Hi there Patrick, Patrick Browne wrote:

Thanks for you very clear explanation. Without committing to some concrete representation such as list I do not know how to specify constructors in the class (see below). As you point out a class may not be appropriate for an actual application, but I am investigating the strengths and weaknesses of class as a unit of *specification*. Regards, Pat

-- Class with functional dependency class QUEUE_SPEC_CLASS2 a q | q -> a where    newC2 :: q a -- ??    sizeC2  :: q a -> Int    restC2  :: q a -> Maybe (q a)    insertC2 :: q a -> a -> q a -- Without committing to some concrete representation such as list I do not know how to specify constructor for insertC2 ?? =  ?? insertC2  newC2 a = newC2 -- wrong isEmptyC2  :: q a -> Bool    isEmptyC2 newC2  = True --   isEmptyC2 (insertC2 newC2 a) = False wrong

You are probably confusing the type class system with something from OOP. A type class captures a pattern in the way a type is used. The corresponding concrete representation of that pattern is then written in the instance definition: class Stacklike s where emptyStack :: s a push :: a -> s a -> s a rest :: s a -> Maybe (s a) top :: s a -> Maybe a pop :: s a -> Maybe (a, s a) pop s = liftA2 (,) (top s) (rest s) instance Stacklike [] where emptyStack = [] push = (:) top = foldr (\x _ -> Just x) Nothing rest [] = Nothing rest (Push _ xs) = Just xs data MyStack a = Empty | Push a (MyStack a) instance Stacklike MyStack where emptyStack = Empty push = Push top Empty = Nothing top (Push x _) = Just x rest Empty = Nothing rest (Push _ xs) = Just xs Greets, Ertugrul -- Not to be or to be and (not to be or to be and (not to be or to be and (not to be or to be and ... that is the list monad.