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.
The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits
2 Pith papers cite this work. Polarity classification is still indexing.
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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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2026 2representative citing papers
The sheaf condition on a design presheaf over an architectural site is equivalent to pairwise overlap compatibility and yields unique global designs from compatible local ones, with the equivalence machine-verified in Lean 4.
citing papers explorer
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Compositional Dynamics in Learning and Mechanics
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.
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Sheaves as a Means of Maintaining Consistency in Model-based Systems Engineering
The sheaf condition on a design presheaf over an architectural site is equivalent to pairwise overlap compatibility and yields unique global designs from compatible local ones, with the equivalence machine-verified in Lean 4.