[Haskell-cafe] IO is not a monad

[Lennart Augustsson]

Could you explain why would a class Seq not be sufficient?
If there were a class Seq, I'd not want functions to be in
that class.

	-- Lennart

On Jan 23, 2007, at 08:57 , Yitzchak Gale wrote:

> I wrote:
>>> Prelude> let f .! g = ((.) $! f) $! g
>>> Prelude> let f = undefined :: Int -> IO Int
>>> Prelude> f `seq` 42
>>> *** Exception: Prelude.undefined
>>> Prelude> ((>>= f) . return) `seq` 42
>>> 42
>>> Prelude> ((>>= f) .! return) `seq` 42
>>> 42
>
> Duncan Coutts wrote:
>> Perhaps I'm missing something but I don't see what's wrong.
>
> The monad laws say that (>>= f) . return must be
> identical to f. The above shows that they are not identical
> for IO. Therefore, IO is not a monad.
>
>> I think what you're saying is that you want (>>=) to be strict in  
>> it's
>> second argument. I don't see that this is a requirement of the monad
>> laws.
>
> Oh, no, I don't want that at all! Especially not for []!
> Where would we be then?
>
>> You'll note that you get the same behaviour for other monads like  
>> Maybe
>> and [].
>
> Yes.
>
> I am starting, as a programmer,  from the practical problem
> that strictness properties are badly broken in MTL.
> But no one seems to want to fix it. Although
> it is clear that the current behavior is very wrong,
> no one seems to be able to define exactly what the
> correct behavior should be.
>
> To understand the problem better myself, I want
> to understand better the relationship between
> monads in category theory and strictness.
>
> The most common approach seems to be:
> Make believe that seq does not exist, and
> use the usual Haskell notions of functions
> to form a category. Then try to fix up strictness
> issues as an afterthought, without regard
> to category theory. The result is a mess.
> It would be disappointing to me if that is the
> best we can do.
>
> Another approach that we came up with
> recently on this list is that you can allow
> seq - in its current form - as a morphism,
> but use .! instead of . as composition in the
> category. I find that somewhat attractive,
> because .! essentially means "compose
> functions while preserving strictness/laziness".
>
> Unfortunately, the above paradox shows that
> this is not the complete answer either.
>
> A related issue is the claim that the current
> behavior of seq is wrong in some way.
> I am not convinced that there is any problem
> with the current behavior that \_->_|_ /= _|_,
> nor that changing it would solve any
> problems.
>
> This paradox also shows that an idea mentioned
> here a few days ago by Neil Mitchell:
>
> class Seq a where
>   seq :: a -> b -> b
>
> is also not sufficient.
>
> Thanks,
> Yitz
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