Foundations of brick diagrams

TL;DR

This paper explores the theoretical foundations of 2D graphical languages like string diagrams and pasting diagrams, introduces 'brick diagrams' for visual programming, and discusses their implementation and relationships with other structures.

Contribution

It introduces 'brick diagrams' as a new variant of cubical pasting diagrams and reviews their role in graphical languages and computer implementation.

Findings

Brick diagrams relate to string diagrams and pasting diagrams.

The paper discusses the implementation of these diagrams in a visual programming language.

Provides a literature review on the foundations of 2D graphical languages.

Abstract

We discuss the foundations of 2-dimensional graphical languages, with a view towards their computer implementation in a 'compiler' for monoidal categories. In particular, we discuss the close relationship between string diagrams, pasting diagrams, linear logic proof trees and k-d trees, the last being a data structure from computational geometry and computer graphics that recursively partitions a space. We introduce a minor variant of cubical pasting diagrams, which we call 'brick diagrams', which are used in the Statebox visual programming language. This paper is intended as a discussion and literature review, and contains little mathematics.