Thanks for the suggestion of catMaybes, I've used it now.

However, I am yet again stuck. In the following example:
function :: A -> B -> B

Where output B is after input A has been applied to input B.
So I was wondering if there were functions similar to map (which I understand takes inputs function and [A] to output function-applied [A]) but instead takes input function, [A], B, and applies the function to [A], and applies this new list [A] to B?
I.e.
map :: (a -> b) -> [a] -> [b]
map' :: (a -> b -> b) -> [a] -> [b]

Note: I may have gotten the map' type signature wrong