On Dec 30, 2011, at 11:20 AM, Colin Adams wrote:
>
> On 30 December 2011 17:17, Gregg Reynolds <d...@mobileink.com> wrote:
>
> On Dec 30, 2011, at 11:04 AM, Colin Adams wrote:
>
>>
>>
>> On 30 December 2011 16:59, Gregg Reynolds <d...@mobileink.com> wrote:
>>
>>> On Fri, Dec 30, 2011 at 12:49 AM, Heinrich Apfelmus
>>> <apfel...@quantentunnel.de> wrote:
>>>
>>> The function
>>>
>>> f :: Int -> IO Int
>>> f x = getAnIntFromTheUser >>= \i -> return (i+x)
>>>
>>> is pure according to the common definition of "pure" in the context of
>>> purely functional programming. That's because
>>>
>>> f 42 = f (43-1) = etc.
>>>
>> Conclusion: f 42 != f 42
>>
>> (This seems so extraordinarily obvious that maybe Heinrich has something
>> else in mind.)
>>
>> This seems such an obviously incorrect conclusion.
>>
>> f42 is a funtion for returning a program for returning an int, not a
>> function for returning an int.
>
>
> My conclusion holds: f 42 != f 42. Obviously, so I won't burden you with an
> explanation. ;)
>
> -Gregg
> Your conclusion is clearly erroneous.
>
> proof: f is a function, and it is taking the same argument each time.
> Therefore the result is the same each time.
That's called begging the question. f is not a function, so I guess your proof
is flawed.
It seems pretty clear that we're working with different ideas of what
constitutes a function. When I use the term, I intend what I take to be the
standard notion of a function in computation: not just a unique mapping from
one input to one output, but one where the output is computable from the input.
Any "function" that depends on a non-computable component is by that
definition not a true function. For clarity let's call such critters
quasi-functions, so we can retain the notion of application. Equality cannot
be defined for quasi-functions, for obvious reasons.
f is a quasi-function because it depends on getAnIntFromUser, which is not
definable and is obviously not a function. When applied to an argument like
42, it yields another quasi-function, and therefore "f 42 = f 42" is false, or
at least unknown, and the same goes for f 42 != f 42 I suppose.
-Gregg
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