# Functor-Applicative-Monad Proposal

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
pure :: 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
etc.
```

And for those who really want a list map,

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