Flip Maybe and List

Question

I want a function that takes in a list of Maybe a, and returns Just [a] if all contents are Just a, otherwise returns Nothing.

f :: [Maybe a] -> Maybe [a]
-- f [Just x, Just y ] = Just [x, y]
-- f [Just x, Nothing] = Nothing

I think it doesn't have to be Maybe and List but any Functor Applicative or Monad, but I can't think up the way.

Answer 1

This is a great example of where hoogle comes in handy. It's a search engine where you can enter a type signature and get the functions that match—even if they are more polymorphic.

Entering [Maybe a] -> Maybe [a] we get a bunch of results.

The first one is:

sequence :: Monad m => [m a] -> m [a]

We can try this out in GHCi:

Prelude> let xs = [Just 1, Just 2, Just 3]
Prelude> sequence xs
Just [1,2,3]
Prelude> let xs = [Just 1, Nothing, Just 3]
Prelude> sequence xs
Nothing

Hey, look at that: exactly what we were looking for! So the function you want is sequence which also happens to work for types other than Maybe.