<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
purely	B-Application
functional	I-Application
programming	I-Application
usually	O
designates	O
a	O
programming	O
paradigm	O
—	O
a	O
style	O
of	O
building	O
the	O
structure	O
and	O
elements	O
of	O
computer	O
programs	O
—	O
that	O
treats	O
all	O
computation	O
as	O
the	O
evaluation	O
of	O
mathematical	O
functions	O
.	O
</s>
<s>
Program	O
state	O
and	O
mutable	B-Application
objects	I-Application
are	O
usually	O
modeled	O
with	O
temporal	O
logic	O
,	O
as	O
explicit	O
variables	O
that	O
represent	O
the	O
program	O
state	O
at	O
each	O
step	O
of	O
a	O
program	O
execution	O
:	O
a	O
variable	O
state	O
is	O
passed	O
as	O
an	O
input	O
parameter	O
of	O
a	O
state-transforming	O
function	O
,	O
which	O
returns	O
the	O
updated	O
state	O
as	O
part	O
of	O
its	O
return	O
value	O
.	O
</s>
<s>
Purely	B-Application
functional	I-Application
programming	I-Application
consists	O
of	O
ensuring	O
that	O
functions	O
,	O
inside	O
the	O
functional	B-Language
paradigm	I-Language
,	O
will	O
only	O
depend	O
on	O
their	O
arguments	O
,	O
regardless	O
of	O
any	O
global	O
or	O
local	O
state	O
.	O
</s>
<s>
A	O
pure	B-Application
functional	I-Application
subroutine	O
only	O
has	O
visibility	O
of	O
changes	O
of	O
state	O
represented	O
by	O
state	O
variables	O
included	O
in	O
its	O
scope	O
.	O
</s>
<s>
The	O
exact	O
difference	O
between	O
pure	O
and	O
impure	O
functional	B-Language
programming	I-Language
is	O
a	O
matter	O
of	O
controversy	O
.	O
</s>
<s>
Sabry	O
's	O
proposed	O
definition	O
of	O
purity	O
is	O
that	O
all	O
common	O
evaluation	B-Language
strategies	I-Language
(	O
call-by-name	O
,	O
call-by-value	O
,	O
and	O
call-by-need	O
)	O
produce	O
the	O
same	O
result	O
,	O
ignoring	O
strategies	O
that	O
error	O
or	O
diverge	O
.	O
</s>
<s>
A	O
program	O
is	O
usually	O
said	O
to	O
be	O
functional	B-Language
when	O
it	O
uses	O
some	O
concepts	O
of	O
functional	B-Language
programming	I-Language
,	O
such	O
as	O
first-class	B-Application
functions	I-Application
and	O
higher-order	B-Language
functions	I-Language
.	O
</s>
<s>
However	O
,	O
a	O
first-class	B-Application
function	I-Application
need	O
not	O
be	O
purely	O
functional	B-Language
,	O
as	O
it	O
may	O
use	O
techniques	O
from	O
the	O
imperative	B-Application
paradigm	I-Application
,	O
such	O
as	O
arrays	B-Data_Structure
or	O
input/output	O
methods	B-Language
that	O
use	O
mutable	B-Application
cells	O
,	O
which	O
update	O
their	O
state	O
as	O
side	O
effects	O
.	O
</s>
<s>
In	O
fact	O
,	O
the	O
earliest	O
programming	O
languages	O
cited	O
as	O
being	O
functional	B-Language
,	O
IPL	B-Language
and	O
Lisp	B-Language
,	O
are	O
both	O
"	O
impure	O
"	O
functional	B-Language
languages	I-Language
by	O
Sabry	O
's	O
definition	O
.	O
</s>
<s>
Purely	B-Application
functional	I-Application
data	I-Application
structures	I-Application
are	O
persistent	B-Application
.	O
</s>
<s>
Persistency	O
is	O
required	O
for	O
functional	B-Language
programming	I-Language
;	O
without	O
it	O
,	O
the	O
same	O
computation	O
could	O
return	O
different	O
results	O
.	O
</s>
<s>
Functional	B-Language
programming	I-Language
may	O
use	O
persistent	B-Application
non-purely	O
functional	O
data	B-General_Concept
structures	I-General_Concept
,	O
while	O
those	O
data	B-General_Concept
structures	I-General_Concept
may	O
not	O
be	O
used	O
in	O
purely	O
functional	B-Language
programs	I-Language
.	O
</s>
<s>
Each	O
evaluation	B-Language
strategy	I-Language
which	O
ends	O
on	O
a	O
purely	O
functional	B-Language
program	I-Language
returns	O
the	O
same	O
result	O
.	O
</s>
<s>
Purely	B-Application
functional	I-Application
programming	I-Application
simplifies	O
parallel	B-Operating_System
computing	I-Operating_System
since	O
two	O
purely	O
functional	B-Language
parts	O
of	O
the	O
evaluation	O
never	O
interact	O
.	O
</s>
<s>
Purely	B-Application
functional	I-Application
data	I-Application
structures	I-Application
are	O
often	O
represented	O
in	O
a	O
different	O
way	O
than	O
their	O
imperative	B-Application
counterparts	O
.	O
</s>
<s>
For	O
example	O
,	O
array	B-Data_Structure
with	O
constant-time	O
access	O
and	O
update	O
is	O
a	O
basic	O
component	O
of	O
most	O
imperative	B-Application
languages	I-Application
and	O
many	O
imperative	B-Application
data-structures	O
,	O
such	O
as	O
hash	B-Algorithm
table	I-Algorithm
and	O
binary	B-Application
heap	I-Application
,	O
are	O
based	O
on	O
arrays	B-Data_Structure
.	O
</s>
<s>
Arrays	B-Data_Structure
can	O
be	O
replaced	O
by	O
map	B-Application
or	O
random	O
access	O
list	O
,	O
which	O
admits	O
purely	O
functional	B-Language
implementation	O
,	O
but	O
the	O
access	O
and	O
update	O
time	O
is	O
logarithmic	O
.	O
</s>
<s>
Therefore	O
,	O
purely	B-Application
functional	I-Application
data	I-Application
structures	I-Application
can	O
be	O
used	O
in	O
languages	O
which	O
are	O
non-functional	O
,	O
but	O
they	O
may	O
not	O
be	O
the	O
most	O
efficient	O
tool	O
available	O
,	O
especially	O
if	O
persistency	O
is	O
not	O
required	O
.	O
</s>
<s>
In	O
general	O
,	O
conversion	O
of	O
an	O
imperative	B-Application
program	I-Application
to	O
a	O
purely	O
functional	B-Language
one	O
also	O
requires	O
ensuring	O
that	O
the	O
formerly-mutable	O
structures	O
are	O
now	O
explicitly	O
returned	O
from	O
functions	O
that	O
update	O
them	O
,	O
a	O
program	O
structure	O
called	O
store-passing	B-Application
style	I-Application
.	O
</s>
<s>
A	O
purely	O
functional	B-Language
language	I-Language
is	O
a	O
language	O
which	O
only	O
admits	O
purely	B-Application
functional	I-Application
programming	I-Application
.	O
</s>
<s>
Purely	O
functional	B-Language
programs	I-Language
can	O
however	O
be	O
written	O
in	O
languages	O
which	O
are	O
not	O
purely	O
functional	B-Language
.	O
</s>
