On Jun 7, 2012, at 5:21 PM, Conal Elliott wrote:
Oh, yeah. Thanks, Sjoerd.
I wonder if there's some way not to require Monad. Some sort of ApplicativeFix instead. Hm.
Something like this:
instance (Contravariant p, ApplicativeFix f) => Applicative (Q' p f) where pure a = Q' (pure (pure a)) Q' fs <*> Q' as = Q' $ \r -> uncurry ($) <$> afix (\ ~(f, a) -> (,) <$> fs (contramap ($ a) r) <*> as (contramap (f $) r))
This works with this ApplicativeFix class:
class Applicative f => ApplicativeFix f where afix :: (a -> f a) -> f a
At first I thought there would be no instance for this that would not also be a monad. But actually the list instance for MonadFix looks more like an instance for ZipList:
mfix (\x -> [1:1:zipWith (+) x (tail x), 1:zipWith (+) x x])
gives [[1,1,2,3,5,8…], [1,2,4,8,16,32,64…]], and mfix (\x -> [f x, g x, h x]) = [fix f, fix g, fix h]. For a list monad instance I would expect results with a mixture of f, g and h (but that would not be productive). Btw, you've asked this before and you got an interesting response: http://haskell.1045720.n5.nabble.com/recursive-programming-in-applicative-fu... -- Sjoerd Visscher https://github.com/sjoerdvisscher/blog