Control.Monad.Identity

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.

Documentation

newtype Identity a

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.

Constructors

Identity

Fields

runIdentity :: a

Instances

Monad Identity

Functor Identity

MonadFix Identity

Applicative Identity