    -- |
    -- 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)