-- Import our simplified Prelude:
import SimplePrelude

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

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

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


-- Computes the n-th Fibonacci number (inefficient exponential version).
fib :: Int -> Int
fib n = if n == 0 then 0
                  else if n == 1
                         then 1
                         else fib (n-1) + fib (n-2)

-- Computes the n-th Fibonacci number (efficient version).
fib2 :: Int -> Int
fib2 n = fib2iter 0 1 n

fib2iter :: Int -> Int -> Int -> Int
fib2iter fibn fibnplus1 n =
  if n==0 then fibn
          else fib2iter fibnplus1 (fibn + fibnplus1) (n-1)

-- Computes the n-th Fibonacci number (efficient version with local decl.).
fib3 :: Int -> Int
fib3 n = iter 0 1 n
 where
  iter :: Int -> Int -> Int -> Int
  iter fibn fibnplus1 n =
    if n==0 then fibn
            else iter fibnplus1 (fibn + fibnplus1) (n-1)

-- Computes the n-th Fibonacci number (efficient version with local decl.).
fib4 :: Int -> Int
fib4 n = let iter fibn fibnplus1 n =
               if n==0 then fibn
                       else iter fibnplus1 (fibn + fibnplus1) (n-1)
         in iter 0 1 n

test = let x = 2
           y = let z = x + x*2
               in z*z
       in y - x

-- Check if a number is prime.
isPrim :: Int -> Bool
isPrim n = n > 1 && notDivide (div n 2)
 where
  notDivide m = m == 1 || mod n m /= 0 && notDivide (m - 1)
  -- notDivide n m = m == 1 || (mod n m /= 0 && notDivide n (m - 1))