Map

The collection where each element has been transformed by $f$; with several collections, combines them element-wise (like zip), to the length of the shortest.

✓ checked against that system · ! checked, with disagreements (hover a chip)Fungrim entryWolfram LanguageMap!↗

Map(f, xs)$[f(x_1), f(x_2), \ldots]$ — $f$ applied to each element of $xs$.

Map(f, xs, ys, …)combines several collections element-wise (like zip), to the length of the shortest — $[f(x_1, y_1), f(x_2, y_2), \ldots]$.

Map(f)the operator form, $\mathrm{Map}(f)(xs) = \mathrm{Map}(f, xs)$.

Typed signatures

Type	Package	Applies
(any) -> any	combinatoricsreplaces compute-engine	always
(mapping: (T) any -> U, collection<T>+) -> indexed_collection where T, U	compute-engine	always

Domain: Collections

Details

• The mapping function is always the first argument, opposite Fold/Scan.
• With one collection, equivalent to [f(x) for x in xs]; with several, zipWith.

Examples

Basic #

Map Square over $[1,2,3,4]$

live ↗

In$\mathrm{Map}(\mathrm{Square}, \bigl\lbrack1, 2, 3, 4\bigr\rbrack)$Out$\bigl\lbrack1, 4, 9, 16\bigr\rbrack$

Map a lambda adding 1 to each element

live ↗

In$\mathrm{Map}(()↦\operatorname{\_}+1, \bigl\lbrack1, 2, 3\bigr\rbrack)$Out$\bigl\lbrack2, 3, 4\bigr\rbrack$

Map Add over two collections zips them

live ↗

In$\mathrm{Map}(\mathrm{Add}, \bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack10, 20, 30\bigr\rbrack)$Out$\bigl\lbrack11, 22, 33\bigr\rbrack$

Map a pure function over a list

live ↗

In$\mathrm{Map}(x↦x^2, \bigl\lbrack1, 2, 3, 4\bigr\rbrack)$Out$\bigl\lbrack1, 4, 9, 16\bigr\rbrack$

live ↗

In$\mathrm{Map}(f, \bigl\lbrack a, b, c, d, k\bigr\rbrack)$Out$\bigl\lbrack f(a), f(b), f(c), f(d), f(k)\bigr\rbrack$

live ↗

In$\mathrm{Map}(f, \bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d, k\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack f(\bigl\lbrack a, b\bigr\rbrack), f(\bigl\lbrack c, d, k\bigr\rbrack)\bigr\rbrack$

live ↗

In$\mathrm{Map}(f, \bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d, k\bigr\rbrack\bigr\rbrack, \bigl\lbrack2\bigr\rbrack)$Out$\bigl\lbrack f(\bigl\lbrack a, b\bigr\rbrack, 2)\bigr\rbrack$

live ↗

In$\mathrm{Map}(f)\lhd\bigl\lbrack a, b, c, d\bigr\rbrack$Out$\bigl\lbrack f(a), f(b), f(c), f(d)\bigr\rbrack$

Scope #

Maps only the first level, so deeper nesting is left intact

live ↗

In$\mathrm{Map}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack f(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack)\bigr\rbrack$

A symbolic head wraps each element

live ↗

In$\mathrm{Map}(f, \bigl\lbrack a, b, c\bigr\rbrack)$Out$\bigl\lbrack f(a), f(b), f(c)\bigr\rbrack$

Extra lists supply further arguments, giving $f(x, 2)$ on the single element

live ↗

In$\mathrm{Map}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack2\bigr\rbrack)$Out$\bigl\lbrack f(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, 2)\bigr\rbrack$

live ↗

In$\mathrm{Map}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack0, 2\bigr\rbrack)$Out$\bigl\lbrack f(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, 0)\bigr\rbrack$

live ↗

In$\mathrm{Map}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack0, ∞\bigr\rbrack)$Out$\bigl\lbrack f(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, 0)\bigr\rbrack$

live ↗

In$\mathrm{Map}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack2, -3\bigr\rbrack)$Out$\bigl\lbrack f(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, 2)\bigr\rbrack$

Applications #

live ↗

In$\mathrm{Map}(\operatorname{\_1}↦\operatorname{\_1}+\bigl\lbrack x, y\bigr\rbrack, \bigl\lbrack\bigl\lbrack1, 1\bigr\rbrack, \bigl\lbrack2, 2\bigr\rbrack, \bigl\lbrack3, 3\bigr\rbrack, \bigl\lbrack4, 4\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack x+1, y+1\bigr\rbrack, \bigl\lbrack x+2, y+2\bigr\rbrack, \bigl\lbrack x+3, y+3\bigr\rbrack, \bigl\lbrack x+4, y+4\bigr\rbrack\bigr\rbrack$

live ↗

In$\mathrm{Map}(\mathrm{Reverse}, \bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d\bigr\rbrack, \bigl\lbrack k, f\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack b, a\bigr\rbrack, \bigl\lbrack d, c\bigr\rbrack, \bigl\lbrack f, k\bigr\rbrack\bigr\rbrack$

Properties #

Mapping over an empty collection returns empty

live ↗

In$\mathrm{Map}(\mathrm{Square}, \bigl\lbrack\bigr\rbrack)$Out$\bigl\lbrack\bigr\rbrack$

An exact square root stays exact where possible

live ↗

In$\mathrm{Map}(\mathrm{Sqrt}, \bigl\lbrack1, 2, 3, 4\bigr\rbrack)$Out$\bigl\lbrack1, \sqrt{2}, \sqrt{3}, 2\bigr\rbrack$

Symbolic elements are wrapped, not evaluated

live ↗

In$\mathrm{Map}(f, \bigl\lbrack x, y, z\bigr\rbrack)$Out$\bigl\lbrack f(x), f(y), f(z)\bigr\rbrack$

live ↗

In$\mathrm{Map}(f, \bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c\bigr\rbrack, \bigl\lbrack\bigl\lbrack d\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack0, ∞\bigr\rbrack)$Out$\bigl\lbrack f(\bigl\lbrack a, b\bigr\rbrack, 0), f(\bigl\lbrack c\bigr\rbrack, ∞)\bigr\rbrack$

About

Examples	20
Checked against	Wolfram Language 13 agree5 differmathlib4 2 agree
Crosswalk	Fungrim entry ×18Wolfram Language

Implementation

mappedmathlib4packages/oracle/src/mappings.ts

One list, the function applied to each element as a ℚ (a ℕ or ℤ where its body needs one). A function whose body has no mathlib4 binding, or a list of another element type, is not emitted.

See also: Tabulate, Fold, Filter