The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits

David I. Spivak

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arXiv · 1305.0297

The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits

David I. Spivak

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Abstract

Wiring diagrams, as seen in digital circuits, can be nested hierarchically and thus have an aspect of self-similarity. We show that wiring diagrams form the morphisms of an operad $\mcT$, capturing this self-similarity. We discuss the algebra $\Rel$ of mathematical relations on $\mcT$, and in so doing use wiring diagrams as a graphical language with which to structure queries on relational databases. We give the example of circuit diagrams as a special case. We move on to show how plug-and-play devices and also recursion can be formulated in the operadic framework as well. Throughout we include many examples and figures.

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David I. Spivak. 2013-05-01. The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits. https://arxiv.org/abs/1305.0297

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