The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous studies to automate formalization focused on powerful search algorithms, no attempts were made to take advantage of available informal proofs. In this work, we introduce Draft, Sketch, and Prove (DSP), a method that maps informal proofs to formal proof sketches, and uses the sketches to guide an automated prover by directing its search to easier sub-problems. We investigate two relevant setups where informal proofs are either written by humans or generated by a language model. Our experiments and ablation studies show that large language models are able to produce well-structured formal sketches that follow the same reasoning steps as the informal proofs. Guiding an automated prover with these sketches enhances its performance from 20.9% to 39.3% on a collection of mathematical competition problems.

本文介绍了一种名为DSP的方法，可以将非正式证明映射到正式证明草图并指导自动证明器，使其搜索更容易的子问题。实验证明语言模型能够产生结构良好的正式草图，并将其指导自动证明器，从而提高性能达到39.3%。

Draft, Sketch, and Prove: 用非正式证明指导形式化定理证明器