Personal tools

Functor-Applicative-Monad Proposal

From HaskellWiki

(Difference between revisions)
Jump to: navigation, search
(Undo revision 38092 by Jesin (Talk) (maybe that's going a bit far for this one proposal))
(GHC Proposal)

Revision as of 10:28, 3 January 2011

The standard class hierarchy is a consequence of Haskell's historical development, rather than logic. The
, and
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 [
], [
], and [
]. A monad which requires custom handling for pattern match failures can implement
; otherwise, a failed pattern match will error in the same way as is does for pure code.
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
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
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.

1 GHC Proposal

A subset of this proposal has been formally proposed for GHC. The patches attached to the ticket make Applicative into a superclass of Monad, but does not deprecate any names.

2 See also