[Haskell-cafe] Re: what is inverse of mzero and return?
Jules Bean
jules at jellybean.co.uk
Tue Jan 25 07:10:50 EST 2005
On 25 Jan 2005, at 11:49, Keean Schupke wrote:
> Jules Bean wrote:
>
>> A monad T is a (endo)functor T : * -> * where * is the category of
>> types, together with a multiplication mu and a unit eta.
>
> So, * is the category of Types, and functions on type (which map
> values to values), and T is
> an endofunctor (mapping functions on type to functions on type).
T is an endofunctor (mapping functions on types to functions on types
*and* types to types) : functors map not only morphisms but also
objects.
>
> How does this affect the IO monad though?
>
> m >>= (\a -> mzero) === mzero
>
> If we consider the state monad, surely the above makes no comment on
> what
> the final state should be, only the final value returned...
>
> Or is MonadPlus not definable on State monads?
I don't know. The reason I don't know, is I can't actually find written
down the laws that MonadPlus is 'supposed' to obey. I agree with the OP
(ashley, IIRC) that mzero and the IO monad behave in a surprising way.
I would think that the closest I could get to a 'sane' definition of
MonadPlus for State Monads is something which for mzero goes into a
'special state' representing exception (with undefined for a value, I
suppose), and for mplus tries the left branch, if that goes into the
exception state then tries the right branch.
> If it is then considering IO === ST RealWorld, would imply that the
> actions
> of the IO monad are not important as long as the final value returned
> is
> mzero?
Well, mzero isn't a return value in the IO monad, it's an exception.
But yes, I agree with you that the (plausible) laws I have seen for
MonadPlus seem to say that mzero should ignore the actions. But this in
practice is not how IO behaves.
Jules
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