module Q where
import Test.QuickCheck

data Q a = Q [a] [a] deriving (Eq,Show)
----------------------------
empty   :: Q a
add     :: a -> Q a -> Q a
remove  :: Q a -> Q a 
front   :: Q a -> a
isEmpty :: Q a -> Bool
---------------------------

empty = Q [] []
add x (Q fs bs)      = q fs (x:bs)
remove (Q (f:fs) bs) = q fs bs
isEmpty (Q fs bs)    = null fs -- && null bs
front (Q (f:fs) bs)  = f

-- smart constructor 
q :: [a] -> [a] -> Q a
q [] bs = Q (reverse bs) []
q fs bs = Q fs bs

-- invariant

-- properties of operators

-- Equivalence of slow and fast queues
-- convert :: Q Int -> SlowQ.Q Int


{- -- Random generator for queues
   -- For now this is magic; see lecture 3B!
instance Arbitrary a => Arbitrary (Q a) where
  arbitrary = 
   do front <- arbitrary
      back <- arbitrary
      return (q front back)
 -}