1. 列表表示

module Queue(Queue,emptyQueue,queueEmpty,enqueue,dequeue,front) where 

newtype Queue a = Q [a]
    deriving Show 

emptyQueue :: Queue a 
emptyQueue = Q []

queueEmpty :: Queue a -> Bool
queueEmpty (Q []) = True 
queueEmpty (Q _) = False

enqueue :: a -> Queue a -> Queue a 
enqueue x (Q q) = Q (q ++ [x])

dequeue :: Queue a -> Queue a 
dequeue (Q (_:xs)) = Q xs 
dequeue (Q []) = error "dequeue: empty queue"

front :: Queue a -> a 
front (Q (x:_)) = x
front (Q []) = error "front: empty queue"

2. 使用兩個(gè)列表

module Queue(Queue,emptyQueue,queueEmpty,enqueue,dequeue,front) where 

newtype Queue a = Q ([a], [a])

emptyQueue :: Queue a 
emptyQueue = Q ([], [])

queueEmpty :: Queue a -> Bool
queueEmpty (Q ([], [])) = True 
queueEmpty _ = False

enqueue :: a -> Queue a -> Queue a 
enqueue x (Q ([], [])) = Q ([x], [])
enqueue y (Q (xs, ys)) = Q (xs, y:ys)

dequeue :: Queue a -> Queue a 
dequeue (Q ([], [])) = error "dequeue: empty queue"
dequeue (Q ([], ys)) = Q (tail $ reverse ys, [])
dequeue (Q (x:xs, ys)) = Q (xs, ys)

front :: Queue a -> a 
front (Q ([], [])) = error "front: empty queue"
front (Q ([], ys)) = last ys
front (Q (x:xs, ys)) = x

instance (Show a) => Show (Queue a) where 
    showsPrec p (Q (front, rear)) str = 
        showString "Q " (showList (front ++ reverse rear) str)

參考

Algorithms: A Functional Programming Approach