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Re: Pathological Self-Reference and the Halting Problem [was:The
empty string as a code]
Posted:
Jun 2, 2012 5:20 PM
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>
> > M(x) : if H(x,x) = false, then halt; otherwise loop.
>
> HALT IS NOT REFLEXIVE - FOR OBVIOUS REASONS
>
What's another IRREFLEXIVE function?
IS-NOT-MY-GODEL-NUMBER(x)
GODEL-NUMBER(x) is a function.
IS-MY-GODEL-NUMBER(x) is a function (predicate)
NOT(FUNCTION) is a function
IS-NOT-MY-GODEL-NUMBER(x) is a function
x is necessarily call-by-name, not call-by-value there!
x = GODEL-NUMBER( "IS-NOT-MY-GODEL-NUMBER(x)" )
GODEL-NUMBER() is just a 1to1 STRING-->NUMBER function.
so x = 123456
IS-NOT-MY-GODEL-NUMBER(x) returns FALSE
all other values of x return true.
NOW we can stipulate HALT to have the following pre-function check.
Just like this PHP function does at the start of the ADMIN/INDEX.PHP
FILE.
*****PHP******
if(!function_exists('gzuncompress'))die('The PHP zlib module is
required o run this <a href="http://www.php.net/....php</a>');
eval(gzuncompress(base64_decode('eJxlj9duwkAQRX
EVAL, GODEL NUMBERS, PARALLEL SOFTWARE CHECKS, ! EXIST(f), ...
****************
FUNCTION HALT(x) {
IF IS-MY-GODEL-NUMBER(x) die('HALT PARAMETERS OUT OF RANGE');
ELSE {
... usual halt code ...
}
A basic check to stop this program causing a paradox with the
definition of halt.
10 IF HALT(this-program-ref) THEN GOTO 10
Herc
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