[Haskell-cafe] On the purity of Haskell

[Conal Elliott]

On Fri, Dec 30, 2011 at 12:49 AM, Heinrich Apfelmus <
apfelmus at 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.
>
> Put differently, the function always returns the same IO action, i.e. the
> same value (of type  IO Int) when given the same parameter.
>

Two questions trouble me:

How can we know whether this claim is true or not?

What does the claim even mean, i.e., what does "the same IO action" mean,
considering that we lack a denotational model of IO?

 - Conal
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