Summary of Lean Copilot: Large Language Models As Copilots For Theorem Proving in Lean, by Peiyang Song et al.
Lean Copilot: Large Language Models as Copilots for Theorem Proving in Lean
by Peiyang Song, Kaiyu Yang, Anima Anandkumar
First submitted to arxiv on: 18 Apr 2024
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: Machine Learning (cs.LG); Logic in Computer Science (cs.LO); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Neural theorem proving combines large language models (LLMs) with proof assistants like Lean to rigorously verify formal proofs, eliminating hallucination. While existing neural theorem provers can offer valuable suggestions, they struggle to prove novel theorems autonomously, where human insights are crucial. This paper introduces Lean Copilot, a framework for running LLM inference natively in Lean, enabling users to build proof automation tools that integrate seamlessly into their workflow. Users can utilize pretrained models or bring their own, which run locally or on the cloud. Lean Copilot suggests proof steps, completes proof goals, and selects relevant premises. Experimental results on the Mathematics in Lean textbook demonstrate its effectiveness compared to rule-based proof automation (aesop). When assisting humans, Lean Copilot requires 2.08 manually-entered proof steps on average, while automating 74.2% proof steps, outperforming aesop by 85%. The paper opens sources all code and artifacts under a permissive MIT license. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper combines special computer programs called large language models with another type of program that checks math proofs for mistakes. Right now, these programs can give us some good ideas, but they struggle to help us prove new math theorems without any help from humans. The authors created a new tool called Lean Copilot that makes it easier for users to build their own math-proof checking tools. Users can use pre-made models or create their own and run them on their computers or online. This tool helps with finding proof steps, completing math problems, and picking the right parts of a proof. The authors tested this tool on some math textbook problems and found that it works better than an older method called aesop. When humans are involved, this tool only needs 2-3 manual steps to prove a theorem, while automating about 74% of the work. |
Keywords
» Artificial intelligence » Hallucination » Inference
