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TreeMapAt
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TreeMapAt

Updated in 14[Experimental]

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TreeMapAt[f,tree,pos]

applies f to the data at the position specified by pos in tree.

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TreeMapAt[f,tree,{pos1,pos2,…}]

applies f to the data at several positions.

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TreeMapAt[f,pos]

represents an operator form of TreeMapAt that can be applied to a tree.

Details and Options

  • TreeMapAt applies a function to parts of the data at any position in a Tree object.
  • TreeMapAt[f,tree,{i,j,…}] applies the function f to the data at position {i,j,…}.
  • TreeMapAt can use the position specifications returned by TreePosition as well as extended forms as used in functions such as TreeInsert and TreeReplacePart. »
  • An individual position specification pos can be given as {part1,part2,…}, where part specifications parti include:
  • ithe i^(th) child
    -ithe i^(th) child from the end
    {i1,i2,…}the list of children with part numbers i1, i2, …
    Allall children
    m;;nchildren m through n
    "key"the child whose key is "key"
    Key[k]the child with an arbitrary key k
    TreeLevel[levelspec]the subtrees on levels specified by levelspec
    TreeCases[pattern]the subtrees with data matching pattern
    TreeSelect[crit]the subtrees for which crit gives True
  • In TreeMapAt[f,tree,{p1,p2,…}], {p1,p2,…} is interpreted as a list of individual position specifications if all the pi are lists. Otherwise, {p1,p2,…} will be taken to be an individual position specification. »
  • TreeMapAt works on trees containing an Association of subtrees, using the same specification for keys as in Part. »
  • TreeMapAt applies f repeatedly to a particular position if that position is mentioned more than once in the list of positions. »
  • TreeMapAt[f,pos][tree] is equivalent to TreeMapAt[f,tree,pos].
  • TreeMapAt has the same options as Tree.

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

Map f at the data of the second child of a tree:

In[2]:=2
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https://wolfram.com/xid/0n4ltygsyz8-55oin9
Out[2]=2

Map at any position:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-h1n0n1
Out[1]=1

Map at several positions:

In[2]:=2
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https://wolfram.com/xid/0n4ltygsyz8-hsh07
Out[2]=2

Use the operator form of TreeMapAt:

In[1]:=1
✖
https://wolfram.com/xid/0n4ltygsyz8-yn1603
Out[1]=1

Scope  (14)Survey of the scope of standard use cases

Part Specifications  (9)

Map at the third child:

In[2]:=2
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https://wolfram.com/xid/0n4ltygsyz8-4pz5ah
Out[2]=2

Map at the second child from the end:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-wnnn1z
Out[1]=1

Map at all children:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-5eqii1
Out[1]=1

Map at odd positions:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-087ui1
Out[1]=1

Use Key to specify position:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-gpohgs
Out[1]=1

For string keys, Key is not needed:

In[2]:=2
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https://wolfram.com/xid/0n4ltygsyz8-urimp2
Out[2]=2

Map on a range of levels:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-bovysl
Out[1]=1

Map at data matching a pattern:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-5hhn38
Out[1]=1

Map at subtrees with exactly two children:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-0ebjdg
Out[1]=1

Map using different specifications:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-8ffzed
Out[1]=1

Associations  (5)

Map onto a tree containing an association by key:

In[2]:=2
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https://wolfram.com/xid/0n4ltygsyz8-qn2p2g
Out[2]=2

If the key is a string, the Key wrapper is optional:

In[4]:=4
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https://wolfram.com/xid/0n4ltygsyz8-kbt6kw
Out[4]=4

Map onto a tree containing an association by key:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-6vaf4l
Out[1]=1

Map onto a tree containing an association by position:

In[2]:=2
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https://wolfram.com/xid/0n4ltygsyz8-snbzmi
Out[2]=2

Map at several subtrees of a tree containing an association:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-0bktbf
Out[1]=1

Map at a nested subtree of a tree containing an association:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-hhn55c
Out[1]=1

Map at several nested subtrees of a tree containing an association:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-npbjue
Out[1]=1

Properties & Relations  (8)Properties of the function, and connections to other functions

TreeMap[f,tree,levelspec] is equivalent to TreeMapAt[f,tree,TreeLevel[levelspec]]:

In[3]:=3
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https://wolfram.com/xid/0n4ltygsyz8-39l2x5
Out[3]=3

Construct a tree from the heads in an expression:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-etw6wf
Out[1]=1

TreeMapAt maps at the data of subtrees of a tree:

In[2]:=2
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https://wolfram.com/xid/0n4ltygsyz8-58qu1q
Out[2]=2

This corresponds to mapping at the heads and leaves in an expression:

In[3]:=3
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https://wolfram.com/xid/0n4ltygsyz8-6l8grk
Out[3]=3

MapAt can map at the heads and leaves directly:

In[4]:=4
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https://wolfram.com/xid/0n4ltygsyz8-ekzn6g
In[5]:=5
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https://wolfram.com/xid/0n4ltygsyz8-lzlujp
Out[5]=5

If pos is not a list, pos and {pos} are equivalent specifications:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-l4o1qg
In[2]:=2
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https://wolfram.com/xid/0n4ltygsyz8-c1li3w
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0n4ltygsyz8-ktswny
Out[3]=3

TreeMapAt[f,tree,{{i1,j1,…},{i2,j2,…},…}] is equivalent to …@TreeMapAt[f,{i2,j2,…}]@TreeMapAt[f,{i1,j1,…}]@tree:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-c64486
In[2]:=2
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https://wolfram.com/xid/0n4ltygsyz8-ehlm16
Out[2]=2

This extends to the empty list:

In[3]:=3
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https://wolfram.com/xid/0n4ltygsyz8-hd3wyw
Out[3]=3

Mapping at position {} applies the function to the data of the root node:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-wl3t8
Out[1]=1

TreeMapAt applies f repeatedly if a position is mentioned repeatedly:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-532gy
Out[1]=1

TreeMapAt can use the lists of positions returned by TreePosition:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-tspq6e
In[2]:=2
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https://wolfram.com/xid/0n4ltygsyz8-redf11
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0n4ltygsyz8-vu0873
Out[3]=3

This is the data returned by TreeExtract:

In[4]:=4
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https://wolfram.com/xid/0n4ltygsyz8-rumkf4
Out[4]=4

TreeMapAt[f,tree,{p1,p2,…}] treats {p1,p2,…} as a list of individual position specifications if all the pi are lists:

In[1]:=1
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https://wolfram.com/xid/0n4ltygsyz8-otyc2w

For {{1,2},{3,4}}, the data at positions {1,2} and {3,4} is modified:

In[2]:=2
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https://wolfram.com/xid/0n4ltygsyz8-rd9htt
Out[2]=2

If any pi is not a list, {p1,p2,…} is treated as a list of part specifications:

In[3]:=3
✖
https://wolfram.com/xid/0n4ltygsyz8-6pftch
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0n4ltygsyz8-5xamjx
Out[4]=4

For {{{1,2},{3,4}}}, parts 3 and 4 of parts 1 and 2 are modified:

In[5]:=5
✖
https://wolfram.com/xid/0n4ltygsyz8-1inecb
Out[5]=5

Possible Issues  (2)Common pitfalls and unexpected behavior

TreeMapAt[f,tree,{}] does not map f because the list of positions is empty:

In[2]:=2
✖
https://wolfram.com/xid/0n4ltygsyz8-sg9n6y
Out[2]=2

TreeMapAt[f,tree,{{}}] maps f at position {}, which corresponds to the root node:

In[4]:=4
✖
https://wolfram.com/xid/0n4ltygsyz8-fhig6f
Out[4]=4

A list of lists in the second argument is always interpreted as a list of position specifications:

In[1]:=1
✖
https://wolfram.com/xid/0n4ltygsyz8-ejwcun
In[2]:=2
✖
https://wolfram.com/xid/0n4ltygsyz8-pulhcd
Out[2]=2

As a result, specifications that are equivalent in Part may be treated differently by TreeMapAt:

In[3]:=3
✖
https://wolfram.com/xid/0n4ltygsyz8-hrlioq
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0n4ltygsyz8-dnpae4
Out[4]=4

Use a list of lists if consistency between Part and TreeMapAt is needed:

In[5]:=5
✖
https://wolfram.com/xid/0n4ltygsyz8-07ps0b
Out[5]=5
Wolfram Research (2021), TreeMapAt, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeMapAt.html (updated 2024).
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Wolfram Research (2021), TreeMapAt, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeMapAt.html (updated 2024).

Text

Wolfram Research (2021), TreeMapAt, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeMapAt.html (updated 2024).

✖
Wolfram Research (2021), TreeMapAt, Wolfram Language function, https://reference.wolfram.com/language/ref/TreeMapAt.html (updated 2024).

CMS

Wolfram Language. 2021. "TreeMapAt." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/TreeMapAt.html.

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Wolfram Language. 2021. "TreeMapAt." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/TreeMapAt.html.

APA

Wolfram Language. (2021). TreeMapAt. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TreeMapAt.html

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Wolfram Language. (2021). TreeMapAt. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TreeMapAt.html

BibTeX

@misc{reference.wolfram_2025_treemapat, author="Wolfram Research", title="{TreeMapAt}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/TreeMapAt.html}", note=[Accessed: 15-April-2025 ]}

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@misc{reference.wolfram_2025_treemapat, author="Wolfram Research", title="{TreeMapAt}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/TreeMapAt.html}", note=[Accessed: 15-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_treemapat, organization={Wolfram Research}, title={TreeMapAt}, year={2024}, url={https://reference.wolfram.com/language/ref/TreeMapAt.html}, note=[Accessed: 15-April-2025 ]}

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@online{reference.wolfram_2025_treemapat, organization={Wolfram Research}, title={TreeMapAt}, year={2024}, url={https://reference.wolfram.com/language/ref/TreeMapAt.html}, note=[Accessed: 15-April-2025 ]}