D correctly simulated by pure function H cannot possibly reach its, own line 06

On 5/26/2024 3:05 AM, Mikko wrote:

On 2024-05-25 11:42:59 +0000, olcott said:
 

On 5/25/2024 4:59 AM, Mikko wrote:

On 2024-05-24 16:57:36 +0000, olcott said:
>

On 5/24/2024 10:01 AM, Fred. Zwarts wrote:

Op 23.mei.2024 om 18:52 schreef olcott:

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       }
>
The above template refers to an infinite set of H/D pairs where D is
correctly simulated by pure function H. This was done because many
reviewers used the shell game ploy to endlessly switch which H/D was
being referred to.
>
*Correct Simulation Defined*
This is provided because every reviewer had a different notion of
correct simulation that diverges from this notion.
>
In the above case a simulator is an x86 emulator that correctly emulates
at least one of the x86 instructions of D in the order specified by the
x86 instructions of D.
>
This may include correctly emulating the x86 instructions of H in the
order specified by the x86 instructions of H thus calling H(D,D) in
recursive simulation.
>
*Execution Trace*
Line 11: main() invokes H(D,D); H(D,D) simulates lines 01, 02, and 03 of
D. This invokes H(D,D) again to repeat the process in endless recursive
simulation.

>
The case can be simplified even more (D is not needed):
>

>
We are ONLY asking about whether D correctly simulated by pure function H can possibly reach its own final state at line 06 and halt.
>
Because H is a pure function we know that H halts.

>
We don't know that H halts. The OP said the opposite:
>

>
The above references *pure function* H thus we do know
that the spec *requires* H to halt.
https://en.wikipedia.org/wiki/Pure_function

 In that case the spec requires halting, though OP was not clar about that.
 

On 2024-05-23 16:52:21 +0000, olcott said:

*Execution Trace*
Line 11: main() invokes H(D,D); H(D,D) simulates lines 01, 02, and 03 of
D. This invokes H(D,D) again to repeat the process in endless recursive
simulation.

 Here OP is clear: H does not halt when both arguments are D.
 Therefore H does not conform to the spec.
 

To repeat in endless recursve simulation makes halting impossible.
Apparently OP's interpretation of "pure function" does not imply
halting.
>

>
Every H is required to halt and return a value.
To make things simple every H returns the meaningless 56.
It is endless recursive simulation until H halts.

 No, it isn't. "endless recursive simulation" means that H does not halt.
Thereis no "unless" in the OP.
 

I had to make the subject line of the thread a little less accurate
so that people could get the gist of what I was saying. Now I have
made it precise.
*Now I will unify the two subject lines*
No matter how many steps of D correctly simulated by pure function H
are simulated D never reaches its final state at its own line 06 and
halts because D remains stuck in recursive simulation.
That H is a pure function means that H eventually halts and returns
some value. We can say H returns the meaningless value of 56.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer