Data/Functor/Identity.hs

    -- |
    -- Module      :  Data.Functor.Identity
    -- Copyright   :  (c) Andy Gill 2001,
    --                (c) Oregon Graduate Institute of Science and Technology 2001
    -- License     :  BSD-style (see the file LICENSE)
    --
    -- Maintainer  :  ross@soi.city.ac.uk
    -- Stability   :  experimental
    -- Portability :  portable
    --
    -- The identity functor and monad.
    --
    -- This trivial type constructor serves two purposes:
    --
    -- * It can be used with functions parameterized by functor or monad classes.
    --
    -- * It can be used as a base monad to which a series of monad
    --   transformers may be applied to construct a composite monad.
    --   Most monad transformer modules include the special case of
    --   applying the transformer to 'Identity'.  For example, @State s@
    --   is an abbreviation for @StateT s 'Identity'@.

    module Data.Functor.Identity (
        Identity(..),
       ) where

    import Control.Applicative
    import Control.Monad
    import Control.Monad.Fix
    import Data.Foldable (Foldable(foldMap))
    import Data.Traversable (Traversable(traverse))

    -- | Identity functor and monad.
    newtype Identity a = Identity { runIdentity :: a }

    -- ---------------------------------------------------------------------------
    -- Identity instances for Functor and Monad

    instance Functor Identity where
        fmap f m = Identity (f (runIdentity m))

    instance Foldable Identity where
        foldMap f (Identity x) = f x

    instance Traversable Identity where
        traverse f (Identity x) = Identity <$> f x

    instance Applicative Identity where
        pure a = Identity a
        Identity f <*> Identity x = Identity (f x)

    instance Monad Identity where
        return a = Identity a
        m >>= k  = k (runIdentity m)

    instance MonadFix Identity where
        mfix f = Identity (fix (runIdentity . f))