-- Computes the factorial of a number
fac :: Integer -> Integer
fac n = if n == 0 then 1 else n * fac (n - 1)

{-

fac 2 = if 2 == 0 then 1 else 2 * fac (2 - 1)
      = if False  then 1 else 2 * fac (2 - 1)
      = 2 * fac (2 - 1)
      = 2 * fac 1
      = 2 * if 1 == 0 then 1 else 1 * fac (1 - 1)
      = 2 * if False  then 1 else 1 * fac (1 - 1)
      = 2 * 1 * fac (1 - 1)
      = 2 * 1 * fac 0
      = 2 * 1 * if 0 == 0 then 1 else 0 * fac (0 - 1)
      = 2 * 1 * if True   then 1 else 0 * fac (0 - 1)
      = 2 * 1 * 1
      = 2 * 1
      = 2

-}

-- Computes the n-th Fibonacci number
fib1 :: Integer -> Integer
fib1 n = if n == 0 then 0
                   else if n == 1 then 1
                                  else fib1 (n - 1) + fib1 (n - 2)


-- Computes the n-th Fibonacci number with accumulators:
fib2 :: Integer -> Integer
fib2 n = fib2iter 0 1 n
 where
  fib2iter fibn fibnp1 n = if n == 0
                             then fibn
                             else fib2iter fibnp1 (fibn + fibnp1) (n - 1)

-- Computes the n-th Fibonacci number with accumulators:
fib3 :: Integer -> Integer
fib3 n =
 let fib3iter fibn fibnp1 n = if n == 0
                                then fibn
                                else fib3iter fibnp1 (fibn + fibnp1) (n - 1)
 in fib3iter 0 1 n

--f :: Int -> Int
f :: Float -> Float
f x = 2 * (let y = 3 * x
               z = x + y
           in 45 * z + y) + 2 * x

-- Is a number prime?
isPrim :: Int -> Bool
isPrim n = (n /= 1) && isSmallerDiv (div n 2)
 where
  isSmallerDiv d = d == 1 || ( mod n d /= 0 && isSmallerDiv (d - 1) )