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Mathematics > Category Theory

arXiv:2404.02679 (math)
[Submitted on 3 Apr 2024]

Title:Rendering string diagrams recursively

Authors:Celia Rubio-Madrigal, Jules Hedges
View a PDF of the paper titled Rendering string diagrams recursively,
by Celia Rubio-Madrigal and Jules Hedges
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    Abstract:String diagrams are a graphical language used to
    represent processes that can be composed sequentially or in
    parallel, which correspond graphically to horizontal or vertical
    juxtaposition. In this paper we demonstrate how to compute the
    layout of a string diagram by folding over its algebraic
    representation in terms of sequential and parallel composition
    operators. The algebraic representation can be seen as a term of
    a free monoidal category or a proof tree for a small fragment of
    linear logic. This contrasts to existing non-compositional
    approaches that use graph layout techniques. The key innovation
    is storing the diagrams in binary space-partition trees,
    maintaining a right-trapezoidal shape for the diagram's outline
    as an invariant.
    We provide an implementation in Haskell, using an existing
    denotational graphics library called Diagrams. Our renderer also
    supports adding semantics to diagrams to serve as a compiler,
    with matrix algebra used as an example.

Subjects: Category Theory (math.CT); Computational Geometry (cs.CG)
Cite as:  arXiv:2404.02679 [math.CT]
          (or arXiv:2404.02679v1 [math.CT] for this version)
          https://doi.org/10.48550/arXiv.2404.02679
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Jules Hedges [view email]
[v1] Wed, 3 Apr 2024 12:22:24 UTC (621 KB)
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