Fix, Not Just Resample: Bounded Compiler-Guided Repair in Lean 4
Source
arxiv.org
Author
Haotian Deng, Chris Farber, Sonal Narasimha, Samskrithi Sivakumar, Yexiang Xue
Date
Why it matters
Shows that one bounded repair attempt using compiler feedback captures most of the gain over resampling. This pattern transfers to any agentic loopThe cycle an agent runs in: decide, call a tool, read the result, decide again — repeating until the goal is met or a stop condition fires.Full definition → with a precise verifier.
Key takeaways · AI-distilled
Instead of discarding a Lean tactic the compiler rejects, the method feeds the error message to a repair model and fixes that step in place, with at most R repair attempts per step on top of K sampled candidates.
The authors report up to a 32% relative solve-rate gain over sampling alone and 82 extra theorems on a 1,990-theorem LeanDojo subset, with gains largest when the sampling budget is small. Repair costs extra runtime.
The first repair attempt captured 84-96% of the total gain, and nearly all of it came from shallow tactic-execution failures rather than structural errors such as type mismatches. On Lean Workbook the approach nearly doubled the solve rate with zero regressions.
Terms in this piece · Glossary
agentic loop — The cycle an agent runs in: decide, call a tool, read the result, decide again — repeating until the goal is met or a stop condition fires.
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