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ComapApply
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ComapApply

New in 14[Experimental]

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ComapApply[{f1,f2,…},expr]

gives {Apply[f1,expr],Apply[f2,expr],…}.

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represents an operator form of ComapApply that can be applied to an expression.

Details and Options

Examples

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

Replace the head of {1,2} with each element of a list:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-bcjear
Out[1]=1

Use the operator form of ComapApply:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-nbstpo
Out[1]=1

Replace the head of an expression with the values in an association:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-odj9lh
Out[1]=1

Scope  (3)Survey of the scope of standard use cases

Use explicit pure functions:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-b177zc
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqug9da8n4-jt6vyg
Out[2]=2

ComapApply can be used on expressions with any head:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-g2btx8
Out[1]=1

Replace the head of an expression with the values of an Association:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-zq92pg
Out[1]=1

Options  (1)Common values & functionality for each option

Heads  (1)

Apply inside the head as well as arguments:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-nz677s
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqug9da8n4-laj3a
Out[2]=2

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

ComapApply successively replaces the head of an expression with the parts of another expression:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-qiju27
Out[1]=1

MapApply replaces the head of each part of an expression with another expression:

In[2]:=2
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https://wolfram.com/xid/0dqug9da8n4-sin1b
Out[2]=2

Through[p[f,g,…][x,y,…]] is equivalent to ComapApply[p[f,g,…],{x,y,…}]:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-lsocle
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqug9da8n4-pzt1zm
Out[2]=2

Compare this to the operator form of ComapApply:

In[3]:=3
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https://wolfram.com/xid/0dqug9da8n4-0rxctr
Out[3]=3

ComapApply[p[f,g,…],{x,y,…}] can be used even when p[f,g,…][x,y,…] has a value:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-dsppnj
Out[1]=1

When p[f,g,…][x,y,…] has a value, Through cannot be used:

In[2]:=2
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https://wolfram.com/xid/0dqug9da8n4-zz3f9i
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0dqug9da8n4-rkkly9
Out[3]=3

ComapApply[{f1,f2,…},expr] is equivalent to Map[f|->Apply[f,expr],{f1,f2,…}] when the fi have no attributes:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-locw8i
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dqug9da8n4-zkb3ce
Out[2]=2

ComapApply can replace the head of an expression with parts inside held expressions without allowing evaluation to proceed:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-nvkef8
Out[1]=1

Use ReleaseHold to allow evaluation to proceed:

In[2]:=2
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https://wolfram.com/xid/0dqug9da8n4-pywof2
Out[2]=2

If only some arguments are held, only those arguments will not evaluate further:

In[3]:=3
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https://wolfram.com/xid/0dqug9da8n4-yo0lq2
In[4]:=4
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https://wolfram.com/xid/0dqug9da8n4-u1l366
Out[4]=4

Use Unevaluated to replace the head of an expression with different expressions without evaluating it first:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-lp8w4v
Out[1]=1

The expression is evaluated first by default:

In[2]:=2
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https://wolfram.com/xid/0dqug9da8n4-emed18
Out[2]=2

Use Unevaluated to replace the head of an expression with the parts of an expression without evaluating it first:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-n5e5cs
Out[1]=1

The expression is evaluated first by default:

In[2]:=2
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https://wolfram.com/xid/0dqug9da8n4-2cdpsw
Out[2]=2

ComapApply can be parallelized automatically:

In[1]:=1
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https://wolfram.com/xid/0dqug9da8n4-jjasnc
Out[1]=1
Wolfram Research (2024), ComapApply, Wolfram Language function, https://reference.wolfram.com/language/ref/ComapApply.html.
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Wolfram Research (2024), ComapApply, Wolfram Language function, https://reference.wolfram.com/language/ref/ComapApply.html.

Text

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

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

CMS

Wolfram Language. 2024. "ComapApply." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ComapApply.html.

✖
Wolfram Language. 2024. "ComapApply." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ComapApply.html.

APA

Wolfram Language. (2024). ComapApply. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComapApply.html

✖
Wolfram Language. (2024). ComapApply. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComapApply.html

BibTeX

@misc{reference.wolfram_2025_comapapply, author="Wolfram Research", title="{ComapApply}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/ComapApply.html}", note=[Accessed: 09-July-2025 ]}

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@misc{reference.wolfram_2025_comapapply, author="Wolfram Research", title="{ComapApply}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/ComapApply.html}", note=[Accessed: 09-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_comapapply, organization={Wolfram Research}, title={ComapApply}, year={2024}, url={https://reference.wolfram.com/language/ref/ComapApply.html}, note=[Accessed: 09-July-2025 ]}

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@online{reference.wolfram_2025_comapapply, organization={Wolfram Research}, title={ComapApply}, year={2024}, url={https://reference.wolfram.com/language/ref/ComapApply.html}, note=[Accessed: 09-July-2025 ]}