Re: Who here understands that the last paragraph is Necessarily true?

On 7/14/24 10:38 AM, olcott wrote:

On 7/14/2024 3:09 AM, Mikko wrote:

On 2024-07-13 20:15:56 +0000, olcott said:
>

typedef void (*ptr)();
int HHH(ptr P);
>
void Infinite_Loop()
{
   HERE: goto HERE;
}
>
void Infinite_Recursion()
{
   Infinite_Recursion();
}
>
void DDD()
{
   HHH(DDD);
}
>
int main()
{
   HHH(Infinite_Loop);
   HHH(Infinite_Recursion);
   HHH(DDD);
}
>
Any input that must be aborted to prevent the non
termination of HHH necessarily specifies non-halting
behavior or it would never need to be aborted.

>
Everyone understands that DDD specifies a halting behaviour if HHH(DDD) does,

  *You can comprehend this is a truism or fail to*
*comprehend it disagreement is necessarily incorrect*
Any input that must be aborted to prevent the non
termination of HHH necessarily specifies non-halting
behavior or it would never need to be aborted.
 Disagreeing with the above is analogous to disagreeing
with arithmetic.
 

But if HHH does abort and return 0, then the full correct simulaton of the input DDD (which need to include that HHH that aborted at the address) will halt, HHH did not "need" to abort.
The fact that the HHH the doesn't abort when given the DDD paired with it doesn't count, as that DDD is a DIFFERENT DDD, as it includes the HHH that it called, which is different.
Trying to exclude the HHH from the definiton of DDD just means that DDD is now  NOT a program, and thus isn't a valid input for a Halt Decider. (The act of the input accessing something outside what it has been defined to have makes it invalid, and if you include that code, it is part of the input, even if not shown explicitily, as part of the conversion of the subjective question to an objective question which deciders are defined to handle).