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

-- Computes the minimum of two numbers
mymin :: Int -> Int -> Int
mymin x y = if x<y then x else y

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


-- Computes the n-th Fibonacci number. Mathematical definition!
fib1 :: Int -> Int
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 the n-th and (n-1)-th Fib. number.
fib2' :: Int -> Int -> Int -> Int
fib2' fibn fibnp1 n = if n==0 then fibn
                              else fib2' fibnp1 (fibn + fibnp1) (n-1)

-- Computes the n-th Fibonacci number.
fib2 :: Int -> Int
fib2 n = fib2' 0 1 n