Theorem proving is an indispensable component in the realms of formal mathematics and computer science. Despite its significance, constructing proofs is a demanding task that is not just time-consuming but also liable to errors due to its complex nature. Mathematicians and researchers, therefore, end up investing substantial amounts of time and energy in this process. Thus, automating parts of this process has been deemed necessary, leading to the development of tools that can assist with theorem proving.
Traditional proof assistants that are presently in use provide an environment where proofs can be written and checked. These tools, however, require users to manually lay out the steps and tactics needed for the proof construction process. This heavily user-dependent approach means that users have to possess extensive knowledge of the steps involved in the process.
To address the limitations of these existing tools, Lean Copilot – a breakthrough AI tool that merges large language models (LLMs) with Lean – has been introduced. The objective of this AI tool is to automate various segments of the proof construction process. Lean Copilot assists users by suggesting tactics, searching for proofs, and selecting relevant premises. Users are offered the flexibility to either employ built-in models or bring their own models for running either on the cloud or locally. With these capabilities, Lean Copilot significantly reduces the reliance on manual input, making the proof construction procedure more efficient.
Lean Copilot is equipped with several features that demonstrate its capabilities. A feature named `suggest_tactics` generates tactic suggestions for proofs that users can effortlessly use by clicking on them. Another feature, `search_proof`, merges LLM-based tactics with Lean’s aesop framework in order to find multi-tactic proofs. These proofs can then be inserted into the editor. The `select_premises` function is another valuable asset. It extracts potentially useful premises from the database, further automating the proof construction process. Users also have the option to run interference on any LLMs within Lean, enabling them to build customised proof automation or other applications seamlessly.
Despite its impressive features, Lean Copilot has its limitations. For instance, Lean might occasionally crash during the restart or editing of a file, necessitating a simple reboot to fix the issue. Additionally, the `select_premises` function retrieves the original version of a premise, which may not always meet the user’s expectations. Temporary alternatives like renaming theorems can be employed to tackle these challenges to some extent.
In conclusion, Lean Copilot is a promising tool that aims at addressing the challenges found in theorem proving by aligning large language models with Lean. It automates various aspects of the proof construction procedure, making it less dependent on manual input and more efficient. While it does have a few limitations, the capabilities of Lean Copilot highlight its potential to significantly streamline the workflows of scientists and researchers in the fields of computer science and formal mathematics.
