Premise Selection and External Provers for HOL4

TL;DR

This paper introduces an extension to HOL4 that integrates machine learning-based premise selection and automated theorem proving, improving proof automation and dependency discovery in HOL4, similar to prior systems for other proof assistants.

Contribution

It presents the first machine learning-based premise selection system for HOL4, adapting HOLyHammer for HOL4 and demonstrating its effectiveness on the HOL4 standard library.

Findings

HOLyHammer achieves high-quality premise predictions for HOL4.

The system automatically finds proof dependencies reconstructible by Metis.

Performance is comparable to HOL Light experiments.

Abstract

Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that provides machine learning-based premise selection and automated reasoning also for HOL4. We efficiently record the HOL4 dependencies and extract features from the theorem statements, which form a basis for premise selection. HOLyHammer transforms the HOL4 statements in the various TPTP-ATP proof formats, which are then processed by the ATPs. We discuss the different evaluation settings: ATPs, accessible lemmas, and premise numbers. We measure the performance of HOLyHammer on the HOL4 standard library. The results are combined accordingly and compared with the HOL Light experiments, showing a comparably high quality of predictions. The system directly benefits HOL4 users by automatically finding proofs dependencies that can be reconstructed by Metis.