module BS
where

dieZahl :: Integer
dieZahl =  6 * (3 + 4)

square          :: Integer -> Integer
square x        = x * x

smaller         :: (Integer, Integer) -> Integer
smaller (x,y)   = if x <= y then x else y

smallerc        :: Integer -> (Integer -> Integer)
smallerc x y    =  if x <= y then x else y

three           :: Integer -> Integer
three x         =  3

infinity        :: Integer
infinity        = infinity + 1

multiply        :: (Integer, Integer) -> Integer
multiply (x, y) =  if x == 0 then 0 else x * y

double, double2 :: Integer -> Integer

double  x       =  x + x
double2 x       =  2 * x

plus            :: (Integer, Integer) -> Integer
plus (x, y)     = x + y

incr            :: Integer -> Integer
incr y          = plus (1, y)

plusc           :: Integer -> (Integer -> Integer)
plusc x y       = x + y

incrc           :: Integer -> Integer
incrc           = plusc 1

twice           :: (Integer -> Integer) -> (Integer -> Integer)
twice f x       = f (f x)

quad            :: Integer -> Integer
quad            = twice square

quad'           :: Integer -> Integer
quad'           =  square . square

signum          :: Integer -> Integer
signum x
  | x < 0       = -1
  | x == 0      = 0
  | x > 0       = 1

fact            :: Integer -> Integer
fact n
  | n < 0       = error "fact with negative argument"
  | n == 0      = 1
  | n > 0       = n * fact (n - 1)

f       :: Float -> Float -> Float
f x y   = (a + 1) * (a + 2)
          where
          a = (x + y) / 2

f2      :: Float -> Float -> Float
f2 x y  = (a + 1) * (b + 2)
          where
          a = m / 2
          b = m / 3
          m = x + y