WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

UpValues
✖
UpValues

✖

gives a list of transformation rules corresponding to all upvalues (values for g[…,f[…],…]) defined for the symbol f.

✖
UpValues["symbol"]

gives a list of transformation rules corresponding to all upvalues defined for the symbol named "symbol" if it exists.

Details and Options

  • UpValues[f] also gives rules corresponding to g[…,f,…].
  • When evaluating an expression, matching upvalues are applied before matching downvalues. »
  • If a function has attribute HoldAllComplete, no upvalues are applied prior to entering the body of the function. »
  • UpValues are typically defined using UpSet, UpSetDelayed, TagSet or TagSetDelayed.
  • You can specify the upvalues for f by making an assignment of the form UpValues[f]=list.
  • The list returned by UpValues has elements of the form HoldPattern[lhs]:>rhs.

Examples

open allclose all

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

Define an upvalue for a symbol g using TagSetDelayed:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-g7dmym

Define an upvalue using UpSetDelayed:

In[2]:=2
✖
https://wolfram.com/xid/0binok32-x05u6n

These are the upvalues associated with g:

In[3]:=3
✖
https://wolfram.com/xid/0binok32-cfxz30
Out[3]=3

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

UpValues returns rules corresponding to upvalues defined for a symbol:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-ej5l4f
In[2]:=2
✖
https://wolfram.com/xid/0binok32-hwcsbv
Out[2]=2

Create several values:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-vbp451

Obtain the upvalues of symbols whose names start with x:

In[2]:=2
✖
https://wolfram.com/xid/0binok32-qemtic
Out[2]=2

UpValues can be used to set the values directly:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-fnyunm
In[2]:=2
✖
https://wolfram.com/xid/0binok32-o1jvud
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0binok32-fi993w
Out[3]=3

Applications  (2)Sample problems that can be solved with this function

The resulting rules are in the order given:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-x0ymvo
In[3]:=3
✖
https://wolfram.com/xid/0binok32-c7zzt7
Out[3]=3
In[5]:=5
✖
https://wolfram.com/xid/0binok32-lcusj6
Out[5]=5

Now reorder the definitions:

In[6]:=6
✖
https://wolfram.com/xid/0binok32-mejklw
Out[6]=6
In[7]:=7
✖
https://wolfram.com/xid/0binok32-d5hgcx
Out[7]=7

Copy a symbol's definitions to another symbol:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-vlfjkm
In[2]:=2
✖
https://wolfram.com/xid/0binok32-3qya6g
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0binok32-s3n84l
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0binok32-61ai2p
Out[4]=4

Properties & Relations  (7)Properties of the function, and connections to other functions

Values can be defined by immediate or delayed assignments:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-0u43ux
In[3]:=3
✖
https://wolfram.com/xid/0binok32-4vbarr
Out[3]=3

HoldPattern is used to protect the rules from their own definitions:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-eeylic
In[2]:=2
✖
https://wolfram.com/xid/0binok32-dt1z0i
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0binok32-do5nb
Out[3]=3

UpValues["sym"] will issue a message if the specified symbol does not exist:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-g0zu8z
Out[1]=1

If the symbol exists but has no definitions, an empty list is returned:

In[2]:=2
✖
https://wolfram.com/xid/0binok32-1bblgi
Out[2]=2

Definition and Information display upvalues but do not return them as values:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-bgcyj
In[2]:=2
✖
https://wolfram.com/xid/0binok32-iprh14
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0binok32-njo2fh

UpValues returns a value that can be used in a program:

In[4]:=4
✖
https://wolfram.com/xid/0binok32-in70p
Out[4]=4

Evaluation of an expression involves applying matching upvalues:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-ilxq7d
In[2]:=2
✖
https://wolfram.com/xid/0binok32-cn8i41
Out[2]=2

Matching upvalues are used before matching downvalues in evaluation:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-t5y2ul
In[2]:=2
✖
https://wolfram.com/xid/0binok32-wda5v9
In[3]:=3
✖
https://wolfram.com/xid/0binok32-r9h2a1
Out[3]=3

The upvalue for g is used prior to the downvalue for f:

In[4]:=4
✖
https://wolfram.com/xid/0binok32-7lvacr
Out[4]=4

Compare with a manual application of the upvalue and downvalue:

In[5]:=5
✖
https://wolfram.com/xid/0binok32-3xb42l
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0binok32-t78qyf
Out[6]=6

Define an upvalue for g that applies for all heads:

In[1]:=1
✖
https://wolfram.com/xid/0binok32-n1ygnt
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0binok32-huf63q
Out[2]=2

Even if a function has attribute HoldAll, the upvalue will be applied during evaluation:

In[3]:=3
✖
https://wolfram.com/xid/0binok32-8ht5xk
Out[3]=3

If a function has attribute HoldAllComplete, the upvalue will not be applied:

In[4]:=4
✖
https://wolfram.com/xid/0binok32-jbf42v
Out[4]=4
Wolfram Research (1991), UpValues, Wolfram Language function, https://reference.wolfram.com/language/ref/UpValues.html (updated 1996).
✖
Wolfram Research (1991), UpValues, Wolfram Language function, https://reference.wolfram.com/language/ref/UpValues.html (updated 1996).

Text

Wolfram Research (1991), UpValues, Wolfram Language function, https://reference.wolfram.com/language/ref/UpValues.html (updated 1996).

✖
Wolfram Research (1991), UpValues, Wolfram Language function, https://reference.wolfram.com/language/ref/UpValues.html (updated 1996).

CMS

Wolfram Language. 1991. "UpValues." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/UpValues.html.

✖
Wolfram Language. 1991. "UpValues." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/UpValues.html.

APA

Wolfram Language. (1991). UpValues. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UpValues.html

✖
Wolfram Language. (1991). UpValues. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UpValues.html

BibTeX

@misc{reference.wolfram_2025_upvalues, author="Wolfram Research", title="{UpValues}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/UpValues.html}", note=[Accessed: 04-April-2025 ]}

✖
@misc{reference.wolfram_2025_upvalues, author="Wolfram Research", title="{UpValues}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/UpValues.html}", note=[Accessed: 04-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_upvalues, organization={Wolfram Research}, title={UpValues}, year={1996}, url={https://reference.wolfram.com/language/ref/UpValues.html}, note=[Accessed: 04-April-2025 ]}

✖
@online{reference.wolfram_2025_upvalues, organization={Wolfram Research}, title={UpValues}, year={1996}, url={https://reference.wolfram.com/language/ref/UpValues.html}, note=[Accessed: 04-April-2025 ]}