tiposAlgebricos.hs

data Expr = Lit Int |
            Add Expr Expr |
            Sub Expr Expr
                        deriving Show

data List t = Nil | Cons t (List t)
                        deriving (Eq,Ord,Show)



data Tree t = NilT |
              Node t (Tree t) (Tree t)
                        deriving (Eq,Ord,Show)


-- Defina as seguintes funções

showExpr :: Expr -> String
showExpr (Lit n) = show n
showExpr (Add a b) = showExpr a ++ " + " ++ showExpr b
showExpr (Sub a b) = showExpr a ++ " - " ++ showExpr b


toList :: List t -> [t]
toList Nil = []
toList (Cons n l) = n : (toList l)

fromList :: [t] -> List t
fromList [] = Nil
fromList (a:as) = Cons a (fromList as)

depth :: Tree t -> Int
depth NilT = 0
depth (Node n l r) = 1 + maxi (depth l) (depth r)
   where maxi a b
           | a > b = a
           | otherwise = b         

colapse :: Tree t -> [t]
colapse NilT = []
colapse (Node n l r) = [n] ++ colapse l ++ colapse r

mapTree :: (t -> u) -> Tree t -> Tree u
mapTree f NilT = NilT   
mapTree f (Node n l r) = Node (f n) (mapTree f l) (mapTree f r)

tree1 = (Node 1 (Node 2 (NilT) (NilT)) (Node 3 (NilT) (NilT)))
tree2 = (Node "abrir" (Node "fechar" (NilT) (NilT)) (Node "exercitar" (NilT) (NilT)))