```init' [x] = []
init' (x:xs) = x:(init' xs)

last' [x] = x
last' (_:xs) = last' xs

reverse' [] = []
reverse' (x:xs) = (reverse' xs) ++ [x]

take' 0 xs = []
take' n (x:xs) = x:(take' (n-1) xs)

repeat' x = x:(repeat' x)

-- laziness!!
replicate' n x = take n (repeat' x)

-- don't try this in Scheme!!
ifThenElse x y z = if x then y else z

fact n = ifThenElse (n == 0) 1 (n*fact(n-1))

drop' 0 xs = xs
drop' n (x:xs) = drop (n-1) xs

product' [] = 1
product' (x:xs) = x*(product' xs)

cycle' xs = xs ++ (cycle' xs)

-- tuples
fst (x, _) = x

snd (_, y) = y

zip' [] _ = []
zip' (x:xs) (y:ys) = (x,y):(zip' xs ys)

-- curried tail fact
fact :: (Num t) => t -> t -> t
fact 0 acc = acc
fact x acc = fact (x-1) (x*acc)

-- uncurried tail fact
fact' :: (Num t) => (t, t) -> t
fact' (0, acc) = acc
fact' (x, acc) = fact' (x-1, x*acc)

-- uncurry is like apply
fact' (x, acc) = (uncurry fact) (x, acc)

-- point free
fact' = uncurry fact

-- curry is like the opposite of apply
fact x acc = (curry fact') x acc

-- point free
fact = curry fact'

-- multiple return values
funny (x, acc) = (x+1, x*acc)

church _ 0 = id
church f n = f . (church f (n-1))

xs !! n = head \$ (church tail n)

funnyFact n = snd \$ (church funny n) (1,1)
```