Is there a simple existing library that provides views of data types in terms of unit, product and sum? Here's what I threw together for my own use. I used associated types, though functional dependencies would work as well. class HasView t where type View t view :: t -> View t unview :: View t -> t -- View instances instance HasView (Maybe a) where type View (Maybe a) = Either () a view Nothing = (Left ()) view (Just a) = (Right a) unview (Left ()) = Nothing unview (Right a) = (Just a) instance HasView [a] where type View [a] = Either () (a,[a]) view [] = (Left ()) view (a:as) = (Right (a,as)) unview (Left ()) = [] unview (Right (a,as)) = (a:as) onView2 :: (HasView a, HasView b, HasView c) => (View a -> View b -> View c) -> (a -> b -> c) onView2 op a b = unview (view a `op` view b) Thanks, - Conal