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MapAll[f,expr]

or f//@expr applies f to every subexpression in expr.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Heads  
Applications  
Properties & Relations  
See Also
Tech Notes
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History
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MapAll

MapAll[f,expr]

or f//@expr applies f to every subexpression in expr.

Details and Options

  • MapAll[f,expr] is equivalent to Map[f,expr,{0,Infinity}].
  • MapAll[f,expr,Heads->True] applies f to heads in expr, and their parts.
  • If expr is an Association object, MapAll[f,expr] applies f only to the values in the association. »
  • If expr is a SparseArray object or structured array, MapAll[f,expr] applies f to the values or subarrays just as it would on the corresponding ordinary list. »

Examples

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Basic Examples  (2)

Apply f to every subpart of an expression:

Wolfram Language code: MapAll[f, {{a, b}, {c}, {{d}}}]

Alternative input form:

Wolfram Language code: f //@ {{a, b}, {c}, {{d}}}

Apply h to every value in associations:

Wolfram Language code: MapAll[h, <|a -> <|b -> c|>, d -> {<|e -> f|>}|>]

Scope  (4)

MapAll can be used on expressions with any head:

Wolfram Language code: MapAll[f, a + b + c + d]
Wolfram Language code: MapAll[f, x ^ 2 + y ^ 2]

The function can be mapped onto the heads as well:

Wolfram Language code: MapAll[f, {a, b, c}, Heads -> True]

MapAll can be used on sparse arrays:

Wolfram Language code: SparseArray[{1 -> 1, 3 -> 3}]
Wolfram Language code: MapAll[f, %]

Use MapAll with structured arrays, such as SymmetrizedArray:

Wolfram Language code: SymmetrizedArray[{{1, 2} -> 1, {1, 3} -> 2, {2, 3} -> 3}, {3, 3}, Antisymmetric[All]]
Wolfram Language code: f //@ %

Options  (1)

Heads  (1)

Apply f to heads as well as ordinary parts of expressions:

Wolfram Language code: MapAll[f, {a, b}, Heads -> True]
Wolfram Language code: MapAll[f, {a, b}]

Applications  (1)

Show nesting structure of an expression:

Wolfram Language code: Integrate[1 / (x ^ 3 - 1), x]
Wolfram Language code: Framed //@ %

Properties & Relations  (2)

MapAll is equivalent to a specific level specification in Map:

Wolfram Language code: Map[f, {{a, b}, {c}, {{d}}}, {0, ∞}]
Wolfram Language code: MapAll[f, {{a, b}, {c}, {{d}}}]

MapAll maps also around the whole expression; Map[f,expr,∞] does not:

Wolfram Language code: MapAll[f, {{a, b}, {c, d}}]
Wolfram Language code: Map[f, {{a, b}, {c, d}}, ∞]
Wolfram Research (1988), MapAll, Wolfram Language function, https://reference.wolfram.com/language/ref/MapAll.html.

Text

Wolfram Research (1988), MapAll, Wolfram Language function, https://reference.wolfram.com/language/ref/MapAll.html.

CMS

Wolfram Language. 1988. "MapAll." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MapAll.html.

APA

Wolfram Language. (1988). MapAll. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MapAll.html

BibTeX

@misc{reference.wolfram_2026_mapall, author="Wolfram Research", title="{MapAll}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/MapAll.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_mapall, organization={Wolfram Research}, title={MapAll}, year={1988}, url={https://reference.wolfram.com/language/ref/MapAll.html}, note=[Accessed: 12-June-2026]}