Functor-Applicative-Monad Proposal

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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

class Monad m => MonadFail m where
    fail :: String -> m a

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].

A monad which requires custom handling for pattern match failures can implement MonadFail; otherwise, a failed pattern match will error in the same way as is does for pure code.

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

Context alias would also be a great help with backwards compatibility. The class system extension proposal may also help.

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.

See also