The standard class hierarchy is a consequence of Haskell's historical development, rather than logic. The
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 [
ap], and [
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 etc.
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.
Another variant might be to split a
Pointed class from the
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
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.