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Functor-Applicative-Monad Proposal

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(pure -> return)
(Note about the possibility of splitting off a Pointed class)
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listMap = map
 
listMap = map
 
</haskell>
 
</haskell>
  +
  +
Another variant might be to split a <hask>Pointed</hask> class from the <hask>Applicative</hask> class.
  +
  +
<haskell>
  +
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
  +
</haskell>
  +
  +
Such <hask>Pointed</hask> 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.
   
 
[[Category:Proposals]]
 
[[Category:Proposals]]

Revision as of 15:48, 7 December 2010

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
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
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.