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>Control.Monad.Fix</TITLE
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>base-4.1.0.0: Basic libraries</TD
><TD CLASS="topbut"
><A HREF="index.html"
>Contents</A
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><TD CLASS="topbut"
><A HREF="doc-index.html"
>Index</A
></TD
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><FONT SIZE="6"
>Control.Monad.Fix</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
></TR
><TR
><TD CLASS="section1"
>Description</TD
></TR
><TR
><TD CLASS="doc"
><P
>Monadic fixpoints.
</P
><P
>For a detailed discussion, see Levent Erkok's thesis,
 <EM
>Value Recursion in Monadic Computations</EM
>, Oregon Graduate Institute, 2002.
</P
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Synopsis</TD
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></TD
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><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
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><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="#t%3AMonadFix"
>MonadFix</A
> m  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="#v%3Amfix"
>mfix</A
> ::  (a -&gt; m a) -&gt; m a</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Afix"
>fix</A
> ::  (a -&gt; a) -&gt; 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"
>class</SPAN
> <A HREF="Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A NAME="t:MonadFix"
><A NAME="t%3AMonadFix"
></A
></A
><B
>MonadFix</B
> m  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
><P
>Monads having fixed points with a 'knot-tying' semantics.
 Instances of <TT
><A HREF="Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
></TT
> should satisfy the following laws:
</P
><DL
><DT
><EM
>purity</EM
></DT
><DD
>
      <TT
><TT
><A HREF="Control-Monad-Fix.html#v%3Amfix"
>mfix</A
></TT
> (<TT
><A HREF="Control-Monad.html#v%3Areturn"
>return</A
></TT
> . h)  =  <TT
><A HREF="Control-Monad.html#v%3Areturn"
>return</A
></TT
> (<TT
><A HREF="Control-Monad-Fix.html#v%3Afix"
>fix</A
></TT
> h)</TT
>
</DD
><DT
><EM
>left shrinking</EM
> (or <EM
>tightening</EM
>)</DT
><DD
>
      <TT
><TT
><A HREF="Control-Monad-Fix.html#v%3Amfix"
>mfix</A
></TT
> (\x -&gt; a &gt;&gt;= \y -&gt; f x y)  =  a &gt;&gt;= \y -&gt; <TT
><A HREF="Control-Monad-Fix.html#v%3Amfix"
>mfix</A
></TT
> (\x -&gt; f x y)</TT
>
</DD
><DT
><EM
>sliding</EM
></DT
><DD
>
      <TT
><TT
><A HREF="Control-Monad-Fix.html#v%3Amfix"
>mfix</A
></TT
> (Control.Monad.liftM h . f)  =  Control.Monad.liftM h (<TT
><A HREF="Control-Monad-Fix.html#v%3Amfix"
>mfix</A
></TT
> (f . h))</TT
>,
      for strict <TT
>h</TT
>.
</DD
><DT
><EM
>nesting</EM
></DT
><DD
>
      <TT
><TT
><A HREF="Control-Monad-Fix.html#v%3Amfix"
>mfix</A
></TT
> (\x -&gt; <TT
><A HREF="Control-Monad-Fix.html#v%3Amfix"
>mfix</A
></TT
> (\y -&gt; f x y))  =  <TT
><A HREF="Control-Monad-Fix.html#v%3Amfix"
>mfix</A
></TT
> (\x -&gt; f x x)</TT
>
</DD
></DL
><P
>This class is used in the translation of the recursive <TT
>do</TT
> notation
 supported by GHC and Hugs.
</P
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
>Methods</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A NAME="v:mfix"
><A NAME="v%3Amfix"
></A
></A
><B
>mfix</B
> ::  (a -&gt; m a) -&gt; m a</TD
></TR
><TR
><TD CLASS="doc"
>The fixed point of a monadic computation.
 <TT
><TT
><A HREF="Control-Monad-Fix.html#v%3Amfix"
>mfix</A
></TT
> f</TT
> executes the action <TT
>f</TT
> only once, with the eventual
 output fed back as the input.  Hence <TT
>f</TT
> should not be strict,
 for then <TT
><TT
><A HREF="Control-Monad-Fix.html#v%3Amfix"
>mfix</A
></TT
> f</TT
> would diverge.
</TD
></TR
></TABLE
></TD
></TR
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><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:MonadFix')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:MonadFix" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> []</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> <A HREF="System-IO.html#t%3AIO"
>IO</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> <A HREF="Data-Maybe.html#t%3AMaybe"
>Maybe</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> ((-&gt;) r)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> (<A HREF="Control-Monad-ST.html#t%3AST"
>ST</A
> s)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> (<A HREF="Control-Monad-ST-Lazy.html#t%3AST"
>ST</A
> s)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:fix"
><A NAME="v%3Afix"
></A
></A
><B
>fix</B
> ::  (a -&gt; a) -&gt; a</TD
></TR
><TR
><TD CLASS="doc"
><TT
><TT
><A HREF="Control-Monad-Fix.html#v%3Afix"
>fix</A
></TT
> f</TT
> is the least fixed point of the function <TT
>f</TT
>,
 i.e. the least defined <TT
>x</TT
> such that <TT
>f x = x</TT
>.
</TD
></TR
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></TD
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>Produced by <A HREF="http://www.haskell.org/haddock/"
>Haddock</A
> version 2.4.2</TD
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