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 _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
