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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: How do computations actually work?
Date: Sat, 24 May 2025 17:48:29 -0400
Organization: i2pn2 (i2pn.org)
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On 5/24/25 11:18 AM, olcott wrote:
> On 5/24/2025 2:47 AM, Mikko wrote:
>> On 2025-05-23 02:47:40 +0000, olcott changed the subject to
>>> How do computations actually work?
>>
>> Each computation works differently. It does not matter how it works as
>> long as there are instructions that fully specify how that computation
>> shall be performed.
>>
> 
> All termination analyzers are required to report on the
> behavior that their input finite string specifies.
> 
> int main()
> {
>    DD(); // the HHH that DD calls cannot report on the
> }       // behavior of its caller. That is just not
>          // the way that these things work.
> 
> int sum(int x int y) { return x + y; }
> computes the sum of its inputs according to the rules of arithmetic.
> 
> Does not compute any function
> int sum(int x int y) { return 5; }

Sure, that is a function.

Why isn't it, It is the function

For all x, y, (x,y) -> 5


or the funciton commonly named "5"

> 
> Does not compute the function of sum correctly.
> int sum(int x int y) { x + x; }
> 

But it is a function, just not the right function.

Just as your HHH doesn't compute the right resuit, as the correct result 
is DEFINED by the results of running the program represented by the 
input, and seeing if it will halt in finite time or run for unbounded steps.

So, your HHH is just as correct as sum(x, y) { return x+x; }