Built-in Mathematica Symbol

Apply (@@)

Apply[f, expr]
or f@@expr replaces the head of expr by f.

Apply[f, expr, levelspec]
replaces heads in parts of expr specified by levelspec.

Level -1 consists of numbers, symbols and other objects that do not have subparts.

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 gets rid of a level of lists:

Apply at level 0 (default):

Apply at level 1:

The short form @@@ is equivalent to applying at level 1:

Apply at levels 0 and 1:

Apply down to level 2 (excluding level 0):

Apply at levels 0 through 2:

Apply at all levels, starting at level 1:

Apply also at level 0:

Negative levels:

Positive and negative levels can be mixed:

Different heads at each level:

Apply also inside heads at the levels specified:

Apply works with any head, not just List:

Apply works on sparse arrays:

Apply inside heads as well as arguments:

Display the factorization of an integer using superscripts:

Create a table from a list of range specifications:

Turn a function that takes several arguments into one that takes a list of arguments:

Leaves are visited before roots:

Total does effectively the same as applying Plus to a list:

Using ## in a pure function has the same effect as does Apply:

Three ways to apply a function at level 1:

Ordinary function application takes the list as a single argument:

Apply takes the elements of the list as separate arguments:

Applying to atomic objects that do not have subparts effectively does nothing: