# Functor-Applicative-Monad Proposal

### From HaskellWiki

The standard class hierarchy is a consequence of Haskell's historical development, rather than logic. The , , and type classes could be defined as:
This would eliminate the necessity of declaring a Monad instance for every Applicative, and eliminate the need for sets of duplicate functions such as [, , , ], [, ], and [, ].
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 .
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.
class from the class.
Such 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.

Functor

Applicative

Monad

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

fmap

liftM

map

liftA

(<*>)

ap

concat

join

fail

mzero

Pointed

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 aPointed

Applicative

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