Learning to Repair Lean Proofs from Compiler Feedback

Evan Wang, Simon Chess, Daniel Lee, Siyuan Ge, Ajit Mallavarapu, Vasily Ilin

Track: long paper (up to 8 pages)

Keywords: Lean, formal verification, proof repair, compiler feedback, supervised learning, theorem proving

TL;DR: Supervised training on compiler-annotated Lean proof errors enables language models to learn effective proof repair, addressing a gap left by existing datasets that contain only correct proofs.

Abstract: As neural theorem provers become increasingly agentic, the ability to interpret and act on compiler feedback is critical. However, existing Lean datasets consist almost exclusively of correct proofs, offering little supervision for understanding and repairing failures. We study Lean proof repair as a supervised learning problem: given an erroneous proof and compiler feedback, predict both a corrected proof and a natural-language diagnosis grounded in the same feedback. We introduce APRIL (Automated Proof Repair in Lean), a dataset of 260,000 supervised tuples pairing systematically generated proof failures with compiler diagnostics and aligned repair and explanation targets. Training language models on APRIL substantially improves repair accuracy and feedback-conditioned reasoning; in our single-shot repair evaluation setting, a finetuned 4B-parameter model outperforms the strongest open-source baseline. We view diagnostic-conditioned supervision as a complementary training signal for feedback-using provers.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Submission Number: 23