Theorem proving is an essential process in formal mathematics and computer science, involving the verification of mathematical theorems by deriving logical inferences. However, it is also a notoriously complicated and laborious process, often fraught with errors. There have been several attempts to develop tools to streamline the theorem proving process, but most tools currently available require heavy user input, requiring users to have an in-depth understanding of the steps required.
Looking to address this, a new AI tool called Lean Copilot is introduced. By merging large language models (LLMs) with the Lean theorem proving system, this tool helps to automate portions of theorem proving, making it more efficient and less reliant on user expertise. Lean Copilot brings several innovations to the process.
First, the ‘suggest_tactics’ function that provides users with tactic suggestions for their proofs, reducing the need for manual input. Built on AI inference, this feature also enables users to validate the strategy adequacy and decide which to apply on their proofs.
Second, the ‘search_proof’ function, which merges the tactics suggested by the LLM with the aesop framework, a tool that combines different tactics to find multi-tactic proofs. This function considerably speeds up the process, allowing the proof to be more efficiently constructed.
Third, the ‘select_premises’ function helps point out potential premises from a set database that can be used while proving the theorem. It is yet another feature reducing the cognitive load on the user, making the theorem proving process even faster.
Users have the flexibility to run inference on any existing LLMs in Lean to create personalized proof automation, significantly enhancing the potential applications of Lean Copilot. Despite these capabilities, there are a few challenges to be aware of, such as Lean occasionally crashing during file editing or restarting, requiring a simple reset. Additionally, the ‘select_premises’ feature retrieves the original premise form, which might not meet users’ expectations.
In conclusion, Lean Copilot, by integrating Large Language Models with Lean, presents a promising advance in theorem proving, making this intricate process more efficient and less reliant on user input. Even though the tool comes with a few challenges, its powerful features have the potential to vastly improve the workflow of mathematicians and computer science researchers, enhancing the pace and accuracy of theorem proving.
