[Haskell-cafe] The Applicative Functor Monad

[Ryan Ingram]

I think that there's no solution for your problem as stated, besides
going with something like type-indexed monads, which leads you down
the no-implicit-prelude path.

But to see one obvious reason why this is the case: can you tell me
what the type of "returnAF" is?

Also, one of the monad laws is
   m >>= return   =   m

I don't see how this can possibly be the case with the definition of
bindAF you have given.

  -- ryan

On Tue, Dec 23, 2008 at 5:50 PM, Jeremy Shaw <jeremy at n-heptane.com> wrote:
> Hello,
>
> I want to make a Monad which is almost exactly like the Writer monad,
> except instead of using mappend to glue Monoids together, it uses <*>
> to glue applicative functors together.
>
> Here is the code:
>
> import Control.Applicative
> import Data.Monoid
>
> -- * Sample Implementation of the Writer Monad
>
> data Writer w a = Writer { runWriter :: (w, a) }
>
> instance (Monoid w) => Monad (Writer w) where
>    return a = Writer (mempty, a)
>    (>>=) = bindWriter
>
> bindWriter :: (Monoid w) => Writer w a -> (a -> Writer w b) -> Writer w b
> bindWriter (Writer (w,a)) f =
>    let (Writer (w', b)) = f a
>    in Writer (w `mappend` w', b)
>
> -- * Sample Implementation of the Applicative Functor Monad
>
> data AF af a = AF { runAF :: (af, a) }
>
> bindAF :: (Applicative f) => AF (f (a -> b)) x -> (x -> AF (f a) y) -> AF (f b) y
> bindAF (AF (f, x)) g =
>    let (AF (a, y)) = g x
>    in AF (f <*> a, y)
>
> -- instance (Applicative f) => Monad (AF (f ...
>
> As you can see, the similarity is striking. Alas, AF and bindAF do not
> quite have the right type signatures to be used for an instance of the
> Monad class. Is there some clever work-around I missing? (Aside from,
> -fno-implicit-prelude).
>
> Thanks!
>
> - jeremy
> _______________________________________________
> Haskell-Cafe mailing list
> Haskell-Cafe at haskell.org
> http://www.haskell.org/mailman/listinfo/haskell-cafe
>