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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Categorically exhaustive reasoning applied to the decision to abort
Date: Sat, 30 Mar 2024 09:09:23 +0200
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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?

-- 
Mikko