Hi,
indeed, this is called "ap" in Control.Monad.  So if we have an instance of Monad, all that needs to be done to support the other instances is:

instance (SameContextAsTheMonadInstance) => Functor MyType where fmap = liftM
instance (SameContextAsTheMonadInstance) => Applicative MyType where pure = return; (<*>) = ap

Furthermore, this is only in the cases where we are defining the type from scratch, and not using a library like monadLib or MTL, otherwise a simple "deriving" is sufficient.

-Iavor

On Wed, Jan 5, 2011 at 12:29 PM, Tony Morris <tonymorris@gmail.com> wrote:
On 06/01/11 04:58, Isaac Dupree wrote:
> Tony, you're missing the point... Alexey isn't making a complete patch
> to GHC/base libraries, just a hacky-looking demonstration.  Alexey is
> saying that in a class hierarchy (such as if Functor => Monad were a
> hierarchy, or for that matter "XFunctor"=>"XMonad" or Eq => Ord), it
> is still possible to define the superclass functions (fmap) in terms
> of the subclass functions (return and >>=) (such as writing a functor
> instance in which "fmap f m = m >>= (return . f)").  This has always
> been true in Haskell, it just might not have been obvious.
>
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Oh right sorry. I thought a stronger point was being made.

Then perhaps it's also worth pointing out that (<*>) can be written
using (>>=) and return:
f <*> a = f >>= \ff -> a >>= \aa -> return (ff aa)

--
Tony Morris
http://tmorris.net/



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