Wiring Diagram – Build a Wall & Roof (SMC / Operad View)

Hover a wire to highlight one named object (type) flowing through the composition; click a type in the sidebar to pin the highlight. Colours are a visual aid; exact compatibility depends on port types and interfaces, not a shared colour or resource family.

Semantics & Checks

Selection

None — hover a wire or click a type.

Meaning

You’re seeing one typed wire (object) traced across the composite.

Validity

Acyclic by construction (no feedback loops; progress is left→right).

Diagnostics

Running…

Quick intuition

Treat each box as a morphism in a strict symmetric monoidal category of construction resources; “labour” and “design” are explicit wires so you can see where reuse/hand‑off happens.

Wire types (objects)

Click a type to highlight its path; click again to unpin.

Processes (boxes / morphisms)

“Under certain conditions…”

A pragmatic move is to model each process as a guarded morphism (precondition + postcondition/acceptance). These lists suggest obligations to formalise; this page does not implement a general calculus for propagating preconditions or proving that downstream requirements follow.

This is the project‑manager translation of the categorical “contract algebra” trick: boxes are still morphisms, but you attach a predicate to each interface and compose predicates along the wiring diagram.

Signature

Choose a set τ of wire types and an object for each type in an SMC. In the selected typed, acyclic wiring syntax, an interface is an ordered input/output pair; its algebra carrier is the corresponding hom-set. Diagrams act by tensor, composition, identities and symmetry. This specifies an interpretation under those choices, not a blanket equivalence with every operad algebra.

Objects

Boxes

Composite boundary signature

This is the outer input/output signature, not a fully written composition term. It preserves this earlier model's omitted peg-kit return; consult the current resource essay for the complete returned-resource boundary.

Laws used implicitly

Strictness: no bracketing in ⊗; units suppressed.
Interchange: (f∘g)⊗(h∘k) = (f⊗h)∘(g⊗k).
Progress / acyclicity: the induced “feeds‑into” relation on boxes is a partial order.

Reference anchor: Patterson–Spivak–Vagner, Wiring diagrams as normal forms for computing in symmetric monoidal categories (ACT 2020 proceedings, EPTCS 333, 2021).