Haskell语言学习笔记(63)Dicidable
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2024-01-29 19:19:40
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Dicidable
class Divisible f => Decidable f where
lose :: (a -> Void) -> f a
choose :: (a -> Either b c) -> f b -> f c -> f a
lost :: Decidable f => f Void
lost = lose id
chosen :: Decidable f => f b -> f c -> f (Either b c)
chosen = choose id
Predicate 是个 Decidable
newtype Predicate a = Predicate { getPredicate :: a -> Bool }
instance Decidable Predicate where
lose f = Predicate $ \a -> absurd (f a)
choose f (Predicate g) (Predicate h) = Predicate $ either g h . f
Comparison 是个 Decidable
newtype Comparison a = Comparison { getComparison :: a -> a -> Ordering }
instance Decidable Comparison where
lose f = Comparison $ \a _ -> absurd (f a)
choose f (Comparison g) (Comparison h) = Comparison $ \a b -> case f a of
Left c -> case f b of
Left d -> g c d
Right{} -> LT
Right c -> case f b of
Left{} -> GT
Right d -> h c d
应用 Decidable
Prelude Data.Functor.Contravariant Data.Functor.Contravariant.Divisible> getPredicate (choose (\x -> if x `mod` 2==1 then Left (x `div` 2) else Right (x `div` 2)) (Predicate (<2)) (Predicate (<3))) 5
False
Prelude Data.Functor.Contravariant Data.Functor.Contravariant.Divisible> getPredicate (choose (\x -> if x `mod` 2==1 then Left (x `div` 2) else Right (x `div` 2)) (Predicate (<2)) (Predicate (<3))) 4
True
参考链接
ZuriHac 2015 - Discrimination is Wrong: Improving Productivity“`