<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
graph	B-Application
reduction	I-Application
implements	O
an	O
efficient	O
version	O
of	O
non-strict	O
evaluation	O
,	O
an	O
evaluation	B-Language
strategy	I-Language
where	O
the	O
arguments	O
to	O
a	O
function	O
are	O
not	O
immediately	O
evaluated	O
.	O
</s>
<s>
This	O
form	O
of	O
non-strict	O
evaluation	O
is	O
also	O
known	O
as	O
lazy	O
evaluation	O
and	O
used	O
in	O
functional	B-Language
programming	I-Language
languages	I-Language
.	O
</s>
<s>
The	O
above	O
reduction	O
sequence	O
employs	O
a	O
strategy	O
known	O
as	O
outermost	O
tree	B-Application
reduction	O
.	O
</s>
<s>
The	O
same	O
expression	O
can	O
be	O
evaluated	O
using	O
innermost	O
tree	B-Application
reduction	O
,	O
yielding	O
the	O
reduction	O
sequence	O
:	O
</s>
<s>
Represented	O
as	O
a	O
tree	B-Application
,	O
the	O
expression	O
above	O
looks	O
like	O
this	O
:	O
</s>
<s>
This	O
is	O
where	O
the	O
term	O
tree	B-Application
reduction	O
comes	O
from	O
.	O
</s>
<s>
When	O
represented	O
as	O
a	O
tree	B-Application
,	O
we	O
can	O
think	O
of	O
innermost	O
reduction	O
as	O
working	O
from	O
the	O
bottom	O
up	O
,	O
while	O
outermost	O
works	O
from	O
the	O
top	O
down	O
.	O
</s>
<s>
Hence	O
we	O
have	O
graph	B-Application
reduction	I-Application
.	O
</s>
<s>
Now	O
evaluation	O
with	O
outermost	O
graph	B-Application
reduction	I-Application
can	O
proceed	O
as	O
follows	O
:	O
</s>
<s>
Outermost	O
graph	B-Application
reduction	I-Application
is	O
referred	O
to	O
as	O
lazy	O
evaluation	O
and	O
innermost	O
graph	B-Application
reduction	I-Application
is	O
referred	O
to	O
as	O
eager	O
evaluation	O
.	O
</s>
<s>
Combinator	B-Application
graph	I-Application
reduction	I-Application
is	O
a	O
fundamental	O
implementation	O
technique	O
for	O
functional	B-Language
programming	I-Language
languages	I-Language
,	O
in	O
which	O
a	O
program	O
is	O
converted	O
into	O
a	O
combinator	B-Application
representation	O
which	O
is	O
mapped	O
to	O
a	O
directed	O
graph	O
data	B-General_Concept
structure	I-General_Concept
in	O
computer	O
memory	O
,	O
and	O
program	O
execution	O
then	O
consists	O
of	O
rewriting	O
parts	O
of	O
this	O
graph	O
(	O
"	O
reducing	O
"	O
it	O
)	O
so	O
as	O
to	O
move	O
towards	O
useful	O
results	O
.	O
</s>
<s>
The	O
concept	O
of	O
a	O
graph	B-Application
reduction	I-Application
that	O
allows	O
evaluated	O
values	O
to	O
be	O
shared	O
was	O
first	O
developed	O
by	O
Chris	O
Wadsworth	O
in	O
his	O
1971	O
Ph.D.	O
dissertation	O
.	O
</s>
<s>
In	O
1976	O
David	O
Turner	O
incorporated	O
lazy	O
evaluation	O
into	O
SASL	B-Language
using	O
combinators	B-Application
.	O
</s>
<s>
SASL	B-Language
was	O
an	O
early	O
functional	B-Language
programming	I-Language
language	I-Language
first	O
developed	O
by	O
Turner	O
in	O
1972	O
.	O
</s>
