[Haskell-beginners] question about list processing

What would be an elegant way of writing this computeHead :: (a -> [b]) -> [a] -> [b] Where when [a] is null, it returns a null list, but when [a] contains one or more elements, it applies the given function to the head of a and returns that? Is there some existing typeclass operator that facilitates this? You can write computeHead _ [] = [] computeHead f (x:_) = f x But that first line seems suspicious to me... it makes me think about how in the list Monad, an empty list falls through. But I can't quite make it work.