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

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Basic 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:

Wolfram Research (1991), DownValues, Wolfram Language function, https://reference.wolfram.com/language/ref/DownValues.html (updated 2022).

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: 19-July-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: 19-July-2025 ]}