Apply

Apply[f,expr]

or f@@expr replaces the head of expr by f.

Apply[f,expr,{1}]

or f@@@expr replaces heads at level 1 of expr by f.

Apply[f,expr,levelspec]

replaces heads in parts of expr specified by levelspec.

Apply[f]

represents an operator form of Apply that can be applied to an expression.

Details and Options

  • Apply uses standard level specifications:
  • nlevels 1 through n
    Infinitylevels 1 through Infinity
    {n}level n only
    {n1,n2}levels n1 through n2
  • The default value for levelspec in Apply is {0}.
  • f@@@expr is equivalent to Apply[f,expr,{1}].
  • A positive level n consists of all parts of expr specified by n indices.
  • A negative level -n consists of all parts of expr with depth n.
  • Level -1 consists of numbers, symbols, and other objects that do not have subparts.
  • Level 0 corresponds to the whole expression.
  • Apply always effectively constructs a complete new expression and then evaluates it.
  • Apply operates on SparseArray objects just as it would on the corresponding ordinary lists.
  • Apply operates on values only in Association objects.
  • Apply[f][expr] is equivalent to Apply[f,expr].

Examples

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Basic Examples  (7)

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Apply gets rid of a level of lists:

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Use the operator form of Apply:

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Applying f to an Association keeps only values:

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Applying a List to an Association is equivalent to Values:

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Apply f at the second level:

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Apply f at several levels:

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Scope  (10)

Generalizations & Extensions  (2)

Options  (1)

Applications  (4)

Properties & Relations  (5)

Possible Issues  (1)

See Also

Map  Scan  Construct  Level  Operate  MapThread  Through  Total  Sequence  Function

Tutorials

Related Workflows

Introduced in 1988
(1.0)
| Updated in 2014
(10.0)