Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. This paper removes these barriers by introducing LeanDojo: an open-source Lean playground consisting of toolkits, data, models, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs, providing valuable data for premise selection: a key bottleneck in theorem proving. Using this data, we develop ReProver (Retrieval-Augmented Prover): the first LLM-based prover that is augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo's program analysis capability to identify accessible premises and hard negative examples, which makes retrieval much more effective. Furthermore, we construct a new benchmark consisting of 96,962 theorems and proofs extracted from Lean's math library. It features challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research.

本文介绍了 LeanDojo：一个开源、可交互的证明环境，它从Lean中提取了证明中的数据及注释，提供了有价值的前提数据，以便于选取前提。 我们使用此数据，开发了 ReProver：第一个增加检索功能的基于LLM的证明程序。其成本低廉，只需要一台GPU进行一周的训练，并且可以有效地选择定理中的前提。我们构建了一个包含96962个定理和证明的新基准，并将其用于培训和评估。实验结果表明，相对于非检索基线和GPT-4，ReProver非常有效。我们发布了代码和数据集，以促进进一步的研究。

LeanDojo：具备检索增强语言模型的定理证明