Logipedia: a multi-system encyclopedia of formal proofs

TL;DR

Logipedia aims to create a multi-system online encyclopedia of formal proofs using a standard language, enhancing usability and sustainability across different proof systems by leveraging logical frameworks and reverse mathematics.

Contribution

It introduces a multi-system proof encyclopedia based on a standard language, addressing interoperability and preservation issues in formal proof libraries.

Findings

Proofs can be translated across systems using the standard language.

Logipedia enhances proof library usability and longevity.

The approach leverages logical frameworks and reverse mathematics.

Abstract

Libraries of formal proofs are an important part of our mathematical heritage, but their usability and sustainability is poor. Indeed, each library is specific to a proof system, sometimes even to some version of this system. Thus, a library developed in one system cannot, in general, be used in another and when the system is no more maintained, the library may be lost. This impossibility of using a proof developed in one system in another has been noted for long and a remediation has been proposed: as we have empirical evidence that most of the formal proofs developed in one of these systems can also be developed in another, we can develop a standard language, in which these proofs can be translated, and then used in all systems supporting this standard. Logipedia is an attempt to build such a multi-system online encyclopedia of formal proofs expressed in such as standard language. It is based on two main ideas: the use of a logical framework and of reverse mathematics.