DownValues [f]
gives a list of transformation rules corresponding to all downvalues (values for f[…]) defined for the symbol f.
DownValues ["symbol"]
gives a list of transformation rules corresponding to all downvalues defined for the symbol named "symbol" if it exists.
DownValues
DownValues [f]
gives a list of transformation rules corresponding to all downvalues (values for f[…]) defined for the symbol f.
DownValues ["symbol"]
gives a list of transformation rules corresponding to all downvalues defined for the symbol named "symbol" if it exists.
Details and Options
- You can specify the downvalues for f by making an assignment of the form DownValues [f]=list.
- The list returned by DownValues has elements of the form HoldPattern [lhs]:>rhs.
Examples
open all close allBasic Examples (1)
Define values for a function f:
These are the downvalues associated with f:
Scope (3)
DownValues returns rules corresponding to definitions made for a symbol:
Create several functions:
Obtain the downvalues of functions whose names start with f:
DownValues can be used to set the values directly:
Applications (2)
The resulting rules are in the order given:
Now reorder the definitions:
Copy a symbol's definitions to another symbol:
Properties & Relations (5)
Values can be defined by immediate or delayed assignments:
HoldPattern is used to protect the rules from their own definitions:
Without the HoldPattern , the left-hand side would have evaluated:
DownValues ["sym"] will issue a message if the specified symbol does not exist:
If the symbol exists but has no definitions, an empty list is returned:
Definition and Information display downvalues but do not return them as values:
DownValues returns a value that can be used in a program:
Evaluation of an expression involves applying rules for its head:
See Also
Set SetDelayed SubValues UpValues OwnValues Information ValueQ Clear ClearAll Save DownValuesFunction
Function Repository: DefinedSymbols ExtractDownValues SymbolDependencies WithCachedValues
Tech Notes
Related Guides
History
Introduced in 1991 (2.0) | Updated in 1996 (3.0) ▪ 2022 (13.2)
Text
Wolfram Research (1991), DownValues, Wolfram Language function, https://reference.wolfram.com/language/ref/DownValues.html (updated 2022).
CMS
Wolfram Language. 1991. "DownValues." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/DownValues.html.
APA
Wolfram Language. (1991). DownValues. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DownValues.html
BibTeX
@misc{reference.wolfram_2025_downvalues, author="Wolfram Research", title="{DownValues}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/DownValues.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_downvalues, organization={Wolfram Research}, title={DownValues}, year={2022}, url={https://reference.wolfram.com/language/ref/DownValues.html}, note=[Accessed: 16-November-2025]}