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>Control.Monad.State.Lazy</TITLE
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>mtl-1.1.0.2: Monad transformer library</TD
><TD CLASS="topbut"
><A HREF="index.html"
>Contents</A
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>Control.Monad.State.Lazy</FONT
></TD
><TD ALIGN="right"
><TABLE CLASS="narrow" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="infohead"
>Portability</TD
><TD CLASS="infoval"
>non-portable (multi-param classes, functional dependencies)</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
></TR
><TR
><TD
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="section4"
><B
>Contents</B
></TD
></TR
><TR
><TD
><DL
><DT
><A HREF="#1"
>The State Monad
</A
></DT
><DT
><A HREF="#2"
>The StateT Monad
</A
></DT
><DT
><A HREF="#3"
>Examples
</A
></DT
></DL
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Description</TD
></TR
><TR
><TD CLASS="doc"
><P
>Lazy state monads.
</P
><P
>This module is 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
><P
>See below for examples.
</P
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><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"
>module <A HREF="Control-Monad-State-Class.html"
>Control.Monad.State.Class</A
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3AState"
>State</A
> s a = <A HREF="#v%3AState"
>State</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3ArunState"
>runState</A
> :: s -&gt; (a, s)</TD
></TR
></TABLE
>}</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AevalState"
>evalState</A
> ::  <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s a -&gt; s -&gt; a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AexecState"
>execState</A
> ::  <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s a -&gt; s -&gt; s</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AmapState"
>mapState</A
> ::  ((a, s) -&gt; (b, s)) -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s a -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s b</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AwithState"
>withState</A
> ::  (s -&gt; s) -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s a -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3AStateT"
>StateT</A
> s m a = <A HREF="#v%3AStateT"
>StateT</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3ArunStateT"
>runStateT</A
> :: s -&gt; m (a, s)</TD
></TR
></TABLE
>}</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AevalStateT"
>evalStateT</A
> :: <A HREF="../base/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m a -&gt; s -&gt; m a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AexecStateT"
>execStateT</A
> :: <A HREF="../base/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m a -&gt; s -&gt; m s</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AmapStateT"
>mapStateT</A
> ::  (m (a, s) -&gt; n (b, s)) -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m a -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s n b</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AwithStateT"
>withStateT</A
> ::  (s -&gt; s) -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m a -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m a</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
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
>module <A HREF="Control-Monad-Trans.html"
>Control.Monad.Trans</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"
>module <A HREF="Control-Monad-State-Class.html"
>Control.Monad.State.Class</A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="1"
><A NAME="1"
>The State Monad
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:State"
><A NAME="t%3AState"
></A
></A
><B
>State</B
> s a </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>A parameterizable state monad where <EM
>s</EM
> is the type of the state
 to carry and <EM
>a</EM
> is the type of the <EM
>return value</EM
>.
</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:State"
><A NAME="v%3AState"
></A
></A
><B
>State</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:runState"
><A NAME="v%3ArunState"
></A
></A
><B
>runState</B
> :: s -&gt; (a, s)</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:State')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:State" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-State-Class.html#t%3AMonadState"
>MonadState</A
> s (<A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="../base/Control-Monad.html#t%3AMonad"
>Monad</A
> (<A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="../base/Control-Monad.html#t%3AFunctor"
>Functor</A
> (<A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="../base/Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> (<A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:evalState"
><A NAME="v%3AevalState"
></A
></A
><B
>evalState</B
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="arg"
>:: </TD
><TD CLASS="rdoc"
></TD
></TR
><TR
><TD CLASS="arg"
>=&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s a</TD
><TD CLASS="rdoc"
>The state to evaluate
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; s</TD
><TD CLASS="rdoc"
>An initial value
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; a</TD
><TD CLASS="rdoc"
>The return value of the state application
</TD
></TR
><TR
><TD CLASS="ndoc" COLSPAN="2"
>Evaluate this state monad with the given initial state,throwing
 away the final state.  Very much like <TT
>fst</TT
> composed with
 <TT
>runstate</TT
>.
</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:execState"
><A NAME="v%3AexecState"
></A
></A
><B
>execState</B
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="arg"
>:: </TD
><TD CLASS="rdoc"
></TD
></TR
><TR
><TD CLASS="arg"
>=&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s a</TD
><TD CLASS="rdoc"
>The state to evaluate
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; s</TD
><TD CLASS="rdoc"
>An initial value
</TD
></TR
><TR
><TD CLASS="arg"
>-&gt; s</TD
><TD CLASS="rdoc"
>The new state
</TD
></TR
><TR
><TD CLASS="ndoc" COLSPAN="2"
>Execute this state and return the new state, throwing away the
 return value.  Very much like <TT
>snd</TT
> composed with
 <TT
>runstate</TT
>.
</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:mapState"
><A NAME="v%3AmapState"
></A
></A
><B
>mapState</B
> ::  ((a, s) -&gt; (b, s)) -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s a -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s b</TD
></TR
><TR
><TD CLASS="doc"
><P
>Map a stateful computation from one (return value, state) pair to
 another.  For instance, to convert numberTree from a function that
 returns a tree to a function that returns the sum of the numbered
 tree (see the Examples section for numberTree and sumTree) you may
 write:
</P
><PRE
> sumNumberedTree :: (Eq a) =&gt; Tree a -&gt; State (Table a) Int
 sumNumberedTree = mapState (\ (t, tab) -&gt; (sumTree t, tab))  . numberTree
</PRE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:withState"
><A NAME="v%3AwithState"
></A
></A
><B
>withState</B
> ::  (s -&gt; s) -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s a -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AState"
>State</A
> s a</TD
></TR
><TR
><TD CLASS="doc"
>Apply this function to this state and return the resulting state.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="2"
><A NAME="2"
>The StateT Monad
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:StateT"
><A NAME="t%3AStateT"
></A
></A
><B
>StateT</B
> s m a </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
><P
>A parameterizable state monad for encapsulating an inner
 monad.
</P
><P
>The StateT Monad structure is parameterized over two things:
</P
><UL
><LI
> s - The state.
</LI
><LI
> m - The inner monad.
</LI
></UL
><P
>Here are some examples of use:
</P
><P
>(Parser from ParseLib with Hugs)
</P
><PRE
>  type Parser a = StateT String [] a
     ==&gt; StateT (String -&gt; [(a,String)])
</PRE
><P
>For example, item can be written as:
</P
><PRE
>   item = do (x:xs) &lt;- get
          put xs
          return x

   type BoringState s a = StateT s Indentity a
        ==&gt; StateT (s -&gt; Identity (a,s))

   type StateWithIO s a = StateT s IO a
        ==&gt; StateT (s -&gt; IO (a,s))

   type StateWithErr s a = StateT s Maybe a
        ==&gt; StateT (s -&gt; Maybe (a,s))
</PRE
></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:StateT"
><A NAME="v%3AStateT"
></A
></A
><B
>StateT</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:runStateT"
><A NAME="v%3ArunStateT"
></A
></A
><B
>runStateT</B
> :: s -&gt; m (a, s)</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:StateT')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:StateT" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Writer-Class.html#t%3AMonadWriter"
>MonadWriter</A
> w m =&gt; <A HREF="Control-Monad-Writer-Class.html#t%3AMonadWriter"
>MonadWriter</A
> w (<A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="../base/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Monad-State-Class.html#t%3AMonadState"
>MonadState</A
> s (<A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Reader-Class.html#t%3AMonadReader"
>MonadReader</A
> r m =&gt; <A HREF="Control-Monad-Reader-Class.html#t%3AMonadReader"
>MonadReader</A
> r (<A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Error-Class.html#t%3AMonadError"
>MonadError</A
> e m =&gt; <A HREF="Control-Monad-Error-Class.html#t%3AMonadError"
>MonadError</A
> e (<A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Trans.html#t%3AMonadTrans"
>MonadTrans</A
> (<A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="../base/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="../base/Control-Monad.html#t%3AMonad"
>Monad</A
> (<A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="../base/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="../base/Control-Monad.html#t%3AFunctor"
>Functor</A
> (<A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="../base/Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> m =&gt; <A HREF="../base/Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> (<A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="../base/Control-Monad.html#t%3AMonadPlus"
>MonadPlus</A
> m =&gt; <A HREF="../base/Control-Monad.html#t%3AMonadPlus"
>MonadPlus</A
> (<A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Trans.html#t%3AMonadIO"
>MonadIO</A
> m =&gt; <A HREF="Control-Monad-Trans.html#t%3AMonadIO"
>MonadIO</A
> (<A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Cont-Class.html#t%3AMonadCont"
>MonadCont</A
> m =&gt; <A HREF="Control-Monad-Cont-Class.html#t%3AMonadCont"
>MonadCont</A
> (<A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:evalStateT"
><A NAME="v%3AevalStateT"
></A
></A
><B
>evalStateT</B
> :: <A HREF="../base/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m a -&gt; s -&gt; m a</TD
></TR
><TR
><TD CLASS="doc"
>Similar to <TT
><A HREF="Control-Monad-State-Lazy.html#v%3AevalState"
>evalState</A
></TT
>
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:execStateT"
><A NAME="v%3AexecStateT"
></A
></A
><B
>execStateT</B
> :: <A HREF="../base/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m a -&gt; s -&gt; m s</TD
></TR
><TR
><TD CLASS="doc"
>Similar to <TT
><A HREF="Control-Monad-State-Lazy.html#v%3AexecState"
>execState</A
></TT
>
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:mapStateT"
><A NAME="v%3AmapStateT"
></A
></A
><B
>mapStateT</B
> ::  (m (a, s) -&gt; n (b, s)) -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m a -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s n b</TD
></TR
><TR
><TD CLASS="doc"
>Similar to <TT
><A HREF="Control-Monad-State-Lazy.html#v%3AmapState"
>mapState</A
></TT
>
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:withStateT"
><A NAME="v%3AwithStateT"
></A
></A
><B
>withStateT</B
> ::  (s -&gt; s) -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m a -&gt; <A HREF="Control-Monad-State-Lazy.html#t%3AStateT"
>StateT</A
> s m a</TD
></TR
><TR
><TD CLASS="doc"
>Similar to <TT
><A HREF="Control-Monad-State-Lazy.html#v%3AwithState"
>withState</A
></TT
>
</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
><TR
><TD CLASS="decl"
>module <A HREF="Control-Monad-Trans.html"
>Control.Monad.Trans</A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="3"
><A NAME="3"
>Examples
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="doc"
><P
>A function to increment a counter.  Taken from the paper
 <EM
>Generalising Monads to Arrows</EM
>, John
 Hughes (<A HREF="http://www.math.chalmers.se/~rjmh/"
>http://www.math.chalmers.se/~rjmh/</A
>), November 1998:
</P
><PRE
> tick :: State Int Int
 tick = do n &lt;- get
           put (n+1)
           return n
</PRE
><P
>Add one to the given number using the state monad:
</P
><PRE
> plusOne :: Int -&gt; Int
 plusOne n = execState tick n
</PRE
><P
>A contrived addition example. Works only with positive numbers:
</P
><PRE
> plus :: Int -&gt; Int -&gt; Int
 plus n x = execState (sequence $ replicate n tick) x
</PRE
><P
>An example from <EM
>The Craft of Functional Programming</EM
>, Simon
 Thompson (<A HREF="http://www.cs.kent.ac.uk/people/staff/sjt/"
>http://www.cs.kent.ac.uk/people/staff/sjt/</A
>),
 Addison-Wesley 1999: &quot;Given an arbitrary tree, transform it to a
 tree of integers in which the original elements are replaced by
 natural numbers, starting from 0.  The same element has to be
 replaced by the same number at every occurrence, and when we meet
 an as-yet-unvisited element we have to find a 'new' number to match
 it with:&quot;
</P
><PRE
> data Tree a = Nil | Node a (Tree a) (Tree a) deriving (Show, Eq)
 type Table a = [a]
</PRE
><PRE
> numberTree :: Eq a =&gt; Tree a -&gt; State (Table a) (Tree Int)
 numberTree Nil = return Nil
 numberTree (Node x t1 t2)
        =  do num &lt;- numberNode x
              nt1 &lt;- numberTree t1
              nt2 &lt;- numberTree t2
              return (Node num nt1 nt2)
     where
     numberNode :: Eq a =&gt; a -&gt; State (Table a) Int
     numberNode x
        = do table &lt;- get
             (newTable, newPos) &lt;- return (nNode x table)
             put newTable
             return newPos
     nNode::  (Eq a) =&gt; a -&gt; Table a -&gt; (Table a, Int)
     nNode x table
        = case (findIndexInList (== x) table) of
          Nothing -&gt; (table ++ [x], length table)
          Just i  -&gt; (table, i)
     findIndexInList :: (a -&gt; Bool) -&gt; [a] -&gt; Maybe Int
     findIndexInList = findIndexInListHelp 0
     findIndexInListHelp _ _ [] = Nothing
     findIndexInListHelp count f (h:t)
        = if (f h)
          then Just count
          else findIndexInListHelp (count+1) f t
</PRE
><P
>numTree applies numberTree with an initial state:
</P
><PRE
> numTree :: (Eq a) =&gt; Tree a -&gt; Tree Int
 numTree t = evalState (numberTree t) []
</PRE
><PRE
> testTree = Node &quot;Zero&quot; (Node &quot;One&quot; (Node &quot;Two&quot; Nil Nil) (Node &quot;One&quot; (Node &quot;Zero&quot; Nil Nil) Nil)) Nil
 numTree testTree =&gt; Node 0 (Node 1 (Node 2 Nil Nil) (Node 1 (Node 0 Nil Nil) Nil)) Nil
</PRE
><P
>sumTree is a little helper function that does not use the State monad:
</P
><PRE
> sumTree :: (Num a) =&gt; Tree a -&gt; a
 sumTree Nil = 0
 sumTree (Node e t1 t2) = e + (sumTree t1) + (sumTree t2)
</PRE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="botbar"
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>Haddock</A
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