Common functors as the base of cofree comonads

data Empty a

data Cofree Empty a
   --  = a :< ...  not possible!

data Const c a = Const c

data Cofree (Const c) a
     = a :< Const c

data Writer c a = Writer c a

data Identity a = Identity a

data Cofree Identity a
     = a :< Identity (Cofree Identity a)

data Stream a = Stream a (Stream a)

data Maybe a = Just a
             | Nothing

data Cofree Maybe a
     = a :< Just (Cofree Maybe a)
     | a :< Nothing

data NonEmpty a
     = NECons a (NonEmpty a)
     | NESingle a

data Writer w a = Writer w a

data Cofree (Writer w) a
     = a :< (w, Cofree (Writer w) a)

data Stream (w,a)
     = Stream (w,a) (Stream (w,a))

data WriterT w m a = WriterT (m (w,a))

data Either e a = Left e
                | Right a

data Cofree (Either e) a
     = a :< Left e
     | a :< Right (Cofree (Either e) a)

data Hospitable e a
     = Sorry_AllIHaveIsThis_Here'sWhy a e
     | EatThis a (Hospitable e a)

data NonEmptyT (Writer e) a = NonEmptyT (e,a,[a])

data Reader x a = Reader (x -> a)

data Cofree (Reader x) a
     = a :< (x -> Cofree (Reader x) a)

data Plant x a
     = Plant a (x -> Plant x a)