<s>
and	O
(	O
Bounded	B-Language
loop	I-Language
and	O
Free	O
loop	O
)	O
are	O
simple	O
programming	O
languages	O
designed	O
by	O
Douglas	O
Hofstadter	O
to	O
illustrate	O
a	O
point	O
in	O
his	O
book	O
Gödel	O
,	O
Escher	O
,	O
Bach	O
.	O
</s>
<s>
BlooP	B-Language
is	O
a	O
non-Turing-complete	B-Algorithm
programming	I-Algorithm
language	I-Algorithm
whose	O
main	O
control	O
flow	O
structure	O
is	O
a	O
bounded	B-Language
loop	I-Language
(	O
i.e.	O
</s>
<s>
All	O
programs	O
in	O
the	O
language	O
must	O
terminate	O
,	O
and	O
this	O
language	O
can	O
only	O
express	O
primitive	B-Architecture
recursive	I-Architecture
functions	I-Architecture
.	O
</s>
<s>
FlooP	B-Language
is	O
identical	O
to	O
BlooP	B-Language
except	O
that	O
it	O
supports	O
unbounded	O
loops	O
;	O
it	O
is	O
a	O
Turing-complete	O
language	O
and	O
can	O
express	O
all	O
computable	O
functions	O
.	O
</s>
<s>
For	O
example	O
,	O
it	O
can	O
express	O
the	O
Ackermann	O
function	O
,	O
which	O
(	O
not	O
being	O
primitive	B-Architecture
recursive	I-Architecture
)	O
cannot	O
be	O
written	O
in	O
BlooP	B-Language
.	O
</s>
<s>
Borrowing	O
from	O
standard	O
terminology	O
in	O
mathematical	O
logic	O
,	O
Hofstadter	O
calls	O
FlooP	B-Language
's	O
unbounded	O
loops	O
MU-loops	O
.	O
</s>
<s>
Like	O
all	O
Turing-complete	O
programming	O
languages	O
,	O
FlooP	B-Language
suffers	O
from	O
the	O
halting	O
problem	O
:	O
programs	O
might	O
not	O
terminate	O
,	O
and	O
it	O
is	O
not	O
possible	O
,	O
in	O
general	O
,	O
to	O
decide	O
which	O
programs	O
do	O
.	O
</s>
<s>
BlooP	B-Language
and	I-Language
FlooP	I-Language
can	O
be	O
regarded	O
as	O
models	O
of	O
computation	O
,	O
and	O
have	O
sometimes	O
been	O
used	O
in	O
teaching	O
computability	O
.	O
</s>
<s>
Control	O
flow	O
constructs	O
include	O
bounded	B-Language
loops	I-Language
,	O
conditional	B-Language
statements	I-Language
,	O
ABORT	O
jumps	O
out	O
of	O
loops	O
,	O
and	O
QUIT	O
jumps	O
out	O
of	O
blocks	O
.	O
</s>
<s>
BlooP	B-Language
does	O
not	O
permit	O
recursion	O
,	O
unrestricted	O
jumps	O
,	O
or	O
anything	O
else	O
that	O
would	O
have	O
the	O
same	O
effect	O
as	O
the	O
unbounded	O
loops	O
of	O
FlooP	B-Language
.	O
</s>
<s>
The	O
example	O
below	O
,	O
which	O
implements	O
the	O
Ackermann	O
function	O
,	O
relies	O
on	O
simulating	O
a	O
stack	O
using	O
Gödel	O
numbering	O
:	O
that	O
is	O
,	O
on	O
previously	O
defined	O
numerical	O
functions	O
PUSH	O
,	O
POP	O
,	O
and	O
TOP	O
satisfying	O
PUSH	O
[	O
N	O
,	O
S ]	O
>	O
0	O
,	O
TOP	O
[	O
PUSH	O
[	O
N	O
,	O
S ] ]	O
=	O
N	O
,	O
and	O
POP	O
[	O
PUSH	O
[	O
N	O
,	O
S ] ]	O
=	O
S	O
.	O
Since	O
an	O
unbounded	O
MU-LOOP	O
is	O
used	O
,	O
this	O
is	O
not	O
a	O
legal	O
BlooP	B-Language
program	O
.	O
</s>
