module Proof.Propositional.Empty (Empty(..), withEmpty, withEmpty') where
import Data.Void (Void, absurd)
import GHC.Generics
import Unsafe.Coerce (unsafeCoerce)
class Empty a where
eliminate :: a -> x
default eliminate :: (Generic a, GEmpty (Rep a)) => a -> x
eliminate = geliminate . from
class GEmpty f where
geliminate :: f a -> x
instance GEmpty f => GEmpty (M1 i t f) where
geliminate (M1 a) = geliminate a
instance (GEmpty f, GEmpty g) => GEmpty (f :+: g) where
geliminate (L1 a) = geliminate a
geliminate (R1 b) = geliminate b
instance Empty c => GEmpty (K1 i c) where
geliminate (K1 a) = eliminate a
instance GEmpty V1 where
geliminate = \ case {}
deriving instance (Empty a, Empty b) => Empty (Either a b)
deriving instance Empty Void
newtype MagicEmpty e a = MagicEmpty (Empty e => a)
withEmpty :: forall a b. (a -> Void) -> (Empty a => b) -> b
withEmpty neg k = unsafeCoerce (MagicEmpty k :: MagicEmpty a b) (absurd . neg)
withEmpty' :: forall a b. (forall c. a -> c) -> (Empty a => b) -> b
withEmpty' neg k = unsafeCoerce (MagicEmpty k :: MagicEmpty a b) neg