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HoldForm
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HoldForm

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HoldForm[expr]

prints as the expression expr, with expr maintained in an unevaluated form.

Details

  • HoldForm allows you to see the output form of an expression without performing normal evaluation of the expression.
  • HoldForm has attribute HoldAll and performs no operation on its arguments.
  • HoldForm is removed by ReleaseHold. »
  • HoldForm is generated by default by Trace and related functions and can be inserted as a wrapper by such functions as ToExpression and Extract. »
  • Even though expr itself is not evaluated, HoldForm[expr] may still evaluate if expr is of the form f[args] and upvalues for f have been defined. »

Examples

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

Addition in held form:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-gehmya
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Out[1]=1

An unevaluated assignment:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-hin9jx
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Out[1]=1

An unevaluated power:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-bqu14
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Out[1]=1

Evaluate the expression by applying ReleaseHold:

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In[2]:=2
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https://wolfram.com/xid/0e7rn70q-d8u38
Direct link to example
Out[2]=2

Scope  (2)Survey of the scope of standard use cases

Display a sum of squares in unevaluated form:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-ewvasf
Direct link to example
Out[1]=1

View the unevaluated form of an extracted part:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-gzoe32
Direct link to example
Out[1]=1

Applications  (1)Sample problems that can be solved with this function

Show a formula and its evaluation:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-6ee4x6
Direct link to example
Out[1]=1

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

HoldForm displays without a wrapper:

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In[4]:=4
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https://wolfram.com/xid/0e7rn70q-cx2bwj
Direct link to example
Out[4]=4

See the FullForm expression:

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In[5]:=5
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https://wolfram.com/xid/0e7rn70q-b2rdw6
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Hold displays the held expression with a wrapper:

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In[3]:=3
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https://wolfram.com/xid/0e7rn70q-mvpsfg
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Out[3]=3

Use Evaluate to force evaluation of an argument of HoldForm:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-1f6029
Direct link to example
Out[1]=1

Sequence splicing and Splice still happen inside HoldForm:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-tvflnf
Direct link to example
Out[1]=1
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In[2]:=2
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https://wolfram.com/xid/0e7rn70q-37l8jn
Direct link to example
Out[2]=2

Use HoldCompleteForm to suppress even such transformations:

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In[3]:=3
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https://wolfram.com/xid/0e7rn70q-13c8km
Direct link to example
Out[3]=3
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In[4]:=4
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https://wolfram.com/xid/0e7rn70q-hjywh7
Direct link to example
Out[4]=4

Upvalues work inside HoldForm:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-h3hq1f
Direct link to example
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In[2]:=2
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https://wolfram.com/xid/0e7rn70q-iqgm7p
Direct link to example
Out[2]=2

They do not work inside HoldCompleteForm:

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In[3]:=3
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https://wolfram.com/xid/0e7rn70q-x7zf8f
Direct link to example
Copy to clipboard.
In[4]:=4
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https://wolfram.com/xid/0e7rn70q-deuaum
Direct link to example
Out[4]=4

ReleaseHold removes one level of HoldForm:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-8eioml
Direct link to example
Out[1]=1

HoldForm gives an object that is never evaluated:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-fz4q9x
Direct link to example
Out[1]=1

Copy the output and paste it into an input cell. The 1+2 is still unevaluated:

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In[2]:=2
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https://wolfram.com/xid/0e7rn70q-yfbnlk
Direct link to example
Out[2]=2

Defer gives an object whose evaluation is merely deferred until it is explicitly given as Wolfram Language input:

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In[3]:=3
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https://wolfram.com/xid/0e7rn70q-89d539
Direct link to example
Out[3]=3

Copy the output and paste it into an input cell. The 1+2 is evaluated:

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In[4]:=4
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https://wolfram.com/xid/0e7rn70q-kvbktt
Direct link to example
Out[4]=4

HoldForm maintains expressions in unevaluated form, and all parts are inactive:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-msg88u
Direct link to example
Out[1]=1

Inactivate maintains symbols in inactive form and allows parts of expressions to be inactive:

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In[2]:=2
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https://wolfram.com/xid/0e7rn70q-60zrj6
Direct link to example
Out[2]=2

HoldForm can be used to freeze the result of ToExpression before it is evaluated:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-gwv81u
Direct link to example
Out[1]=1

Possible Issues  (1)Common pitfalls and unexpected behavior

HoldPattern[expr] is equivalent to expr for pattern matching but maintains expr in an unevaluated form:

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In[1]:=1
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https://wolfram.com/xid/0e7rn70q-h09mjp
Direct link to example
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In[9]:=9
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https://wolfram.com/xid/0e7rn70q-iwiq6c
Direct link to example
Out[9]=9

HoldForm[expr] is not equivalent to expr for pattern matching:

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In[3]:=3
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https://wolfram.com/xid/0e7rn70q-4xf38h
Direct link to example
Copy to clipboard.
In[10]:=10
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https://wolfram.com/xid/0e7rn70q-f3zfis
Direct link to example
Out[10]=10

Only a literal HoldForm expression is matched:

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In[11]:=11
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https://wolfram.com/xid/0e7rn70q-5yfzhj
Direct link to example
Out[11]=11
Wolfram Research (1988), HoldForm, Wolfram Language function, https://reference.wolfram.com/language/ref/HoldForm.html.
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Wolfram Research (1988), HoldForm, Wolfram Language function, https://reference.wolfram.com/language/ref/HoldForm.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_holdform, author="Wolfram Research", title="{HoldForm}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/HoldForm.html}", note=[Accessed: 04-April-2025 ]}

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@misc{reference.wolfram_2025_holdform, author="Wolfram Research", title="{HoldForm}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/HoldForm.html}", note=[Accessed: 04-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_holdform, organization={Wolfram Research}, title={HoldForm}, year={1988}, url={https://reference.wolfram.com/language/ref/HoldForm.html}, note=[Accessed: 04-April-2025 ]}

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@online{reference.wolfram_2025_holdform, organization={Wolfram Research}, title={HoldForm}, year={1988}, url={https://reference.wolfram.com/language/ref/HoldForm.html}, note=[Accessed: 04-April-2025 ]}