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

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arxiv 1305.0297 v1 pith:GSW3I6NK submitted 2013-05-01 cs.DB math.CTmath.LO

David I. Spivak This is my paper · ORCID
classification cs.DBmath.CTmath.LO
keywords diagramswiringcircuitsdatabasesgraphicallanguageoperadplug-and-play
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Compositional Dynamics in Learning and Mechanics

    math.CT 2026-06 unverdicted novelty 7.0 of 10

    An operad Arr supplies a single compositional syntax whose two functorial semantics in polynomial coalgebras recover both gradient-based learning and Hamiltonian-style mechanics on wired systems.

  2. Double-functorial representation of regular hyperdoctrines

    math.CT 2025-08 unverdicted novelty 6.0 of 10

    Regular hyperdoctrines are equivalently described as lax symmetric monoidal pseudo double functors from spans to quintets whose monoidal laxators provide companion commuter cells.

  3. Intent Preserving Generation of Diverse and Idiomatic (Code-)Artifacts

    cs.SE 2025-08 conditional novelty 6.0 of 10

    A single abstract data-flow diagram of small typed building blocks serves as the common source from which diverse idiomatic Haskell programs, IO-behavior specifications, and natural-language task descriptions are gene...

  4. Generalised Process Theories

    math.CT 2025-02 conditional novelty 6.0 of 10

    A generalised process theory is an algebra for a wiring operad, subsuming traditional, time-neutral, causal, higher-order, and enriched process theories.

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