Re: Turing Machine computable functions MUST apply finite string transformations to inputs

On 4/30/2025 1:32 PM, olcott wrote:

On 4/30/2025 11:11 AM, Richard Heathfield wrote:

On 30/04/2025 16:44, joes wrote:

Am Wed, 30 Apr 2025 10:09:45 -0500 schrieb olcott:

On 4/29/2025 5:01 AM, Mikko wrote:

>

Irrelevant. There is sufficient agreement what Turing machines are.

>
Turing machine computable functions must apply finite string
transformation rues to inputs to derive outputs.
>
This is not a function that computes the sum(3,2):
int sum(int x, int y) { return 5; }

Yes it is, for all inputs.

>
Not much of a computation, though, is it?
>

 It IS NOT a Turing Computable function

Lying by misuse of terms.
A turing computable function is a mapping for which an algorithm exists to compute it, not the algorithm itself.
Further use of "turing computable function" when what is meant is "algorithm" will result in the former being replaced with the later in future responses to your posts to make it clear what you are actually talking about.

because it does not ever apply any finite
string transformation  rules to its inputs.

Sure it does.  It computes the mapping of all pairs of integers to the number 5.

 THE OUTPUTS MUST CORRESPOND TO THE INPUTS.

And it does, according to the following mapping which is a turning computable function:
For all integers X and Y:
(X,Y) maps to 5

sum(4,3) returns 5 proving that sum is
not an algorithm.
 

Of course it's an algorithm.  It performs a fixed immutable sequence of instructions to compute a result from the input.