Sharing a Library between Proof Assistants: Reaching out to the HOL Family

TL;DR

This paper develops a translation from the STTforall logic in Dedukti to OpenTheory, enabling sharing of libraries like Fermat's little theorem across proof assistants in the HOL family and beyond.

Contribution

It introduces a translation method that facilitates interoperability between different proof systems, allowing library sharing across diverse theorem provers.

Findings

Successfully exported Fermat's little theorem to multiple proof systems

Enabled sharing of arithmetic libraries across proof assistants

Demonstrated interoperability between Dedukti and OpenTheory

Abstract

We observe today a large diversity of proof systems. This diversity has the negative consequence that a lot of theorems are proved many times. Unlike programming languages, it is difficult for these systems to co-operate because they do not implement the same logic. Logical frameworks are a class of theorem provers that overcome this issue by their capacity of implementing various logics. In this work, we study the STTforall logic, an extension of Simple Type Theory that has been encoded in the logical framework Dedukti. We present a translation from this logic to OpenTheory, a proof system and interoperability tool between provers of the HOL family. We have used this translation to export an arithmetic library containing Fermat's little theorem to OpenTheory and to two other proof systems that are Coq and Matita.