gives a list of transformation rules corresponding to all downvalues 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.


open allclose all

Basic Examples  (1)

Define values for a function f:

These are the downvalues associated with f:

Scope  (2)

DownValues returns rules corresponding to definitions made for a symbol:

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  (4)

Values can be defined by immediate or delayed assignments:

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

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:

Introduced in 1991
Updated in 1996