{- |
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 ()
Advanced School of Functional Programming, 1995.
-}
module Control.Monad.Identity (
Identity(..),
) where
import Control.Applicative
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 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))