C:\Documents and Settings\dave\Desktop\Godel, Escher, Bach ...

example of a full B1ooP program would be the definition of the procedure TWO-TO-
THE-THREE-TO-THE, followed by the call
TWO-TO-THE-THREE-TO-THE [2]
which would yield an answer of 512.
If you have only a chain of procedure definitions, then nothing ever gets executed;
they are all just waiting for some call, with specific numerical values, to set them in
motion. It is like a meat grinder waiting for some meat to grind-or rather, a chain of meat
grinders all linked together, each of which is fed from earlier ones ... In the case of meat
grinders, the image is perhaps not so savory; however, in the case of BlooP programs,
such a construct is quite important, and we will call it a "call-less program". This notion
is illustrated in Figure 72.
Now B1ooP is our language for defining predictably terminating calculations. The
standard name for functions which are B1ooP-computable is primitive recursive
functions; and the standard name for properties which can be detected by B1ooP-tests is
primitive recursive predicates. Thus, the function 2 3n is a primitive recursive function;
and the statement "n is a prime number" is a primitive recursive predicate.
It is clear intuitively that the Goldbach property is primitive recursive, and to
make that quite explicit, here is a procedure definition in BlooP, showing how to test for
its presence or absence:
DEFINE PROCEDURE "GOLDBACH?" [N]:
BLOCK 0: BEGIN
CELL(0) 2;
LOOP AT MOST N TIMES:
BLOCK 1: BEGIN
IF {PRIME? [CELL(O)]
AND PRIME? [MINUS [N,CELL(0)]]},
THEN:
BLOCK 2: BEGIN
OUTPUT,# YES;
QUIT BLOCK 0-,
BLOCK 2: END
CELL(0)