reverse' :: [a] -> [a]
reverse' [] = []
reverse' (x:xs) = reverse' xs ++ [x]

reverseH :: [a] -> [a] -> [a]
reverseH [] ys = ys
reverseH (x:xs) ys = reverseH xs (x:ys)

reverse'' :: [a] -> [a]
reverse'' l = reverseH l []


reverseH' :: [a] -> [a] -> [a]
reverseH' l1 l2 = myfoldl  (\ z y -> y:z) l2 l1

reverse''' :: [a] -> [a]
reverse''' l = reverseH' l []



summation :: [Int] -> Int
summation [] = 0
summation (x:xs) = x + summation xs








-- filter
filter' :: (a -> Bool) -> [a] -> [a]
filter' f [] = []
filter' f (x:xs) =
  if f x then x : filter' f xs
  else filter' f xs



length' :: [a] -> Int
length' [] = 0
length' (x:xs) = 1 + length' xs

length'' :: [a] -> Int
length'' l = foldr' (\ x r -> 1 + r) 0 l 

append :: [a] -> [a] -> [a]
append [] y = y
append (x:xs) y = x : append xs y

append' :: [a] -> [a] -> [a]
append' l1 l2 = foldr' (\ x r -> (:) x r) l2 l1

foldr' :: (a -> b -> b) -> b -> [a] -> b
foldr' f x [] = x
foldr' f x (y:ys) = f y (foldr' f x ys)

-- Higher order functions
map' :: (a -> b) -> [a] -> [b]
map' f [] = []
map' f (x:xs) = f x : map' f xs

map'' :: (a -> b) -> [a] -> [b]
map'' f l = foldr' (\ x r -> f x : r) [] l


myfoldl :: (b -> a -> b) -> b -> [a] -> b
myfoldl f x [] = x
myfoldl f x (y:ys) = myfoldl f (f x y) ys


summationH :: [Int] -> Int -> Int
summationH [] x = x
summationH (y:ys) x = summationH ys (y + x)

summation' :: [Int] -> Int
summation' l = summationH l 0


summationH' :: [Int] -> Int -> Int
summationH' l x = myfoldl (\ z y -> y + z) x l

summation'' :: [Int] -> Int
summation'' l = summationH' l 0

data Pair a b = P a b

first :: Pair a b -> a
first (P x y) = x

data Bool' = T | F
  deriving (Show, Eq)

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

l1 :: List Int
l1 = Cons 1 (Cons 2 (Cons 3 Nil))

l2 :: List Int
l2 = Cons 4 (Cons 5 (Cons 6 Nil))

my_append :: List a -> List a -> List a
my_append Nil l = l
my_append (Cons x xs) l = Cons x (my_append xs l)


data Tree a = Leaf | Node a (Tree a) (Tree a)
  deriving (Show, Eq)

tr1 :: Tree Int
tr1 = Node 5 (Node 4 Leaf Leaf) (Node 6 (Node 7 Leaf Leaf) Leaf)