Re: HHH(DD) does correctly reject its input as non-halting --- VERIFIED FACT +++

On 6/13/2025 5:51 AM, Mikko wrote:

On 2025-06-12 15:30:05 +0000, olcott said:
 

int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
>
It is a verified fact that DD() *is* one of the forms
of the counter-example input as such an input would
be encoded in C. Christopher Strachey wrote his in CPL.
>
// rec routine P
//   §L :if T[P] go to L
//     Return §
// https://academic.oup.com/comjnl/article/7/4/313/354243
void Strachey_P()
{
   L: if (HHH(Strachey_P)) goto L;
   return;
}
>
https://academic.oup.com/comjnl/article-abstract/7/4/313/354243? redirectedFrom=fulltext

 Strachey only informally presents the idea of the proof. Formalism
and details needed in a rigorous proof is not shown.
 

It *is* a verified fact DD correctly simulated by HHH
cannot possibly reach its own "return" statement
final halt state.

 That "cannot possibly" is not a part of any verifiable fact as
it is not sufficiently well-defined for a verification. What
cannot be stated cearly and unambiguoulsy cannot be a verified
fact.
 

void DDD()
{
   HHH(DDD);
   return;
}
_DDD()
[00002192] 55             push ebp
[00002193] 8bec           mov ebp,esp
[00002195] 6892210000     push 00002192
[0000219a] e833f4ffff     call 000015d2  // call HHH
[0000219f] 83c404         add esp,+04
[000021a2] 5d             pop ebp
[000021a3] c3             ret
Size in bytes:(0018) [000021a3]
It is a self-evidently true verified fact that DDD
correctly emulated by HHH cannot possibly reach its
own simulated "ret" instruction final halt state in
1 to ∞ steps of correct emulation of DDD by HHH.
Everyone that does not agree has less than a first
year CS student's understanding of the C programming
language.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer