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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Categorically exhaustive reasoning applied to the decision to
 abort
Date: Mon, 1 Apr 2024 09:52:57 -0500
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On 4/1/2024 3:15 AM, Mikko wrote:
> On 2024-03-31 16:29:06 +0000, olcott said:
> 
>> On 3/31/2024 11:17 AM, olcott wrote:
>>> On 3/31/2024 11:08 AM, Mikko wrote:
>>>> On 2024-03-31 14:25:37 +0000, olcott said:
>>>>
>>>>> On 3/31/2024 4:04 AM, Mikko wrote:
>>>>>> On 2024-03-30 13:45:03 +0000, olcott said:
>>>>>>
>>>>>>> On 3/30/2024 2:09 AM, Mikko wrote:
>>>>>>>> On 2024-03-29 14:26:50 +0000, olcott said:
>>>>>>>>
>>>>>>>>> On 3/29/2024 6:10 AM, Mikko wrote:
>>>>>>>>>> On 2024-03-28 15:38:08 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>> On 3/28/2024 9:44 AM, Mikko wrote:
>>>>>>>>>>>> On 2024-03-27 14:04:17 +0000, olcott said:
>>>>>>>>>>>>
>>>>>>>>>>>>> On 3/27/2024 4:32 AM, Mikko wrote:
>>>>>>>>>>>>>> On 2024-03-26 14:41:08 +0000, olcott said:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 3/26/2024 3:50 AM, Mikko wrote:
>>>>>>>>>>>>>>>> On 2024-03-25 22:52:18 +0000, olcott said:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> On 3/24/2024 9:27 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>> On 2024-03-24 02:11:34 +0000, olcott said:
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> On 3/23/2024 7:31 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 3/23/24 7:29 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 3/23/2024 5:58 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>> On 23/03/24 16:02, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> (b) H(D,D) that DOES abort its simulation is correct
>>>>>>>>>>>>>>>>>>>>>>>      (ABOUT THIS ABORT DECISION)
>>>>>>>>>>>>>>>>>>>>>>>      because it would halt and all deciders must 
>>>>>>>>>>>>>>>>>>>>>>> always halt.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> To be a decider it has to give an answer.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> To be a halt decider it has to give an answer that 
>>>>>>>>>>>>>>>>>>>>>> is the same as whether the direct execution of its 
>>>>>>>>>>>>>>>>>>>>>> input would halt.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> That would entail that H must report on different 
>>>>>>>>>>>>>>>>>>>>> behavior
>>>>>>>>>>>>>>>>>>>>> than the behavior that H actually sees thus violate 
>>>>>>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>>>>>>> definition of a decider that must compute the 
>>>>>>>>>>>>>>>>>>>>> mapping from
>>>>>>>>>>>>>>>>>>>>> its inputs...
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Nope.
>>>>>>>>>>>>>>>>>>>> You are just showing yourself to be a stupid liar.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Where in the DEFINITION of Compute the Mapping of 
>>>>>>>>>>>>>>>>>>>> the Input to the Mapped Output does it say that the 
>>>>>>>>>>>>>>>>>>>> decider has to be able to "see" that property of the 
>>>>>>>>>>>>>>>>>>>> input?
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> In order to compute the mapping from an input there 
>>>>>>>>>>>>>>>>>>> must be
>>>>>>>>>>>>>>>>>>> some basis that is directly provided by this input.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> If no such basis is in the input the problem has no 
>>>>>>>>>>>>>>>>>> soution.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> int sum(int x, int y){ return x + y; }
>>>>>>>>>>>>>>>>> sum(3,4) is not allowed to report on the sum of 5 + 6
>>>>>>>>>>>>>>>>> even if you really really believe that it should.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Your and my beliefs don't matter. Testers call the 
>>>>>>>>>>>>>>>> function with
>>>>>>>>>>>>>>>> various pairs of inputs and compare the result to the 
>>>>>>>>>>>>>>>> specification.
>>>>>>>>>>>>>>>> If the result is not what the specification requires 
>>>>>>>>>>>>>>>> then the function
>>>>>>>>>>>>>>>> is wrong and needs be fixed or rejected.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> There is enough information for sum(3,4) to compute the 
>>>>>>>>>>>>>>> sum of 3+4.
>>>>>>>>>>>>>>> There is NOT enough information for sum(3,4) to compute 
>>>>>>>>>>>>>>> the sum of 5+6.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> There is enough information for H1(D,D) to compute 
>>>>>>>>>>>>>>> Halts(D,D).
>>>>>>>>>>>>>>> There is NOT enough information for H(D,D) to compute 
>>>>>>>>>>>>>>> Halts(D,D).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> There is enough information to determine whether the 
>>>>>>>>>>>>>> result is as
>>>>>>>>>>>>>> required by the specification.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> This specification only requires a mapping from H(D,D)
>>>>>>>>>>>>> to Halts(Simulated_by_H(D,D)) and it gets that one correctly.
>>>>>>>>>>>>> D(D) does not halt from the POV of H.
>>>>>>>>>>>>
>>>>>>>>>>>> What "this pecification"? This means the one you refer or 
>>>>>>>>>>>> point to
>>>>>>>>>>>> but you didn't.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Every implementation of H(D,D) that simulates its input must 
>>>>>>>>>>> abort
>>>>>>>>>>> this simulation or never itself halt.
>>>>>>>>>>>
>>>>>>>>>>> int main() { D(D); }   is not a D simulated by H.
>>>>>>>>>>> int main() { H(D,D); } is a D simulated by H.
>>>>>>>>>>
>>>>>>>>>> Does not answer what "this specification" means above.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> *THIS SPECIFICATION*
>>>>>>>>> Every implementation of H(D,D) that simulates its input must abort
>>>>>>>>> this simulation or never itself halt.
>>>>>>>>
>>>>>>>> Are you sure you want to allow that H(D,D) may run un a loop and 
>>>>>>>> never
>>>>>>>> halt and never continue the simulation?
>>>>>>>>
>>>>>>>
>>>>>>> So you didn't understand the: *must abort this simulation* part ?
>>>>>>
>>>>>> I did. I asked whether whether you really mean all that "never iself
>>>>>> halt" means.
>>>>>>
>>>>>
>>>>> 01 void D(ptr x) // ptr is pointer to void function
>>>>> 02 {
>>>>> 03   H(x, x);
>>>>> 04   return;
>>>>> 05 }
>>>>> 06
>>>>> 07 void main()
>>>>> 08 {
>>>>> 09   H(D,D);
>>>>> 10 }
>>>>>
>>>>> *Execution Trace*
>>>>> Line 09: main() invokes H(D,D);
>>>>>
>>>>> *keeps repeating* (unless aborted)
>>>>> Line 03: simulated D(D) invokes simulated H(D,D) that simulates D(D)
>>>>>
>>>>> *Simulation invariant*
>>>>> D correctly simulated by H cannot possibly reach past its own line 03.
>>>>>
>>>>> As soon as line 03 would be simulated  H sees that D would call
>>>>> itself with its same input, then H aborts D.
>>>>
>>>> Looks like you don't know whether you really want to allow that H(D,D)
>>>> may run in a loop and never halt and never continue the simulation.
>>>>
>>>
>>> H(D,D) must halt or it cannot be any kind of decider. My other
>>> reviewers consistently and perpetually lie about whether or
>>> not H(D,D) is correct to abort its simulation.
>>>
>>
>> When I refer to H I am referring to every element of the set of 
>> implementations H that simulate their input.
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