reduce.hs

data List a = Nil
            | Cons a (List a)
              deriving Show

xs = Cons 1 (Cons 2 (Cons 3 Nil))

reduceList f z Nil         = z 
reduceList f z (Cons x xs) = f x (reduceList f z xs)

idList = reduceList Cons Nil

mapList f = reduceList (Cons . f) Nil

filterList p = reduceList (\x xs -> 
                             if p x then Cons x xs
                             else xs) 
                          Nil

mapListIf p f = reduceList (\x xs ->
                              if p x then Cons (f x) xs
                              else Cons x xs)
                           Nil

appendList xs1 xs2 = reduceList Cons xs2 xs1

reverseList = reduceList (\x xs -> xs `appendList` (Cons x Nil)) Nil