Mixing HOL and Coq in Dedukti (Extended Abstract)

TL;DR

This paper presents a method to integrate HOL and Coq developments within Dedukti, enabling interoperability and combined proof capabilities, demonstrated through a sorting algorithm example.

Contribution

It introduces automated translation tools for HOL and Coq into Dedukti, facilitating their integration and combined proof construction.

Findings

Successful translation of HOL and Coq developments into Dedukti

Demonstration of combining proofs from different systems

Example of instantiating a Coq sorting algorithm with HOL natural numbers

Abstract

We use Dedukti as a logical framework for interoperability. We use automated tools to translate different developments made in HOL and in Coq to Dedukti, and we combine them to prove new results. We illustrate our approach with a concrete example where we instantiate a sorting algorithm written in Coq with the natural numbers of HOL.