Refactoring Semigroup/Monoid (was: instance Applicative Data.Map)

[Michael Sloan]

I think we'd rather like to avoid UndecidableInstances in the prelude!

This does bring up an interesting idea, though, as far as using a flat
hierarchy for these classes.  Default method signatures could be used to
provide similar behavior.

http://www.haskell.org/ghc/docs/7.4.2/html/users_guide/type-class-extensions.html#class-default-signatures

I'm not saying that this is a good idea (I think that a good idea would be
closer to my https://github.com/mgsloan/instance-templates proposal - which
I seriously need to rework to be more appealing), but I wonder if this
would work:

  class Applicative f where
    applicative_map :: (a -> b) -> f a -> f b
    default applicative_map :: Monad f => (a -> b) -> f a -> f b
    applicative_map = monad_map
-- ...

  class Monad m where
    monad_map :: (a -> b) -> m a -> m b
    default monad_map :: Applicative m => (a -> b) -> m a -> m b
    monad_map = applicative_map
-- ...

I haven't seen mutually recursive defaultings like this (not sure if even
works) - but could be a nifty trick for some applications.  The defaults in
Applicative are more important, so these could be removed in favor of using
the usual standard defaults in Monad.

-Michael

On Mon, Nov 19, 2012 at 11:00 AM, Tyson Whitehead <twhitehead at gmail.com>wrote:

> On November 19, 2012 12:25:57 Tyson Whitehead wrote:
> > GHC 7.0.4 accepts this with FlexibleInstances and UndecidableInstances,
> but
> > it seems to still have some issues (features?) as it overrides signatures
> >
> >   *Main> :t pure
> >   pure :: Monad f => a -> f a
> >
> > unless you add other instances that are only at the lowel levels.  For
> > example, adding Maybe at the Applicative level to the above [] instance
> >
> >   instance Applicative Maybe where
> >     applicative_apply (Just f) (Just x) = Just (f x)
> >     applicative_apply _        _        = Nothing
> >     applicative_map f (Just x) = Just (f x)
> >     applicative_map _ _        = Nothing
> >     applicative_pure x = Just x
> >
> > gives
> >
> >   *Main> :t pure
> >   pure :: Monad f => a -> f a
> >   *Main> :t Main.fmap
> >   Main.fmap :: Applicative f => (a -> b) -> f a -> f b
>
> Cut and paste mistake there.  That last bit should have been
>
>   *Main> :t pure
>   pure :: Applicative f => a -> f a
>   *Main> :t Main.fmap
>   Main.fmap :: Applicative f => (a -> b) -> f a -> f b
>
> Adding a Functor only instance will make fmap resolve correctly.
>
> Cheers!  -Tyson
>
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