square x = x * x

-- Compute the minimum of two numbers
mymin x y = if x<=y then x else y

fac n = if n==0 then 1 else n * fac (n-1)

-- Compute the n-th Fibonacci number
fib1 n = if n==0 then 0
                 else if n==1
                      then 1
                      else fib1 (n-1) + fib1 (n-2)

fib2' n fibn fibnp1 = if n==0
                      then fibn
                      else fib2' (n-1) fibnp1 (fibn+fibnp1)

fib2 n = fib2' n 0 1

-- with local definitions
fib3 n = g (fib3' n 0 1)
 where
  fib3' n fibn fibnp1 = if n==0
                        then fibn
                        else fib3' (n-1) fibnp1 (fibn+fibnp1)
  g x = x

fib4 n =
 let
  fib3' n fibn fibnp1 = if n==0
                        then fibn
                        else fib3' (n-1) fibnp1 (fibn+fibnp1)
  in  fib3' n 0 1

--f x y = y * (1-y) + (1 + x*y) * (1-y) + x*y
f x y = let a = 1-y
            b = x*y
         in y * a + (1+b) * a + b

-- Vorteil: weniger Parameter zu uebergeben 
isPrim n = n/= 1 && checkDiv (n-1)
 where
  checkDiv m = m==1 || mod n m /= 0 && checkDiv (m-1)