DownValues
DownValues[f]
gives a list of transformation rules corresponding to all downvalues (values for f[…]) defined for the symbol f.
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 allclose allScope (2)
DownValues returns rules corresponding to definitions made for a symbol:
DownValues can be used to set the values directly:
Applications (2)
Properties & Relations (4)
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:
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:
Text
Wolfram Research (1991), DownValues, Wolfram Language function, https://reference.wolfram.com/language/ref/DownValues.html (updated 1996).
CMS
Wolfram Language. 1991. "DownValues." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. 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