Machine-Learned Premise Selection for Lean

Abstract

AbstractWe introduce a machine-learning-based tool for the Lean proof assistant that suggests relevant premises for theorems being proved by a user. The design principles for the tool are (1) tight integration with the proof assistant, (2) ease of use and installation, (3) a lightweight and fast approach. For this purpose, we designed a custom version of the random forest model, trained in an online fashion. It is implemented directly in Lean, which was possible thanks to the rich and efficient metaprogramming features of Lean 4. The random forest is trained on data extracted from – Lean’s mathematics library. We experiment with various options for producing training features and labels. The advice from a trained model is accessible to the user via the "Image missing" tactic which can be called in an editor while constructing a proof interactively.