A Graphical Interface for Category Theory Proofs in Coq

TL;DR

This paper introduces a Coq plugin that provides a graphical interface for category theory proofs, aiming to make abstract concepts more accessible through visualization and interaction within the proof assistant.

Contribution

It presents the first implementation of a graphical interface for categorical proofs integrated into Coq, enhancing understanding and interaction.

Findings

Enabled visualization of categorical proofs in Coq

Facilitated interactive diagrammatic reasoning

Improved accessibility of abstract category theory concepts

Abstract

The importance of category theory in recent developments in both mathematics and in computer science cannot be overstated. However, its abstract nature makes it difficult to understand at first. Graphical languages have been developed to help manage this abstraction, but they have not been used in proof assistants, most of which are text-based. We believe that a graphical interface for categorical proofs integrated in a generic proof assistant would allow students to familiarize themselves with diagrammatic reasoning on concrete proofs that they are already familiar with. We present an implementation of a Coq plugin that enables both visualization and interactions with Coq proofs in a graphical manner.