[Haskell-cafe] Why Kleisli composition is not in the Monad signature?

[Dan Doel]

Lists! The finite kind.

This could mean Seq for instance.
On Nov 30, 2012 9:53 AM, "Brent Yorgey" <byorgey at seas.upenn.edu> wrote:

> On Fri, Nov 30, 2012 at 02:33:54AM +0100, Ben Franksen wrote:
> > Brent Yorgey wrote:
> > > On Thu, Nov 29, 2012 at 03:52:58AM +0100, Ben Franksen wrote:
> > >> Tony Morris wrote:
> > >> > As a side note, I think a direct superclass of Functor for Monad is
> not
> > >> > a good idea, just sayin'
> > >> >
> > >> > class Functor f where
> > >> >   fmap :: (a -> b) -> f a -> f b
> > >> >
> > >> > class Functor f => Apply f where
> > >> >   (<*>) :: f (a -> b) -> f a -> f b
> > >> >
> > >> > class Apply f => Bind f where
> > >> >   (=<<) :: (a -> f b) -> f a -> f b
> > >> >
> > >> > class Apply f => Applicative f where
> > >> >   unit :: a -> f a
> > >> >
> > >> > class (Applicative f, Bind f) => Monad f where
> > >> >
> > >> > Same goes for Comonad (e.g. [] has (=<<) but not counit)
> > >> > ... and again for Monoid, Category, I could go on...
> > >>
> > >> Hi Tony
> > >>
> > >> even though I dismissed your mentioning this on the Haskell' list, I
> do
> > have
> > >> to admit that the proposal has a certain elegance. However, before I
> buy
> > >> into this scheme, I'd like to see some striking examples for types
> with
> > >> natural (or at least useful) Apply and Bind instances that cannot be
> made
> > >> Applicative resp. Monad.
> > >
> > > Try writing an Applicative instances for (Data.Map.Map k).  It can't
> > > be done, but the Apply instance is (I would argue) both natural and
> > useful.
> >
> > I see. So there is one example. Are there more? I'd like to get a feeling
> > for the abstraction and this is hard if there is only a single example.
>
> Any data type which admits structures of arbitrary but *only finite*
> size has a natural "zippy" Apply instance but no Applicative (since
> pure would have to be an infinite structure).  The Map instance I
> mentioned above falls in this category.  Though I guess I'm having
> trouble coming up with other examples, but I'm sure some exist.  Maybe
> Edward knows of other examples.
>
> -Brent
>
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