<s>
Curry	B-Application
is	O
an	O
experimental	O
functional	B-Application
logic	I-Application
programming	I-Application
language	O
,	O
based	O
on	O
the	O
Haskell	B-Language
language	I-Language
.	O
</s>
<s>
It	O
merges	O
elements	O
of	O
functional	B-Language
and	O
logic	B-Language
programming	I-Language
,	O
including	O
constraint	B-Application
programming	I-Application
integration	O
.	O
</s>
<s>
It	O
is	O
nearly	O
a	O
superset	O
of	O
Haskell	B-Language
,	O
lacking	O
support	O
mostly	O
for	O
overloading	O
using	O
type	O
classes	O
,	O
which	O
some	O
implementations	O
provide	O
anyway	O
as	O
a	O
language	O
extension	O
,	O
such	O
as	O
the	O
Münster	O
Curry	B-Application
Compiler	O
.	O
</s>
<s>
A	O
functional	B-Language
program	I-Language
is	O
a	O
set	O
of	O
functions	O
defined	O
by	O
equations	O
or	O
rules	O
.	O
</s>
<s>
A	O
functional	B-Language
computation	O
consists	O
of	O
replacing	O
subexpressions	O
by	O
equal	O
(	O
with	O
regard	O
to	O
the	O
function	O
definitions	O
)	O
subexpressions	O
until	O
no	O
more	O
replacements	O
(	O
or	O
reductions	O
)	O
are	O
possible	O
and	O
a	O
value	O
or	O
normal	O
form	O
is	O
obtained	O
.	O
</s>
<s>
This	O
follows	O
from	O
a	O
fundamental	O
property	O
of	O
pure	O
functional	B-Language
languages	I-Language
,	O
termed	O
referential	O
transparency	O
:	O
the	O
value	O
of	O
a	O
computed	O
result	O
does	O
not	O
depend	O
on	O
the	O
order	O
or	O
time	O
of	O
evaluation	O
,	O
due	O
to	O
the	O
absence	O
of	O
side	O
effects	O
.	O
</s>
<s>
This	O
simplifies	O
the	O
reasoning	O
about	O
and	O
maintenance	O
of	O
pure	O
functional	B-Language
programs	I-Language
.	O
</s>
<s>
As	O
many	O
functional	B-Language
languages	I-Language
like	O
Haskell	B-Language
do	O
,	O
Curry	B-Application
supports	O
the	O
definition	O
of	O
algebraic	O
data	O
types	O
by	O
enumerating	O
their	O
constructors	O
.	O
</s>
<s>
Based	O
on	O
this	O
specification	O
,	O
one	O
can	O
define	O
a	O
function	O
that	O
satisfies	O
this	O
specification	O
by	O
employing	O
logic	B-Language
programming	I-Language
features	O
.	O
</s>
<s>
Similarly	O
to	O
logic	B-Language
languages	I-Language
,	O
functional	B-Language
logic	B-Language
languages	I-Language
provide	O
search	O
for	O
solutions	O
for	O
existentially	O
quantified	O
variables	O
.	O
</s>
<s>
In	O
contrast	O
to	O
pure	O
logic	B-Language
languages	I-Language
,	O
they	O
support	O
equation	O
solving	O
over	O
nested	O
functional	B-Language
expressions	O
so	O
that	O
an	O
equation	O
like	O
yse	O
=	O
is	O
solved	O
by	O
instantiating	O
ys	O
to	O
the	O
list	O
and	O
e	O
to	O
the	O
value	O
.	O
</s>
<s>
In	O
Curry	B-Application
one	O
can	O
define	O
the	O
operation	O
last	O
as	O
follows	O
:	O
</s>
<s>
A	O
conditional	O
equation	O
of	O
the	O
form	O
l	O
c	B-Language
r	O
is	O
applicable	O
for	O
reduction	O
if	O
its	O
condition	O
c	B-Language
has	O
been	O
solved	O
.	O
</s>
<s>
In	O
contrast	O
to	O
purely	O
functional	B-Language
languages	I-Language
where	O
conditions	O
are	O
only	O
evaluated	O
to	O
a	O
Boolean	O
value	O
,	O
functional	B-Language
logic	B-Language
languages	I-Language
support	O
the	O
solving	O
of	O
conditions	O
by	O
guessing	O
values	O
for	O
the	O
unknowns	O
in	O
the	O
condition	O
.	O
</s>
<s>
Narrowing	O
is	O
an	O
extension	O
of	O
logic	B-Language
programming	I-Language
,	O
in	O
that	O
it	O
performs	O
a	O
similar	O
search	O
,	O
but	O
can	O
actually	O
generate	O
values	O
as	O
part	O
of	O
the	O
search	O
rather	O
than	O
just	O
being	O
limited	O
to	O
testing	O
them	O
.	O
</s>
<s>
The	O
Curry	B-Application
examples	O
of	O
the	O
previous	O
section	O
illustrate	O
this	O
.	O
</s>
<s>
Needed	O
narrowing	O
corresponds	O
to	O
a	O
lazy	O
strategy	O
,	O
in	O
contrast	O
to	O
the	O
SLD-resolution	B-Application
strategy	O
of	O
Prolog	B-Language
.	O
</s>
<s>
Curry	B-Application
can	O
express	O
this	O
property	O
also	O
in	O
the	O
following	O
more	O
concise	O
way	O
:	O
</s>
<s>
Haskell	B-Language
does	O
not	O
allow	O
such	O
a	O
declaration	O
since	O
the	O
pattern	O
in	O
the	O
left-hand	O
side	O
contains	O
a	O
defined	O
function	O
(	O
)	O
.	O
</s>
<s>
Such	O
a	O
pattern	O
is	O
also	O
called	O
functional	B-Language
pattern	O
.	O
</s>
<s>
Functional	B-Language
patterns	O
are	O
enabled	O
by	O
the	O
combined	O
functional	B-Language
and	O
logic	B-Language
features	O
of	O
Curry	B-Application
and	O
support	O
concise	O
definitions	O
of	O
tasks	O
requiring	O
deep	O
pattern	O
matching	O
in	O
hierarchical	O
data	O
structures	O
.	O
</s>
<s>
Since	O
Curry	B-Application
is	O
able	O
to	O
solve	O
equations	O
containing	O
function	O
calls	O
with	O
unknown	O
values	O
,	O
its	O
execution	O
mechanism	O
is	O
based	O
on	O
non-deterministic	O
computations	O
,	O
similarly	O
to	O
logic	B-Language
programming	I-Language
.	O
</s>
<s>
The	O
rules	O
defining	O
show	O
an	O
important	O
feature	O
of	O
Curry	B-Application
:	O
all	O
rules	O
are	O
tried	O
in	O
order	O
to	O
evaluate	O
some	O
operation	O
.	O
</s>
<s>
Due	O
to	O
the	O
absence	O
of	O
side	O
effects	O
,	O
a	O
functional	B-Language
logic	B-Language
program	I-Language
can	O
be	O
executed	O
with	O
different	O
strategies	O
.	O
</s>
<s>
To	O
evaluate	O
expressions	O
,	O
Curry	B-Application
uses	O
a	O
variant	O
of	O
the	O
needed	O
narrowing	O
strategy	O
which	O
combines	O
lazy	O
evaluation	O
with	O
non-deterministic	O
search	O
strategies	O
.	O
</s>
<s>
In	O
contrast	O
to	O
Prolog	B-Language
,	O
which	O
uses	O
backtracking	O
to	O
search	O
for	O
solutions	O
,	O
Curry	B-Application
does	O
not	O
fix	O
a	O
particular	O
search	O
strategy	O
.	O
</s>
<s>
Hence	O
,	O
there	O
are	O
implementations	O
of	O
Curry	B-Application
,	O
like	O
,	O
where	O
the	O
user	O
can	O
easily	O
select	O
a	O
search	O
strategy	O
,	O
like	O
depth-first	B-Algorithm
search	I-Algorithm
(	O
backtracking	O
)	O
,	O
breadth-first	B-Algorithm
search	I-Algorithm
,	O
iterative	O
deepening	O
,	O
or	O
parallel	O
search	O
.	O
</s>
