Proof Recommendation System for the HOL4 Theorem Prover

TL;DR

This paper presents a transformer-based proof recommender system tailored for HOL4, which predicts the next proof steps by analyzing proof patterns from extensive theorem libraries, aiding proof development.

Contribution

It introduces a novel proof recommendation tool for HOL4 leveraging transformer models trained on large proof libraries, enhancing proof assistance capabilities.

Findings

High accuracy in predicting next proof steps

Effective integration with HOL4 proof workflows

Improved proof development efficiency

Abstract

We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns from extensive libraries of HOL4 containing proofs of theorems. Consequently, it can accurately predict the next tactic(s) (proof step(s)) based on the history of previously employed tactics. The tool operates by reading a given sequence of tactics already used in a proof process (in our case, it contains at least three tactics), referred to as the current proof state, and provides recommendations for the next optimal proof step(s).