<s>
In	O
mathematics	O
,	O
function	B-Algorithm
application	I-Algorithm
is	O
the	O
act	O
of	O
applying	O
a	O
function	O
to	O
an	O
argument	O
from	O
its	O
domain	B-Algorithm
so	O
as	O
to	O
obtain	O
the	O
corresponding	O
value	O
from	O
its	O
range	B-Algorithm
.	O
</s>
<s>
In	O
this	O
sense	O
,	O
function	B-Algorithm
application	I-Algorithm
can	O
be	O
thought	O
of	O
as	O
the	O
opposite	O
of	O
function	O
abstraction	O
.	O
</s>
<s>
Function	B-Algorithm
application	I-Algorithm
is	O
usually	O
depicted	O
by	O
juxtaposing	O
the	O
variable	O
representing	O
the	O
function	O
with	O
its	O
argument	O
encompassed	O
in	O
parentheses	O
.	O
</s>
<s>
In	O
some	O
instances	O
,	O
a	O
different	O
notation	O
is	O
used	O
where	O
the	O
parentheses	O
are	O
n't	O
required	O
,	O
and	O
function	B-Algorithm
application	I-Algorithm
can	O
be	O
expressed	O
just	O
by	O
juxtaposition	O
.	O
</s>
<s>
The	O
latter	O
notation	O
is	O
especially	O
useful	O
in	O
combination	O
with	O
the	O
currying	B-Application
isomorphism	O
.	O
</s>
<s>
However	O
,	O
functions	O
in	O
curried	B-Application
form	I-Application
can	O
be	O
represented	O
by	O
juxtaposing	O
their	O
arguments	O
:	O
,	O
rather	O
than	O
.	O
</s>
<s>
This	O
relies	O
on	O
function	B-Algorithm
application	I-Algorithm
being	O
left-associative	O
.	O
</s>
<s>
Function	B-Algorithm
application	I-Algorithm
can	O
be	O
trivially	O
defined	O
as	O
an	O
operator	O
,	O
called	O
apply	O
or	O
,	O
by	O
the	O
following	O
definition	O
:	O
</s>
<s>
However	O
,	O
this	O
is	O
perhaps	O
more	O
clearly	O
expressed	O
by	O
using	O
function	B-Application
composition	I-Application
instead	O
:	O
</s>
<s>
Function	B-Algorithm
application	I-Algorithm
in	O
the	O
lambda	B-Language
calculus	I-Language
is	O
expressed	O
by	O
β-reduction	O
.	O
</s>
<s>
The	O
Curry	B-Application
–	O
Howard	O
correspondence	O
relates	O
function	B-Algorithm
application	I-Algorithm
to	O
the	O
logical	O
rule	O
of	O
modus	O
ponens	O
.	O
</s>
