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

@article{Spivak2013TheOO, title={The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits}, author={David I. Spivak}, journal={ArXiv}, year={2013}, volume={abs/1305.0297} }

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…

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