This is the best answer that I have found so far:

In computer programming, a pure function is a function that has the
following properties:

(1) the function return values are identical for identical arguments (no
variation with local static variables, non-local variables, mutable
reference arguments or input streams), and

(2) the function has no side effects (no mutation of local static
variables, non-local variables, mutable reference arguments or
input/output streams).
https://en.wikipedia.org/wiki/Pure_function

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

On 10/21/22 10:56 PM, olcott wrote:
> This is the best answer that I have found so far:
>
> In computer programming, a pure function is a function that has the
> following properties:
>
> (1) the function return values are identical for identical arguments (no
> variation with local static variables, non-local variables, mutable
> reference arguments or input streams), and
>
> (2) the function has no side effects (no mutation of local static
> variables, non-local variables, mutable reference arguments or
> input/output streams).
> https://en.wikipedia.org/wiki/Pure_function
>
>

Mostly, but are missing a few points.

For (1) not only must the return values be identical, but it must ALWAYS
return that value, it can't in some cases not return the value. Its FULL
behavior is consistent for every invocation with the same arguements.
This is because that is the way the Turing Machines work. A Turing
Machine embedded in another machine (any other machine) acts the same as
when it is run by itself (given the same input tape at that point in time).

Also, since Turing Machines can be copied, we must be able to make a
copy of the C function and have it also behave the same, returning the
same values as the original for the same inputs. And it doesn't matter
which copy of the function a given program calls.

Not positive it fhat is a complete list to be sufficient, but it should
get you close.

On 2022-10-22 03:35:52 +0000, Richard Damon said:

> On 10/21/22 10:56 PM, olcott wrote:
>> This is the best answer that I have found so far:
>>
>> In computer programming, a pure function is a function that has the
>> following properties:
>>
>> (1) the function return values are identical for identical arguments
>> (no variation with local static variables, non-local variables, mutable
>> reference arguments or input streams), and
>>
>> (2) the function has no side effects (no mutation of local static
>> variables, non-local variables, mutable reference arguments or
>> input/output streams).
>> https://en.wikipedia.org/wiki/Pure_function
>>
>>
>
> Mostly, but are missing a few points.
>
> For (1) not only must the return values be identical, but it must
> ALWAYS return that value, it can't in some cases not return the value.
> Its FULL behavior is consistent for every invocation with the same
> arguements. This is because that is the way the Turing Machines work. A
> Turing Machine embedded in another machine (any other machine) acts the
> same as when it is run by itself (given the same input tape at that
> point in time).
>
> Also, since Turing Machines can be copied, we must be able to make a
> copy of the C function and have it also behave the same, returning the
> same values as the original for the same inputs. And it doesn't matter
> which copy of the function a given program calls.
>
> Not positive it fhat is a complete list to be sufficient, but it should
> get you close.

Is a function or a program Turing computable if it is not strictly
conforming to the C standard?

Mikko

On 10/22/22 5:00 AM, Mikko wrote:
> On 2022-10-22 03:35:52 +0000, Richard Damon said:
>
>> On 10/21/22 10:56 PM, olcott wrote:
>>> This is the best answer that I have found so far:
>>>
>>> In computer programming, a pure function is a function that has the
>>> following properties:
>>>
>>> (1) the function return values are identical for identical arguments
>>> (no variation with local static variables, non-local variables,
>>> mutable reference arguments or input streams), and
>>>
>>> (2) the function has no side effects (no mutation of local static
>>> variables, non-local variables, mutable reference arguments or
>>> input/output streams).
>>> https://en.wikipedia.org/wiki/Pure_function
>>>
>>>
>>
>> Mostly, but are missing a few points.
>>
>> For (1) not only must the return values be identical, but it must
>> ALWAYS return that value, it can't in some cases not return the value.
>> Its FULL behavior is consistent for every invocation with the same
>> arguements. This is because that is the way the Turing Machines work.
>> A Turing Machine embedded in another machine (any other machine) acts
>> the same as when it is run by itself (given the same input tape at
>> that point in time).
>>
>> Also, since Turing Machines can be copied, we must be able to make a
>> copy of the C function and have it also behave the same, returning the
>> same values as the original for the same inputs. And it doesn't matter
>> which copy of the function a given program calls.
>>
>> Not positive it fhat is a complete list to be sufficient, but it
>> should get you close.
>
> Is a function or a program Turing computable if it is not strictly
> conforming to the C standard?
>
> Mikko
>

I wouldn't think "Strict Conformance" matters one way or the other
(Note, that IS a 'technical word' in C Standard). If a program isn't
Strictly Conforming, then what Turing Machine that it would be the
equivalent of might be a function of the details of the implementation.

So, it comes down to details of definition.

On 10/22/2022 9:05 AM, Richard Damon wrote:
> On 10/22/22 5:00 AM, Mikko wrote:
>> On 2022-10-22 03:35:52 +0000, Richard Damon said:
>>
>>> On 10/21/22 10:56 PM, olcott wrote:
>>>> This is the best answer that I have found so far:
>>>>
>>>> In computer programming, a pure function is a function that has the
>>>> following properties:
>>>>
>>>> (1) the function return values are identical for identical arguments
>>>> (no variation with local static variables, non-local variables,
>>>> mutable reference arguments or input streams), and
>>>>
>>>> (2) the function has no side effects (no mutation of local static
>>>> variables, non-local variables, mutable reference arguments or
>>>> input/output streams).
>>>> https://en.wikipedia.org/wiki/Pure_function
>>>>
>>>>
>>>
>>> Mostly, but are missing a few points.
>>>
>>> For (1) not only must the return values be identical, but it must
>>> ALWAYS return that value, it can't in some cases not return the
>>> value. Its FULL behavior is consistent for every invocation with the
>>> same arguements. This is because that is the way the Turing Machines
>>> work. A Turing Machine embedded in another machine (any other
>>> machine) acts the same as when it is run by itself (given the same
>>> input tape at that point in time).
>>>
>>> Also, since Turing Machines can be copied, we must be able to make a
>>> copy of the C function and have it also behave the same, returning
>>> the same values as the original for the same inputs. And it doesn't
>>> matter which copy of the function a given program calls.
>>>
>>> Not positive it fhat is a complete list to be sufficient, but it
>>> should get you close.
>>
>> Is a function or a program Turing computable if it is not strictly
>> conforming to the C standard?
>>
>> Mikko
>>
>
> I wouldn't think "Strict Conformance" matters one way or the other
> (Note, that IS a 'technical word' in C Standard). If a program isn't
> Strictly Conforming, then what Turing Machine that it would be the
> equivalent of might be a function of the details of the implementation.
>
> So, it comes down to details of definition.
>
>

Yes strict conformance to the C standard it totally irrelevant to
whether or not a C function is Turing computable.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer