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Functor-Applicative-Monad Proposal

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Revision as of 16:06, 21 December 2010 by Gidyn (Talk | contribs)
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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
 
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
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.
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Categories: Proposals | Functor | Applicative Functor | Monad