Learning to Repair Lean Proofs from Compiler Feedback

TL;DR

This paper introduces APRIL, a large dataset for training neural models to repair Lean proofs using compiler feedback, significantly improving proof repair accuracy and reasoning.

Contribution

We created APRIL, a dataset of 260,000 proof failures with diagnostics and repairs, enabling supervised learning for proof repair from compiler feedback.

Findings

Finetuned models outperform open-source baselines in proof repair.

Training on APRIL improves feedback-conditioned reasoning.

The dataset enhances neural theorem prover capabilities.

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. Our dataset is available at https://huggingface.co/datasets/uw-math-ai/APRIL.