Re: Every D(D) simulated by H presents non-halting behavior to H ###

Op 27.mei.2024 om 16:39 schreef olcott:

On 5/27/2024 9:10 AM, Richard Damon wrote:

On 5/27/24 9:52 AM, olcott wrote:

On 5/27/2024 3:11 AM, Mikko wrote:

On 2024-05-26 16:50:21 +0000, olcott said:
>

>
<snip>
So that: *Usenet Article Lookup*
http://al.howardknight.net/
can see the whole message now that
*the Thai spammer killed Google Groups*
>
typedef int (*ptr)();  // ptr is pointer to int function in C
00       int H(ptr p, ptr i);
01       int D(ptr p)
02       {
03         int Halt_Status = H(p, p);
04         if (Halt_Status)
05           HERE: goto HERE;
06         return Halt_Status;
07       }
08
09       int main()
10       {
11         H(D,D);
12         return 0;
13       }
>

When we see that D correctly simulated by pure simulator H would remain
stuck in recursive simulation then we also know that D never reaches its
own line 06 and halts in less than an infinite number of correctly
simulated steps.

>
Which means that H never terminates. You said that by your definition
a function that never terminates is not a pure function. Therefore
H, if it exists, is not a pure function, and the phrase "pure function
H" does not denote.
>

>
*I should have said that more clearly*
*That is why I need reviewers*
*Here it is more clearly*
>
When we hypothesize that H is a pure simulator we see that D correctly
simulated by pure simulator H remains stuck in recursive simulation thus
never reaches its own simulated final state at its line 06 and halts. In
this case H does not halt, thus is neither a pure function nor a
decider.

>
But when you hypothesize that H is actually a "pure simulator" (presumably one that never aborts) then you are creating a D that uses that pure simulator, and are ONLY deriving conclusions for such a D.
>

 When D correctly simulated by pure simulator H cannot possibly reach
its own simulated final state at line 06 and halt in an infinite number
of simulated steps we can conclude that less than an infinite number of
steps is also not enough steps for D to halt.
 

When H correctly simulated by pure simulator H cannot possibly reach
its own simulated final state and halt in an infinite number
of simulated steps we can conclude that less than an infinite number of
steps is also not enough steps for H to halt.