-- Factorial function with conditional:
facif :: Integer -> Integer
facif n = if n == 0 then 1
                    else n * facif (n - 1)

add1 :: Int -> Int -> Int
add1 x y = x + y

add2 :: Int -> (Int -> Int)
add2 x = \y -> x + y

add3 :: (Int,Int) -> Int
add3 (x,y) = x + y

-- Own data types: algebraic data types: enumeration all constructors
-- Constructors: define the actual data

-- data Tau = C1 tau11 ... t1n_1 | ... | Ck tauk1 ... tkn_k

-- Enumeration types:
--data Bool = False | True
data Color = Blue | Green | Yellow

-- Record types:
data Complex = Complex Float Float

-- Variant records: Integer lists
data IntList = Nil | Cons Int IntList

list123 :: IntList
list123 = Cons 1 (Cons 2 (Cons 3 Nil))

-- Binary integer trees:
data IntTree = Leaf Int | Node IntTree IntTree

tree123 :: IntTree
tree123 = Node (Leaf 1) (Node (Leaf 2) (Leaf 3))

addLeaves :: IntTree -> Int
addLeaves (Leaf n)     = n
addLeaves (Node t1 t2) = addLeaves t1 + addLeaves t2