-- | -- 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))