Re: DD specifies non-terminating behavior to HHH --- RECURSIVE CHAIN --- Saving Democracy

On 2/22/2025 11:10 AM, dbush wrote:

On 2/22/2025 11:43 AM, olcott wrote:

On 2/22/2025 5:01 AM, joes wrote:

Am Fri, 21 Feb 2025 21:55:32 -0600 schrieb olcott:

On 2/20/2025 4:00 AM, joes wrote:

>
>

Not even the variable Root in line 502 of Halt7.c?

https://github.com/plolcott/x86utm/blob/master/Halt7.c You are not even
in the correct function.

1059
>

>
Unless we go through a 100% precise sequence of steps
my reviewers will always consistently dodge the point
as they have done for several years.
>
typedef void (*ptr)();
int HHH(ptr P);
>
int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
>
int main()
{
   HHH(DD);
}
>
The first point is DD correctly simulated by HHH cannot
possibly terminate normally by reaching its own "return"
instruction.

 In other words, if the code of HHH is replaced with an unconditional simulator then it can be shown that DD is non-halting and therefore HHH(DD)==0 is correct.
 

Wow finally someone that totally gets it.

Let's test that on another case.
 

01 int F(int i)
02 {
03      if (i<10) {
04          return 0;
05      } else {
06          return F(i+1);
07      }
08 }
09
10 int no_numbers_greater_than_10()
11 {
12      return F(0);
13 }
14
15 int main()
16 {
17   no_numbers_greater_than_10();
18   return 0;
19 }

 The function no_numbers_greater_than_10() checks if any natural number exists that is greater than 10.  It does this by checking all natural numbers one at a time.  If one such number exists it halts and return 0.   If no such number exists, it will run forever as no such number will satisfy the condition.
 

Your code is incomplete. I added main() with line numbers.

We can see that no_numbers_greater_than_10 correctly simulated by F cannot possibly terminate normal by reaching its own "return" instruction.  This means that F correctly reports that no_numbers_greater_than_10 is non-halting.  It further means, since no_numbers_greater_than_10  doesn't halt that there is no natural number greater than 10.
 Agreed?

Here the execution trace that I see:
15, 16, 17, 10, 11, 12, 01, 02, 03, 04, 12, 18, 19
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer