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{-# LANGUAGE InstanceSigs #-}
module Twinplicative where
newtype Identity a
= Identity { runIdentity :: a }
instance Functor Identity where
fmap f (Identity a) = Identity (f a)
newtype Compose f g a =
Compose { getCompose :: f (g a) }
deriving (Eq, Show)
instance (Functor f, Functor g) =>
Functor (Compose f g) where
fmap f (Compose fga) =
Compose $ (fmap . fmap) f fga
-- instance types provided as they may help.
instance (Applicative f, Applicative g)
=> Applicative (Compose f g) where
pure :: a -> Compose f g a
pure x = Compose $ (pure . pure) x
(<*>) :: Compose f g (a -> b)
-> Compose f g a
-> Compose f g b
(Compose f) <*> (Compose a) = Compose $ (fmap (<*>) f) <*> a
instance (Foldable f, Foldable g) =>
Foldable (Compose f g) where
foldMap f (Compose fga) =
(foldMap . foldMap) f fga
instance (Traversable f, Traversable g) =>
Traversable (Compose f g) where
traverse :: Applicative f1 => (a -> f1 b)
-> Compose f g a
-> f1 (Compose f g b)
traverse f (Compose fga) =
Compose <$> (traverse . traverse) f fga
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