English

Foundations of brick diagrams

Category Theory 2019-08-29 v1

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.

Keywords

Cite

@article{arxiv.1908.10660,
  title  = {Foundations of brick diagrams},
  author = {Jules Hedges and Jelle Herold},
  journal= {arXiv preprint arXiv:1908.10660},
  year   = {2019}
}
R2 v1 2026-06-23T10:58:52.887Z