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-- |
-- Module : Data.Functor.Compose
-- Copyright : (c) Ross Paterson 2010
-- License : BSD-style (see the file LICENSE)
--
-- Maintainer : ross@soi.city.ac.uk
-- Stability : experimental
-- Portability : portable
--
-- Composition of functors.
module Data.Functor.Compose (
Compose(..),
) where
import Control.Applicative
import Data.Foldable (Foldable(foldMap))
import Data.Traversable (Traversable(traverse))
-- | Right-to-left composition of functors.
-- The composition of applicative functors is always applicative,
-- but the composition of monads is not always a monad.
newtype Compose f g a = Compose { getCompose :: f (g a) }
instance (Functor f, Functor g) => Functor (Compose f g) where
fmap f (Compose x) = Compose (fmap (fmap f) x)
instance (Foldable f, Foldable g) => Foldable (Compose f g) where
foldMap f (Compose t) = foldMap (foldMap f) t
instance (Traversable f, Traversable g) => Traversable (Compose f g) where
traverse f (Compose t) = Compose <$> traverse (traverse f) t
instance (Applicative f, Applicative g) => Applicative (Compose f g) where
pure x = Compose (pure (pure x))
Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)
instance (Alternative f, Applicative g) => Alternative (Compose f g) where
empty = Compose empty
Compose x <|> Compose y = Compose (x <|> y)
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