在Haskell中将功能更改为Maybe功能

Question

Is it possible to write a function which takes a function like (Something -> Something) , and returns it, but with a type (Maybe Something -> Maybe Something) ?

eg:

f :: Point -> Point
f x = [some code goes here]

makeItMaybe :: (Point -> Point) -> (Maybe Point -> Maybe Point)
makeItMaybe x = ???

I know it has something to do with Monads and Applicatives, but can't really figure out how. I played around a bit with <*> and <$> , but didn't get anywhere.

Any help or pointers in the right direction would be appreciated. Thanks!

Answer 1

I think you are looking for fmap , which has type Functor f => (a -> b) -> fa -> fb . If you replace f by Maybe (since Maybe is a functor) and put the parenthesis un the right place you get (a -> b) -> (Maybe a -> Maybe b) . You were in the right direction with (<$>) , which is just an alias for fmap .

So we have makeItMaybe fx = fmap fx or, more simply, makeItMaybe = fmap .

Answer 2

The function you want is fmap :

makeItMaybe = fmap

fmap is defined by the Functor typeclass:

fmap :: Functor f => (a -> b) -> f a -> f b

Maybe has a functor instance so fmap specialised to Maybe has type

(a -> b) -> Maybe a -> Maybe b

Answer 3

This functions satisfies the signature, but I don't know if it is what you want:

makeItMaybe :: (a -> a) -> (Maybe a -> Maybe a)
makeItMaybe f (Just x) = Just (f x)
makeItMaybe f Nothing  = Nothing

As @baxbaxwalanuksiwe and @Lee pointed out, it is fmap instance of Maybe from the Functor typeclass.