Difference between revisions of "Functor hierarchy proposal"
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| − | Currently the standard libraries include a < |
+ | Currently the standard libraries include a <hask>Functor</hask> class and a <hask>Monad</hask> class, and <hask>Functor</hask> is not a superclass of <hask>Monad</hask>, even though logically every monad is a functor. New classes have been added to HEAD to create a richer hierarchy of Functor classes: |
| + | <haskell> |
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| − | + | class Functor f where |
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| − | + | fmap :: (a -> b) -> f a -> f b |
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| − | + | class Functor f => Applicative f where |
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| − | + | pure :: a -> f a |
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| − | + | (<*>) :: f (a -> b) -> f a -> f b |
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| + | (*>) :: Applicative f => f a -> f b -> f b |
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| ⚫ | |||
| − | + | fa *> fb = (fmap (const id) fa) <*> fb |
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| + | </haskell> |
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| + | I propose that "<hask>pure</hask>" be renamed "<hask>return</hask>", "<hask>*></hask>" be renamed "<hask>>></hask>", and that <hask>Monad</hask> be made a subclass of <hask>Applicative</hask>: |
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| − | satisfying the usual Functor and Monad laws, and |
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| + | <haskell> |
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| − | fmap = ap . return |
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| ⚫ | |||
| − | ap fab fa = fab >>= (\ab -> fmap ab fa) |
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| + | (>>=) :: f a -> (a -> f b) -> f b |
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| − | :(and others) |
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| + | </haskell> |
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The downside of this is that every instance declaration of <tt>Monad</tt> would have to be accompanied by instance declarations for the superclasses. |
The downside of this is that every instance declaration of <tt>Monad</tt> would have to be accompanied by instance declarations for the superclasses. |
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Revision as of 07:02, 25 April 2006
Currently the standard libraries include a Functor class and a Monad class, and Functor is not a superclass of Monad, even though logically every monad is a functor. New classes have been added to HEAD to create a richer hierarchy of Functor classes:
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
(*>) :: Applicative f => f a -> f b -> f b
fa *> fb = (fmap (const id) fa) <*> fb
I propose that "pure" be renamed "return", "*>" be renamed ">>", and that Monad be made a subclass of Applicative:
class (Applicative f) => Monad f where
(>>=) :: f a -> (a -> f b) -> f b
The downside of this is that every instance declaration of Monad would have to be accompanied by instance declarations for the superclasses.