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