Functor-Applicative-Monad Proposal

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Revision as of 15:48, 7 December 2010 by Twhitehead (talk | contribs) (Note about the possibility of splitting off a Pointed class)

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The standard class hierarchy is a consequence of Haskell's historical development, rather than logic. The Functor, Applicative, and Monad type classes could be defined as:

class Functor f where
    map :: (a -> b) -> f a -> f b

class Functor f => Applicative f where
    return :: a -> f a
    (<*>) :: f (a -> b) -> f a -> f b
    (*>) :: f a -> f b -> f b
    (<*) :: f a -> f b -> f a

class Applicative m => Monad m where
    (>>=) :: m a -> (a -> m b) -> m b
    f >>= x = join $ map f x

    join :: m (m a) -> m a
    join x = x >>= id

This would eliminate the necessity of declaring a Monad instance for every Applicative, and eliminate the need for sets of duplicate functions such as [fmap, liftM, map, liftA], [(<*>), ap], and [concat, join].

fail should be removed from Monad; a failed pattern match could error in the same way as is does for pure code. The only sensible uses for fail seem to be synonyms for mzero.

Pointed has not been included due to controversy as to whether it should be a subclass of Functor, a superclass of Functor, independent of Functor, or perhaps it is not sufficiently useful to include at all.

Backward compatibility could be eased with a legacy module, such as:

module Legacy where

fmap :: Functor f => (a -> b) -> f a -> f b
fmap = map

liftA :: Applicative f => (a -> b) -> f a -> f b
liftA = map

liftM :: Monad m => (a -> b) -> m a -> m b
liftM = map

ap :: Monad m => m (a -> b) -> m a -> m b
ap = (<*>)

(>>) :: Monad m => m a -> m b -> m b
(>>) = (*>)

concat :: [[a]] -> [a]
concat = join


And for those who really want a list map,

listMap :: (a -> b) -> [a] -> [b]
listMap = map

Another variant might be to split a Pointed class from the Applicative class.

class Pointed f where
    return :: a -> f a

class (Functor f, Pointed f) => Applicative f where
    (<*>) :: f (a -> b) -> f a -> f b
    (*>) :: f a -> f b -> f b
    (<*) :: f a -> f b -> f a

Such Pointed functionality by itself could be useful, for example, in a DSL in which it is only possible to embed values and not to lift functions to functions over those embedded values.