Proof Search with Cross-Model Synergy on Context-Dependent Theorem Proving
A compiler-guided proof search framework that balances exploration and exploitation for theorem proving in real-world Lean 4 projects Uses dual-model generation and stagnation-triggered resampling to explore diverse starting points, avoiding redundant failed attempts Employs current-best refinement guided by compiler-grounded pairwise comparison to exploit promising proof states Achieves a 12.8 percentage point improvement in average pass rate while reducing LLM calls by 21.9% compared to pass@k
Analysis
TL;DR
- A compiler-guided proof search framework that balances exploration and exploitation for theorem proving in real-world Lean 4 projects
- Uses dual-model generation and stagnation-triggered resampling to explore diverse starting points, avoiding redundant failed attempts
- Employs current-best refinement guided by compiler-grounded pairwise comparison to exploit promising proof states
- Achieves a 12.8 percentage point improvement in average pass rate while reducing LLM calls by 21.9% compared to pass@k baselines within a pass@32 budget
- Evaluated on seven real-world Lean 4 projects from the miniCTX-v2 benchmark
Why It Matters
This work addresses a critical bottleneck in automated theorem proving: the difficulty of leveraging compiler feedback effectively when proofs depend heavily on project-specific context. For AI practitioners building verification tools or working with formal methods, this framework demonstrates how compiler errors can be systematically transformed into search guidance rather than mere failure signals. The improved effectiveness-efficiency tradeoff makes large-scale theorem proving more practical for real-world software verification pipelines.
Technical Details
- Dual-model generation: The framework uses two complementary models to generate diverse proof attempts, ensuring broader exploration of the proof search space and reducing the likelihood of converging on locally optimal but incorrect strategies.
- Stagnation-triggered resampling: When the search process detects that proof attempts are no longer improving (stagnation), the system resamples from alternative starting points rather than continuing to refine a deteriorating proof.
- Compiler-grounded pairwise comparison: Failed proofs are compared pairwise using compiler error signals to identify which attempts provide better starting points for refinement, enabling data-driven exploitation decisions.
- Current-best refinement: The most promising proof state is iteratively refined using compiler feedback, with careful control to prevent later revisions from degrading partially correct proofs.
- Evaluation on miniCTX-v2: Experiments conducted across seven real-world Lean 4 projects, comparing against pass@k baselines under a fixed pass@32 computational budget.
Industry Insight
- The integration of compiler feedback as a search guidance mechanism rather than a binary success/failure signal represents a paradigm shift for formal verification tools; practitioners should consider adopting similar compiler-grounded evaluation strategies in their proof search pipelines.
- The 21.9% reduction in LLM calls while improving pass rates suggests that intelligent search control can significantly lower the cost of theorem proving, making it more viable for industrial-scale verification tasks where API costs are a major constraint.
- The stagnation-triggered resampling approach offers a generalizable pattern for any iterative refinement system where continued refinement of poor starting points wastes resources; this principle extends beyond theorem proving to code generation and synthesis tasks.
Disclaimer: The above content is generated by AI and is for reference only.