Experiences from Exporting Major Proof Assistant Libraries

Abstract

The interoperability of proof assistants and the integration of their libraries is a highly valued but elusive goal in the field of theorem proving. As a preparatory step, in previous work, we translated the libraries of multiple proof assistants, specifically the ones of Coq, HOL Light, IMPS, Isabelle, Mizar, and PVS into a universal format: OMDoc/MMT. Each translation presented great theoretical, technical, and social challenges, some universal and some system-specific, some solvable and some still open. In this paper, we survey these challenges and compare and evaluate the solutions we chose. We believe similar library translations will be an essential part of any future system interoperability solution, and our experiences will prove valuable to others undertaking such efforts.

Coq’s vibrant ecosystem for verification engineering (invited talk)

“…For example, when we ran our export 23 in early 2019, only around 70 of around 250 repositories could be built, including the MathComp libraries (the situation has improved since then)." [31].…”

“…The logical framework for verification should support this by allowing proofs about different components to be composed, and by allowing proofs about the same component at different levels of abstraction. As a practical matter, that means all the proofs should be conducted in the same implementation of the same logic-exporting nontrivial theorems from one logical framework to another is difficult to sustain at scale [31].…”

Reliably Reproducing Machine-Checked Proofs with the Coq Platform

“…In this context, the role of the Platform is not only to provide a convenient way to install Coq along with packages found on the Coq Package Index, but also to curate generally useful packages whose maintainers agree to the Platform's social contract. The coordination signals transmitted by Platform releases also help the Coq ecosystem catch up to new versions more quickly than previously, when few packages were compatible with a new Coq version following its release [17].…”

Making Isabelle Content Accessible in Knowledge Representation Formats

“…Mmt provides the semantics that ties together the three involved levels (logical framework, logic, and library) and provides a uniform high-level API for further processing. [KR20] gives on overview over the theoretical, technical, and social challenges of the OAF exports.…”