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>Control.Monad.Identity</TITLE
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>mtl-1.1.0.2: Monad transformer library</TD
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><A HREF="index.html"
>Contents</A
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>Control.Monad.Identity</FONT
></TD
><TD ALIGN="right"
><TABLE CLASS="narrow" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="infohead"
>Portability</TD
><TD CLASS="infoval"
>portable</TD
></TR
><TR
><TD CLASS="infohead"
>Stability</TD
><TD CLASS="infoval"
>experimental</TD
></TR
><TR
><TD CLASS="infohead"
>Maintainer</TD
><TD CLASS="infoval"
>libraries@haskell.org</TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
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><TR
><TD CLASS="section1"
>Description</TD
></TR
><TR
><TD CLASS="doc"
><DL
><DT
>Computation type:</DT
><DD
> Simple function application.
</DD
><DT
>Binding strategy:</DT
><DD
> The bound function is applied to the input value.
<TT
><TT
><A HREF="Control-Monad-Identity.html#t%3AIdentity"
>Identity</A
></TT
> x &gt;&gt;= f == <TT
><A HREF="Control-Monad-Identity.html#t%3AIdentity"
>Identity</A
></TT
> (f x)</TT
>
</DD
><DT
>Useful for:</DT
><DD
> Monads can be derived from monad transformers applied to the
<TT
><A HREF="Control-Monad-Identity.html#t%3AIdentity"
>Identity</A
></TT
> monad.
</DD
><DT
>Zero and plus:</DT
><DD
> None.
</DD
><DT
>Example type:</DT
><DD
> <TT
><TT
><A HREF="Control-Monad-Identity.html#t%3AIdentity"
>Identity</A
></TT
> a</TT
>
</DD
></DL
><P
>The <TT
>Identity</TT
> 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 <TT
>Identity</TT
> monad
instead of the much simpler act of simply applying functions to their arguments.
The purpose of the <TT
>Identity</TT
> monad is its fundamental role in the theory
of monad transformers.
Any monad transformer applied to the <TT
>Identity</TT
> monad yields a non-transformer
version of that monad.
</P
><P
>Inspired by the paper
  /Functional Programming with Overloading and
      Higher-Order Polymorphism/,
    Mark P Jones (<A HREF="http://web.cecs.pdx.edu/~mpj/"
>http://web.cecs.pdx.edu/~mpj/</A
>)
      Advanced School of Functional Programming, 1995.
</P
></TD
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><TR
><TD CLASS="section1"
>Synopsis</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3AIdentity"
>Identity</A
> a = <A HREF="#v%3AIdentity"
>Identity</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3ArunIdentity"
>runIdentity</A
> :: a</TD
></TR
></TABLE
>}</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
>module <A HREF="../base/Control-Monad.html"
>Control.Monad</A
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
>module <A HREF="../base/Control-Monad-Fix.html"
>Control.Monad.Fix</A
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Documentation</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:Identity"
><A NAME="t%3AIdentity"
></A
></A
><B
>Identity</B
> a </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
><P
>Identity wrapper.
Abstraction for wrapping up a object.
If you have an monadic function, say:
</P
><PRE
>   example :: Int -&gt; Identity Int
   example x = return (x*x)
</PRE
><P
>you can &quot;run&quot; it, using
</P
><PRE
> Main&gt; runIdentity (example 42)
 1764 :: Int
</PRE
><P
>A typical use of the Identity monad is to derive a monad
from a monad transformer.
</P
><PRE
>
-- 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 <TT
><A HREF="Control-Monad-Identity.html#t%3AIdentity"
>Identity</A
></TT
> a
</PRE
><P
>The <TT
><TT
><A HREF="Control-Monad-Identity.html#v%3ArunIdentity"
>runIdentity</A
></TT
></TT
> 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 <TT
>run******</TT
> function.
Because the <TT
>Identity</TT
> monad does not do any computation, its definition
is trivial.
For a better example of this style of monad,
see the <TT
>Control.Monad.State.State</TT
> monad.
</P
></TD
></TR
><TR
><TD CLASS="section4"
>Constructors</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="5" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:Identity"
><A NAME="v%3AIdentity"
></A
></A
><B
>Identity</B
></TD
><TD CLASS="rdoc"
></TD
></TR
><TR
><TD CLASS="body" COLSPAN="2"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:runIdentity"
><A NAME="v%3ArunIdentity"
></A
></A
><B
>runIdentity</B
> :: a</TD
><TD CLASS="rdoc"
></TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Identity')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Identity" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="../base/Control-Monad.html#t%3AMonad"
>Monad</A
> <A HREF="Control-Monad-Identity.html#t%3AIdentity"
>Identity</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="../base/Control-Monad.html#t%3AFunctor"
>Functor</A
> <A HREF="Control-Monad-Identity.html#t%3AIdentity"
>Identity</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="../base/Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> <A HREF="Control-Monad-Identity.html#t%3AIdentity"
>Identity</A
></TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
>module <A HREF="../base/Control-Monad.html"
>Control.Monad</A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
>module <A HREF="../base/Control-Monad-Fix.html"
>Control.Monad.Fix</A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
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