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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)
mapListIf p f = reduceList (\x xs ->
if p x then Cons (f x) xs
else Cons x xs)
appendList xs1 xs2 = reduceList Cons xs2 xs1
reverseList = reduceList (\x xs -> xs `appendList` (Cons x Nil)) Nil
data Tree a = Node a (List (Tree a)) deriving Show
tree = Node 1
(Cons (Node 2 Nil)
(Cons (Node 3
(Cons (Node 5 Nil)
(Cons (Node 6 Nil) Nil)))
(Cons (Node 4 Nil) Nil)))
reduceTree f g z (Node x trees) =
f x (reduceList g z (mapList (reduceTree f g z) trees))
idTree = reduceTree Node Cons Nil
mapTree f = reduceTree (Node . f) Cons Nil
reduceListTree f g z trees =
reduceList f z (mapList (reduceTree g f z) trees)
tree2ListTree tree = Cons tree Nil
mapListTree f = reduceListTree Cons (Node . f) Nil
filterListTree p = reduceListTree (\n@(Node x trees) ts ->
if p x then Cons n ts
else trees `appendList` ts)
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