Sharing HOL4 and HOL Light proof knowledge

TL;DR

This paper explores methods for sharing proof knowledge between HOL4 and HOL Light proof assistants, enhancing proof automation by leveraging cross-library proof dependencies and characteristics, leading to improved proof success rates.

Contribution

It introduces and evaluates techniques for transferring proof knowledge between different provers, combining external learning with internal advice to improve proof automation.

Findings

HOL(y)Hammer can prove 30% of HOL Light problems autonomously.

Using HOL4 knowledge, HOL(y)Hammer improves to 40% proof success.

External knowledge sharing enhances proof automation effectiveness.

Abstract

New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In this paper we propose and evaluate a number of methods, which strengthen proof automation by learning from proof libraries of different provers. Certain conjectures can be proved directly from the dependencies induced by similar proofs in the other library. Even if exact correspondences are not found, learning-reasoning systems can make use of the association between proved theorems and their characteristics to predict the relevant premises. Such external help can be further combined with internal advice. We evaluate the proposed knowledge-sharing methods by reproving the HOL Light and HOL4 standard libraries. The learning-reasoning system HOL(y)Hammer, whose single best strategy could automatically find proofs for 30% of the HOL Light problems, can prove 40% with the knowledge from HOL4.