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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: My reviewers think that halt deciders must report on the behavior
 of their caller
Date: Wed, 4 Jun 2025 22:32:53 -0500
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On 6/4/2025 9:56 PM, dbush wrote:
> On 6/4/2025 10:44 PM, olcott wrote:
>> On 6/4/2025 9:13 PM, dbush wrote:
>>> On 6/4/2025 10:09 PM, olcott wrote:
>>>> On 6/4/2025 8:43 PM, Richard Damon wrote:
>>>>> On 6/4/25 11:50 AM, olcott wrote:
>>>>>> On 6/4/2025 2:04 AM, Mikko wrote:
>>>>>>> On 2025-06-03 21:39:46 +0000, olcott said:
>>>>>>>
>>>>>>>> They all say that HHH must report on the behavior of
>>>>>>>> direct execution of DDD()
>>>>>>>
>>>>>>> No, they don't say that. A halting decider (and a partial halting
>>>>>>> decider when it reports) must report whether the direct execution
>>>>>>> of the computation asked about terminates. Unless that computation
>>>>>>> happens to be DDD() it must report about another behaviour instead
>>>>>>> of DDD().
>>>>>>>
>>>>>>>> yet never bother to notice that the directly executed DDD() is
>>>>>>>> the caller of HHH(DDD).
>>>>>>>
>>>>>>> To say that nobody has noticed that is a lie. Perhaps they have not
>>>>>>> mentioned what is irrelevant to whatever they said. In particular,
>>>>>>> whether DDD() calls HHH(DDD) is irrelevant to the requirement that
>>>>>>> a halting decider must report about a direct exection of the
>>>>>>> computation the input specifies.
>>>>>>>
>>>>>>
>>>>>> *People have ignored this for 90 years*
>>>>>> *People have ignored this for 90 years*
>>>>>> *People have ignored this for 90 years*
>>>>>>
>>>>>> The only possible way that HHH can report on the
>>>>>> direct execution of DDD() is for HHH to report on
>>>>>> the behavior of its caller:
>>>>>
>>>>> So?
>>>>>
>>>>> It *IS* a fact that to be correct, it needs to answer about the 
>>>>> direct executiom of the program that input represents.
>>>>>
>>>>> That is DEFINITION.
>>>>>
>>>>
>>>> Likewise with the definition of Russell's Paradox
>>>> until ZFC showed that this definition is complete
>>>> nonsense.
>>>>
>>>
>>> But unlike Russel's Paradox, which showed a contradiction in the 
>>> axioms of naive set theory, there is no contradiction in the axioms 
>>> of computation theory.  It follows from those axioms that no H exists 
>>> that performs the below mapping, as you have *explicitly* agreed.
>>>
>>
>> int main()
>> {
>>    DDD(); // comp theory does not allow HHH to
>> }        // report on the behavior of its caller.
>>
> 
> 
> int main()
> {
>     DDD();     // this
>     HHH(DDD);  // is not the caller of this: this is 
> }              // asking what the above will do

That is just not the way that computation actually works.
char* WhatIsTheNameOfThePresidentIn2030(int x);
Cannot be derived on the basis of the input.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer