Through

A list or sum of functions, called with the same arguments, distributed over head h.

Wolfram LanguageThrough↗

Through(head(f, g, …)(args…))head(f(args…), g(args…), …) for head = List or Add

Typed signatures

Type	Package	Applies
(any) -> any	combinatorics	always

Domain: Collections

Details

• Only the List and Add head forms are supported — Wolfram's fully general h(f, g)(x) = h(f(x), g(x)) for an arbitrary head h is not.
• compute-engine canonicalizes a call with a compound head ({f, g}(x)) to Apply(head, x), which Through reads directly — it stays lazy so it sees that form BEFORE Apply's own (eager) evaluate runs, which would otherwise try to call List/Add as a function and fail.

Examples

Basic #

live ↗

In$\mathrm{Through}(\bigl\lbrack f, g\bigr\rbrack\lhd x)$Out$\bigl\lbrack f(x), g(x)\bigr\rbrack$

Scope #

live ↗

In$\mathrm{Through}(f+g\lhd x)$Out$g(x)+f(x)$

About

Examples	2
Crosswalk	Wolfram Language

See also: MapThread, Apply