-- | Abstract Data Type Example: Efficient Queues
-- Functional Programming course 2016.
-- Thomas Hallgren
module Queue(Q,empty,add,isEmpty,front,remove) where

data Q a = Q [a] [a] deriving (Show)


-- | An empty queue
empty   :: Q a
empty = smartQ [] []

-- | Add an element at the back
add     :: a -> Q a -> Q a
add x (Q fs bs) = smartQ fs (x:bs)

-- | Check if the queue is empty
isEmpty :: Q a -> Bool
isEmpty (Q [] _) = True
isEmpty _        = False

-- | Inspect the front element
front   :: Q a -> a
front (Q (x:fs) bs) = x

-- | Remove an element from the front
remove  :: Q a -> Q a
remove (Q (x:fs) bs) = smartQ fs bs


-- Invariant: queue not empty => front list not empty

-- A smart constructor

smartQ [] bs = Q (reverse bs) []
smartQ fs bs = Q fs bs

instance Eq a => Eq (Q a) where
  q1 == q2 = toList q1 == toList q2

toList (Q fs bs) = fs++reverse bs