Working with Lean, a popular proof assistant for formalizing mathematics, is challenging sometimes. The process of developing proofs in Lean can be time-consuming and complex, especially for those who are new to the system. This complexity can slow down the progress of formalizing mathematical theories.
Several tools and methods have been developed to assist with proof development in Lean. Traditional approaches include using Lean’s built-in tactics and strategies, as well as consulting extensive documentation and tutorials. While these resources are helpful, they require significant manual effort and expertise to use effectively.
Introducing LLMLean, a new tool that integrates large language models (LLMs) with Lean to provide automated tactic suggestions and proof completions. LLMLean allows users to leverage advanced LLMs either on their local machines or through cloud services such as OpenAI and Together.ai. LLMLean simplifies the proof development process by offering automated assistance, making it more accessible to a wider audience.
LLMLean offers several key features to enhance the user experience. The llmstep tactic suggests the next steps in a proof based on a given prefix, streamlining the proof development process. The llmqed tactic can complete an entire proof, saving users valuable time. LLMLean supports customization through various environment variables, allowing users to select different models and adjust settings to suit their needs. For instance, users can specify the number of suggestions they want to receive or choose between different prompt types.
Users report a significant reduction in the time required to complete proofs, with some seeing improvements of up to 50%. The tool’s accuracy in suggesting relevant tactics and completing proofs has also been highly rated by early adopters. These metrics highlight LLMLean’s potential to transform how proofs are developed in Lean, making the process faster and more efficient.
In conclusion, LLMLean addresses the complexities of working with Lean by providing automated assistance through advanced language models. By integrating with popular cloud services and offering customizable features, LLMLean makes proof development more accessible and efficient. This tool can significantly enhance productivity for new and experienced Lean users, paving the way for more widespread use of formalized mathematics.
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