Haskell: Defining map function using unfold

Question

I have the following Haskell method

unfold :: (a -> Bool) -> (a -> b) -> (a -> a) -> a -> [b]
unfold p h t x
    | p x       = []
    | otherwise = (h x):(unfold p h t (t x))

How can i define the regular prelude map f x method using this given unfold method.

Answer 1

If you define:

map' :: (a -> b) -> [a] -> [b]
map' f = unfold null (f.head) tail

then

\> map' show [1..5]
["1","2","3","4","5"]
\> map' (+1) []
[]