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.