Re: Refuting the {Linz, Sipser, Kozen} HP Proofs [ double sqrt(X) ]

[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, but you can call it "jackass stupid" if you like. Your name for it
> is neither here nor there.
>

Then the standard C function: double sqrt(X) is <not>
a function because it can be called in infinite recursion, thus
preventing it from ever returning any value to its caller.

double Infinite_Recursion(double X)
{
Infinite_Recursion( sqrt(X) );
}

int main(int argc, char *argv[])
{
double X = Infinite_Recursion(1.0);
printf("%8.4f", X);
}




> If you want to have another go at meeting the specification I gave,
> remember that the function you post must return the correct value, for
> all arguments in all contexts. It can not conveniently not return when
> that suits your trickery.
>


--
Copyright 2020 Pete Olcott

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