Matching concepts across HOL libraries

TL;DR

This paper presents an approach for automatically matching similar mathematical concepts across different proof assistant libraries by normalizing properties and applying similarity measures, successfully identifying numerous equivalent concepts.

Contribution

It introduces a normalization and similarity-based method for discovering equivalent concepts across HOL proof assistant libraries, addressing a non-trivial problem.

Findings

Discovered 398 pairs of isomorphic constants and types across HOL libraries.

Effective normalization and similarity measures facilitate concept matching.

Method works well for advanced concepts beyond basic mathematical objects.

Abstract

Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the basic concepts, like natural numbers, matching them between libraries is often straightforward, because of mathematical naming conventions. However, for more advanced concepts, finding similar formalizations in different libraries is a non-trivial task even for an expert. In this paper we investigate automatic discovery of similar concepts across libraries of proof assistants. We propose an approach for normalizing properties of concepts in formal libraries and a number of similarity measures. We evaluate the approach on HOL based proof assistants HOL4, HOL Light and Isabelle/HOL, discovering 398 pairs of isomorphic constants and types.