Is there a name for this kind of lifting a function?


I wrote a Scala function:

def liftOrIdentity[T](f: (T, T) => T) = (a: Option[T], b: Option[T]) => (a, b) match { case (Some(a), None) => Some(a) case (None, Some(b)) => Some(b) case (Some(a), Some(b)) => Some(f(a, b)) case (None, None) => None }

Is there a name for this pattern? It is not quite an applicative functor due to cases 1 and 2. Feel free to answer with Haskell or Scala code.


On collection it is flatten + reduce:

List(a, b).flatten.reduceOption(f) a ++ b reduceOption f // same result


I'm reminded of the Alternative type class in Haskell's Control.Applicative:

class Applicative f => Alternative f where empty :: f a (<|>) :: f a -> f a -> f a

A general version of your function for any instance of Alternative might look like this:

liftOrAlternative :: (Alternative f) => (a -> a -> a) -> f a -> f a -> f a liftOrAlternative f a b = f <$> a <*> b <|> a <|> b <hr />ghci> liftOrAlternative (+) (Just 1) Nothing Just 1 ghci> liftOrAlternative (+) (Just 1) (Just 2) Just 3 ghci> liftOrAlternative (+) Nothing Nothing Nothing <hr />

For Scala, I think the closest analogy to Alternative would be the ApplicativePlus type class from Scalaz.

def liftOrAlternative[A, F[_]: ApplicativePlus](f: (A, A) => A)(a: F[A], b: F[A]): F[A] = f.lift[F].apply(a, b) <+> a <+> b

I admit that liftOrAlternative is not a great name. After reading Twan van Laarhoven's answer, I think his suggestion of unionWith is much better at expressing what the function actually does.


This function is similar to the Haskell containers function

Data.Map.unionWith :: (a -> a -> a) -> Map k a -> Map k a -> Map k a

I think unionWith is a good name for it in general. The more usual applicative operator would be an intersectionWith (aka. zipWith).

Data.Map.intersectionWith :: (a -> b -> c) -> Map k a -> Map k b -> Map k c


In Haskell, there is something similar called <a href="http://hackage.haskell.org/packages/archive/base/latest/doc/html/Control-Monad.html#v%3aliftM2" rel="nofollow">liftM2</a>.

liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r


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