-- Computes the square of a number.
square :: Int -> Int
square x = x * x

-- Computes the mininmum of two numbers.
mini :: Int -> Int -> Int
mini x y = if x <= y then x else y

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

{-
fac 2 = if 2 == 0 then 1 else fac (2 - 1) * 2
      = if False  then 1 else fac (2 - 1) * 2
      = fac (2 - 1) * 2
      = fac 1 * 2
      = (if 1 == 0 then 1 else fac (1 - 1) * 1) * 2
      = (if False  then 1 else fac (1 - 1) * 1) * 2
      = (fac (1 - 1) * 1) * 2
      = (fac 0 * 1) * 2
      ...
      = (1 * 1) * 2
      = 1 * 2
      = 2
-}

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