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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: Wed, 27 Mar 2024 11:32:11 +0200
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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.

-- 
Mikko