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UpSetDelayed
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UpSetDelayed

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lhs^:=rhs

assigns rhs to be the delayed value of lhs, and associates the assignment with symbols that occur at level one in lhs.

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

In[1]:=1
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https://wolfram.com/xid/0dqxv6ietc6-bdq3u3
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-lyc0lc
Out[2]=2

Scope  (6)Survey of the scope of standard use cases

Left-Hand Sides  (5)

An expression with a delayed definition is evaluated every time it is used:

In[1]:=1
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https://wolfram.com/xid/0dqxv6ietc6-bdp7ot
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-be8dyd
Out[2]=2

Make definitions for special and general cases using immediate and delayed assignments:

In[1]:=1
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https://wolfram.com/xid/0dqxv6ietc6-4yu8wt
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-5ntk8t
Out[2]=2

The definition can be associated with a symbol appearing as an argument of the left side:

In[1]:=1
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https://wolfram.com/xid/0dqxv6ietc6-i0zpn8
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-by8ow2
Out[2]=2

The definition can be associated with the head of an argument of the left side:

In[1]:=1
✖
https://wolfram.com/xid/0dqxv6ietc6-p6v3mu
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-bwq2ej
Out[2]=2

If several symbols appear in the left-hand side, upvalues for all of them are defined:

In[1]:=1
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https://wolfram.com/xid/0dqxv6ietc6-cwuh4
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-i5sj72
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0dqxv6ietc6-dmquby
Out[3]=3

Different Kinds of Values  (1)

^:= defines upvalues:

In[1]:=1
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https://wolfram.com/xid/0dqxv6ietc6-ctt9b
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-c9hw5g
Out[2]=2

Properties & Relations  (6)Properties of the function, and connections to other functions

^:= defines upvalues in the same way as using a tag does:

In[1]:=1
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https://wolfram.com/xid/0dqxv6ietc6-ms6j1w
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-cs759y
In[3]:=3
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https://wolfram.com/xid/0dqxv6ietc6-kyd9o
Out[3]=3

A tag defines only one upvalue; ^:= makes definitions for all symbols:

In[1]:=1
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https://wolfram.com/xid/0dqxv6ietc6-erdycr
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-b790ri
In[3]:=3
✖
https://wolfram.com/xid/0dqxv6ietc6-qy5gli
Out[3]=3

The right side of an immediate definition is evaluated when the definition is made:

In[1]:=1
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https://wolfram.com/xid/0dqxv6ietc6-hbiamo
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-l2tdph
Out[2]=2

The right side of a delayed definition is evaluated each time the definition is used:

In[3]:=3
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https://wolfram.com/xid/0dqxv6ietc6-b6q3iz
In[4]:=4
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https://wolfram.com/xid/0dqxv6ietc6-do5ctx
Out[4]=4

Definitions with the same left side overwrite earlier ones:

In[1]:=1
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https://wolfram.com/xid/0dqxv6ietc6-baac38
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-b0zrxa
In[3]:=3
✖
https://wolfram.com/xid/0dqxv6ietc6-jxrnrz
Out[3]=3

Definition prints definitions associated with a symbol:

In[1]:=1
✖
https://wolfram.com/xid/0dqxv6ietc6-xhhoz
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-ey6jfv
Out[2]=2

Information prints various information about a symbol, including any definitions:

In[3]:=3
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https://wolfram.com/xid/0dqxv6ietc6-cp0tko

UpValues returns a list of rules corresponding to any upvalues defined:

In[4]:=4
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https://wolfram.com/xid/0dqxv6ietc6-ezhwhw
Out[4]=4

Delayed assignment introduces a scope that is not affected by global variables:

In[1]:=1
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https://wolfram.com/xid/0dqxv6ietc6-lynxon
In[2]:=2
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https://wolfram.com/xid/0dqxv6ietc6-otatma
In[3]:=3
✖
https://wolfram.com/xid/0dqxv6ietc6-bj9a49
Out[3]=3

Immediate assignment does not introduce a scope:

In[4]:=4
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https://wolfram.com/xid/0dqxv6ietc6-t1bwvy
In[5]:=5
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https://wolfram.com/xid/0dqxv6ietc6-3f04oz
Out[5]=5
Wolfram Research (1988), UpSetDelayed, Wolfram Language function, https://reference.wolfram.com/language/ref/UpSetDelayed.html.
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Wolfram Research (1988), UpSetDelayed, Wolfram Language function, https://reference.wolfram.com/language/ref/UpSetDelayed.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_upsetdelayed, author="Wolfram Research", title="{UpSetDelayed}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/UpSetDelayed.html}", note=[Accessed: 04-May-2025 ]}

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@misc{reference.wolfram_2025_upsetdelayed, author="Wolfram Research", title="{UpSetDelayed}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/UpSetDelayed.html}", note=[Accessed: 04-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_upsetdelayed, organization={Wolfram Research}, title={UpSetDelayed}, year={1988}, url={https://reference.wolfram.com/language/ref/UpSetDelayed.html}, note=[Accessed: 04-May-2025 ]}

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@online{reference.wolfram_2025_upsetdelayed, organization={Wolfram Research}, title={UpSetDelayed}, year={1988}, url={https://reference.wolfram.com/language/ref/UpSetDelayed.html}, note=[Accessed: 04-May-2025 ]}