    {- |
    Module      :  Control.Monad.Identity
    Copyright   :  (c) Andy Gill 2001,
                   (c) Oregon Graduate Institute of Science and Technology 2001,
                   (c) Jeff Newbern 2003-2006,
                   (c) Andriy Palamarchuk 2006
    License     :  BSD-style (see the file libraries/base/LICENSE)

    Maintainer  :  libraries@haskell.org
    Stability   :  experimental
    Portability :  portable

    [Computation type:] Simple function application.

    [Binding strategy:] The bound function is applied to the input value.
    @'Identity' x >>= f == 'Identity' (f x)@

    [Useful for:] Monads can be derived from monad transformers applied to the
    'Identity' monad.

    [Zero and plus:] None.

    [Example type:] @'Identity' a@

    The @Identity@ monad is a monad that does not embody any computational strategy.
    It simply applies the bound function to its input without any modification.
    Computationally, there is no reason to use the @Identity@ monad
    instead of the much simpler act of simply applying functions to their arguments.
    The purpose of the @Identity@ monad is its fundamental role in the theory
    of monad transformers.
    Any monad transformer applied to the @Identity@ monad yields a non-transformer
    version of that monad.

      Inspired by the paper
      /Functional Programming with Overloading and
          Higher-Order Polymorphism/,
        Mark P Jones (<http://web.cecs.pdx.edu/~mpj/>)
          Advanced School of Functional Programming, 1995.
    -}

    module Control.Monad.Identity (
        Identity(..),

        module Control.Monad,
        module Control.Monad.Fix,
       ) where

    import Control.Monad
    import Control.Monad.Fix

    {- | Identity wrapper.
    Abstraction for wrapping up a object.
    If you have an monadic function, say:

    >   example :: Int -> Identity Int
    >   example x = return (x*x)

         you can \"run\" it, using

    > Main> runIdentity (example 42)
    > 1764 :: Int

    A typical use of the Identity monad is to derive a monad
    from a monad transformer.

    @
    -- derive the 'Control.Monad.State.State' monad using the 'Control.Monad.State.StateT' monad transformer
    type 'Control.Monad.State.State' s a = 'Control.Monad.State.StateT' s 'Identity' a
    @

    The @'runIdentity'@ label is used in the type definition because it follows
    a style of monad definition that explicitly represents monad values as
    computations. In this style, a monadic computation is built up using the monadic
    operators and then the value of the computation is extracted
    using the @run******@ function.
    Because the @Identity@ monad does not do any computation, its definition
    is trivial.
    For a better example of this style of monad,
    see the @'Control.Monad.State.State'@ 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 Monad Identity where
        return a = Identity a
        m >>= k  = k (runIdentity m)

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