I don't know what the denotation for this would be, but I can't think of any reasonable ones for which I can write (==) to respect the denotation. For example, is "set A, then set B" equal to "set B, then set A"? Maybe you could argue that they aren't operationally equivalent, but can you guarantee that such reordering are *never* operationally equivalent? How about an action that take an input from stdin and then outputs the result of some computation based on it? How do you compare two such actions? I disagree with Jerzy on the purity of IO, but I don't think this line of argument is bound to be very fruitful.
Jerzy, taking a similar example to that last one, would you say functions are impure just because I can't write a general (==) for them? I don't see what bountiful numbers of operations has to do with purity.
- Jake
On Thu, Aug 08, 2013 at 11:38:08AM +0200, Jerzy Karczmarczuk wrote:
> Tom Ellis:
> >If I were writing a Haskell compiler I could certainly define 'IO' to be a
> >datatype that would allow me to compare 'putStr "c"' to itself. The
> >comparison could not be of operational equivalence, but it would still be
> >possible to compare values in IO in a reasonable sense.
>
> Would you add to all this:
> getLine == getLine
> etc.?
>
> Good luck!
>
> I suspect that you would have to establish also the equality
> relation between functions and between infinite streams.
> And you would end as Giordano Bruno and Jeanne d'Arc. But for
> different reasons.
Not at all. One could simply implement IO as a free monad, to take one
example.
Tom
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