Functor => Applicative => Monad

[Maciej Piechotka]

On Mon, 2010-12-06 at 15:47 +0000, Stephen Tetley wrote:
> Me thinks there's more value that "the next language after Haskell"
> might have such a hierarchy than Haskell itself.
> 
> At Haskell 1.3 I think there was one text book (Davie), possibly none
> at Haskell 1.4 and many at Haskell 98. The value of invalidating 12 or
> so years of documentation for "logic" seems somewhat questionable from
> my perspective. If either proposal were limited to just adding class
> constraints to get the desired hierarchy rather than eliminating
> methods, they might have more legs...

As far as I understend you, you would prefer:

class Functor f where
    fmap :: (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 -> m b -> m b
    (>>) = (*>)
    (>>=) :: m a -> (a -> m b) -> m b
    f >>= x = join $ map f x
    return :: a -> m a
    return = pure
    join :: m (m a) -> m a
    join x = x >>= id

or.

class Functor f where
    fmap :: (a -> b) -> f a -> f b
 
class Functor f => Pointed f where
    point :: a -> f a

class Pointed f => Applicative f where
    pure :: a -> f a
    pure = point
    (<*>) :: 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 -> m b -> m b
    (>>) = (*>)
    (>>=) :: m a -> (a -> m b) -> m b
    f >>= x = join $ map f x
    return :: a -> m a
    return = pure
    join :: m (m a) -> m a
    join x = x >>= id

Regards
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