Re: Refuting the {Linz, Sipser, Kozen} HP Proofs (Functions do not always return values)

[olcott]

On 12/26/2020 6:40 PM, Ben Bacarisse wrote:
> olcott <No...@NoWhere.com> writes:
>
>> On 12/24/2020 6:20 PM, Ben Bacarisse wrote:
>>> olcott <No...@NoWhere.com> writes:
>>>
>>>> On 12/23/2020 8:53 PM, Ben Bacarisse wrote:
>>> <cut>
>>>>> That specification requires that the function must always return a value
>>>>> (in the usual sense of the word for the programming language being used)
>>>>> and that that value accurately reflect whether the computation
>>>>> represented by the function call arguments is or is not a finite one.
>>>>> Not returning a value, in any situation or context, is not permissible.
>>>>> Every call must return, and it must return the correct true/false value.
>>>>
>>>> There is one invocation of Halts() in main() that is not infintely
>>>> recursive and does return a value to its caller.
>>>>
>>>> There is also an infinitely recursive invocation of Halts() from
>>>> H_Hat().
>>>
>>> Which is why Halts does not meet the specification for the function I
>>> asked for.
>>
>> To prove that your requirement is not simply jackass stupid please
>> provide one example of a function that return a result to it caller
>> when its caller invoked this function in infinte recursion.
>
> At least you now agree that your function does not meet the
> specification. Why did you post it? Did you not know it was a fail
> right from the start?
>
> The requirement that some function always return a value is a common
> one,

Many of the functions of the standard C library can be invoked such that
they fail to return any result to their caller:

None of these functions return a result to their caller.

double H_Hat(double P)
{
double Input_Halts = sqrt(H_Hat(P));
}

void H_Hat(u32 P)
{
u32 Input_Halts = Simulate(P, P); // Where P = (u32)H_Hat
}

void H_Hat(u32 P)
{
u32 Input_Halts = Halts(P, P); // Where P = (u32)H_Hat
} // and Halts is based on Simulate


--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein