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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: How do computations actually work?
Date: Sat, 24 May 2025 11:15:32 -0400
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On 5/24/2025 11:13 AM, olcott wrote:
> On 5/24/2025 2:39 AM, Mikko wrote:
>> On 2025-05-23 16:10:19 +0000, olcott said:
>>
>>> On 5/23/2025 2:14 AM, Mikko wrote:
>>>> On 2025-05-23 03:31:15 +0000, olcott said:
>>>>
>>>>> On 5/22/2025 10:23 PM, wij wrote:
>>>>>> On Thu, 2025-05-22 at 21:47 -0500, olcott wrote:
>>>>>>> [cut]
>>>>>>
>>>>>> Q: How do computations actually work?
>>>>>> A: Computation is merely step-by-step algorithm.
>>>>>> Nothing says it has to be TM.
>>>>>>
>>>>>> Do the exercises in textbooks first before any claim of it.
>>>>>>
>>>>>
>>>>> int main()
>>>>> {
>>>>>    DD(); // by what steps can the HHH that DD calls
>>>>> }       // report on the behavior its caller?
>>>>
>>>> If we don't insist that the report be correct:
>>>> 1. guess
>>>> 2. tell what was guessed
>>>
>>> This does not work because all computable functions
>>> that implement termination analyzers must compute
>>> the mapping from their input finite string according
>>> to the behavior that it specifies.
>>
>> Wrong. There is no need to compute "the" mapping if a the report
>> needs not be correct. Some other mapping is enough to produce
>> some report.
>>
> 
> int sum(int x, int y) { return 5; }
> Does not compute any function because it ignores its inputs.
> 

Sure it does.  It computes this function:


For all integers X and Y:

(X,Y) maps to 5


The only requirements for mapping is a function is that inputs 
correspond to outputs as per the given mapping, and the mathematical 
function above is mapped by the above C function "sum".