{-# LANGUAGE RankNTypes, ScopedTypeVariables #-}
{-# LANGUAGE DataKinds, DefaultSignatures, DeriveAnyClass, EmptyCase #-}
{-# LANGUAGE ExplicitNamespaces, FlexibleContexts, FlexibleInstances #-}
{-# LANGUAGE GADTs, KindSignatures, LambdaCase, PolyKinds #-}
{-# LANGUAGE StandaloneDeriving, TupleSections, TypeOperators #-}
module Proof.Propositional.Empty (Empty(..), withEmpty, withEmpty') where
import Data.Void (Void, absurd)
import GHC.Generics
import Unsafe.Coerce (unsafeCoerce)
-- | Type-class for types without inhabitants, dual to @'Proof.Propositional.Inhabited'@.
-- Current GHC doesn't provide selective-instance,
-- hence we don't @'Empty'@ provide instances
-- for product types in a generic deriving (DeriveAnyClass).
--
-- To derive an instance for each concrete types,
-- use @'Proof.Propositional.refute'@.
--
-- Since 0.4.0.0.
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)
-- | Giving falsity witness by proving @'Void'@ from @a@.
-- See also 'withEmpty''.
--
-- Since 0.4.0.0
withEmpty :: forall a b. (a -> Void) -> (Empty a => b) -> b
withEmpty neg k = unsafeCoerce (MagicEmpty k :: MagicEmpty a b) (absurd . neg)
-- | Giving falsity witness by showing @a@ entails everything.
-- See also 'withEmpty'.
--
-- Since 0.4.0.0
withEmpty' :: forall a b. (forall c. a -> c) -> (Empty a => b) -> b
withEmpty' neg k = unsafeCoerce (MagicEmpty k :: MagicEmpty a b) neg