[Haskell-cafe] Type union

[Dmitry Bogatov]

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 at gnu.org>,
Free Software supporter, esperantisto and netiquette guardian.
GPG: 54B7F00D
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