Apply

f@@expr or Apply[f,expr]

replaces the head of expr by f.

f@@@expr or Apply[f,expr,{1}]

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

open all close all

Basic Examples  (7)

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

Apply gets rid of a level of lists:

In[1]:=
Click for copyable input
Out[1]=

Use the operator form of Apply:

In[1]:=
Click for copyable input
Out[1]=

Applying f to an Association keeps only values:

In[1]:=
Click for copyable input
Out[1]=

Applying a List to an Association is equivalent to Values:

In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=

Apply f at the second level:

In[1]:=
Click for copyable input
Out[1]=

Apply f at several levels:

In[1]:=
Click for copyable input
Out[1]=

Scope  (10)

Generalizations & Extensions  (2)

Options  (1)

Applications  (4)

Properties & Relations  (5)

Possible Issues  (1)

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