Hello! I am trying to create type safe boolean formula representation. Main operation is substion of particular value, to get another formula, and function that accept formula to calculate it's value. So target is: a = Conjunction (Var X) (Var Y) is 2 variable formula value (apply (X, True) . apply (Y, True) $ a) -- True and neither value a apply (X, True) . apply (X, False) $ a typechecks. How can I archive it? class Union a b c instance (a ~ b) => Union a b b instance Union a b (a, b) data P = P deriving Show data Q = Q deriving Show class (Show a) => Variable a instance Variable P instance Variable Q data Formula t where Prop :: (Variable b) => b -> Formula b Conjunction :: (Union t1 t2 t3) => Formula t1 -> Formula t2 -> Formula t3 deriving instance Show (Formula t) main = print (Conjunction (Prop P) (Prop Q) :: Int) This complains on ambitious t3. Attempt by typefamilies fails, since type family Union t1 t2 :: * data Void type instance Union a a = a type instance Union (a, b) a = (a, b) type instance Union (a, b) b = (a, b) type instance Union (a, b) c = (a, b, c) type instance Union a (a, b) = (a, b) type instance Union b (a, b) = (a, b) type instance Union c (a, b) = (a, b, c) type instance Union (a, b, c) a = (a, b, c) type instance Union (a, b, c) b = (a, b, c) type instance Union (a, b, c) c = (a, b, c) type instance Union (a, b, c) d = Void type instance Union a (a, b, c) = (a, b, c) type instance Union b (a, b, c) = (a, b, c) type instance Union c (a, b, c) = (a, b, c) type instance Union d (a, b, c) = Void this is somewhy conflicting instances. I am out of ideas. -- Best regards, Dmitry Bogatov <KAction@gnu.org>, Free Software supporter, esperantisto and netiquette guardian. GPG: 54B7F00D