<s>
Binary	B-Application
combinatory	I-Application
logic	I-Application
(	O
BCL	O
)	O
is	O
a	O
computer	O
programming	O
language	O
that	O
uses	O
binary	O
terms	O
0	O
and	O
1	O
to	O
create	O
a	O
complete	O
formulation	O
of	O
combinatory	B-Application
logic	I-Application
using	O
only	O
the	O
symbols	O
0	O
and	O
1	O
.	O
</s>
<s>
Using	O
the	O
S	O
and	O
K	O
combinators	B-Application
,	O
complex	O
boolean	O
algebra	O
functions	O
can	O
be	O
made	O
.	O
</s>
<s>
Utilizing	O
K	O
and	O
S	O
combinators	B-Application
of	O
the	O
Combinatory	B-Application
logic	I-Application
,	O
logical	O
functions	O
can	O
be	O
represented	O
in	O
as	O
functions	O
of	O
combinators	B-Application
:	O
</s>
<s>
The	O
denotational	B-Application
semantics	I-Application
of	O
BCL	O
may	O
be	O
specified	O
as	O
follows	O
:	O
</s>
<s>
Here	O
K	O
and	O
S	O
are	O
the	O
KS-basis	O
combinators	B-Application
,	O
and	O
(	O
)	O
is	O
the	O
application	O
operation	O
,	O
of	O
combinatory	B-Application
logic	I-Application
.	O
</s>
<s>
The	O
operational	O
semantics	O
of	O
BCL	O
,	O
apart	O
from	O
eta-reduction	O
(	O
which	O
is	O
not	O
required	O
for	O
Turing	B-Algorithm
completeness	I-Algorithm
)	O
,	O
may	O
be	O
very	O
compactly	O
specified	O
by	O
the	O
following	O
rewriting	O
rules	O
for	O
subterms	O
of	O
a	O
given	O
term	O
,	O
parsing	B-Language
from	O
the	O
left	O
:	O
</s>
<s>
(	O
Note	O
,	O
for	O
example	O
,	O
that	O
because	O
parsing	B-Language
is	O
from	O
the	O
left	O
,	O
10000	O
is	O
not	O
a	O
subterm	O
of	O
11010000	O
.	O
)	O
</s>
<s>
BCL	O
can	O
be	O
used	O
to	O
replicate	O
algorithms	O
like	O
Turing	B-Architecture
machines	I-Architecture
and	O
Cellular	O
automata	O
,	O
BCL	O
is	O
Turing	B-Algorithm
complete	I-Algorithm
.	O
</s>
