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>base-4.1.0.0: Basic libraries</TD
><TD CLASS="topbut"
><A HREF="index.html"
>Contents</A
></TD
><TD CLASS="topbut"
><A HREF="doc-index.html"
>Index</A
></TD
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><TD CLASS="modulebar"
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><TD
><FONT SIZE="6"
>Control.Arrow</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
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="section4"
><B
>Contents</B
></TD
></TR
><TR
><TD
><DL
><DT
><A HREF="#1"
>Arrows
</A
></DT
><DD
><DL
><DT
><A HREF="#2"
>Derived combinators
</A
></DT
><DT
><A HREF="#3"
>Right-to-left variants
</A
></DT
></DL
></DD
><DT
><A HREF="#4"
>Monoid operations
</A
></DT
><DT
><A HREF="#5"
>Conditionals
</A
></DT
><DT
><A HREF="#6"
>Arrow application
</A
></DT
><DT
><A HREF="#7"
>Feedback
</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"
>Basic arrow definitions, based on
      <EM
>Generalising Monads to Arrows</EM
>, by John Hughes,
      <EM
>Science of Computer Programming</EM
> 37, pp67-111, May 2000.
 plus a couple of definitions (<TT
><A HREF="Control-Arrow.html#v%3AreturnA"
>returnA</A
></TT
> and <TT
><A HREF="Control-Arrow.html#v%3Aloop"
>loop</A
></TT
>) from
      <EM
>A New Notation for Arrows</EM
>, by Ross Paterson, in <EM
>ICFP 2001</EM
>,
      Firenze, Italy, pp229-240.
 See these papers for the equations these combinators are expected to
 satisfy.  These papers and more information on arrows can be found at
 <A HREF="http://www.haskell.org/arrows/"
>http://www.haskell.org/arrows/</A
>.
</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"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Category.html#t%3ACategory"
>Category</A
> a =&gt; <A HREF="#t%3AArrow"
>Arrow</A
> a  <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%3Aarr"
>arr</A
> ::  (b -&gt; c) -&gt; a b c</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Afirst"
>first</A
> ::  a b c -&gt; a (b, d) (c, d)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Asecond"
>second</A
> ::  a b c -&gt; a (d, b) (d, c)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%2A%2A%2A"
>(***)</A
> ::  a b c -&gt; a b' c' -&gt; a (b, b') (c, c')</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%26%26%26"
>(&amp;&amp;&amp;)</A
> ::  a b c -&gt; a b c' -&gt; a b (c, c')</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3AKleisli"
>Kleisli</A
> m a b = <A HREF="#v%3AKleisli"
>Kleisli</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3ArunKleisli"
>runKleisli</A
> :: a -&gt; m b</TD
></TR
></TABLE
>}</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AreturnA"
>returnA</A
> :: <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; a b b</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%5E%3E%3E"
>(^&gt;&gt;)</A
> :: <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; (b -&gt; c) -&gt; a c d -&gt; a b d</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%3E%3E%5E"
>(&gt;&gt;^)</A
> :: <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; a b c -&gt; (c -&gt; d) -&gt; a b d</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%3C%3C%5E"
>(&lt;&lt;^)</A
> :: <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; a c d -&gt; (b -&gt; c) -&gt; a b d</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%5E%3C%3C"
>(^&lt;&lt;)</A
> :: <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; (c -&gt; d) -&gt; a b c -&gt; a b d</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; <A HREF="#t%3AArrowZero"
>ArrowZero</A
> a  <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%3AzeroArrow"
>zeroArrow</A
> ::  a b c</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Arrow.html#t%3AArrowZero"
>ArrowZero</A
> a =&gt; <A HREF="#t%3AArrowPlus"
>ArrowPlus</A
> a  <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%3A%3C%2B%3E"
>(&lt;+&gt;)</A
> ::  a b c -&gt; a b c -&gt; a b c</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; <A HREF="#t%3AArrowChoice"
>ArrowChoice</A
> a  <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%3Aleft"
>left</A
> ::  a b c -&gt; a (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> b d) (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> c d)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Aright"
>right</A
> ::  a b c -&gt; a (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> d b) (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> d c)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%2B%2B%2B"
>(+++)</A
> ::  a b c -&gt; a b' c' -&gt; a (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> b b') (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> c c')</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%7C%7C%7C"
>(|||)</A
> ::  a b d -&gt; a c d -&gt; a (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> b c) d</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; <A HREF="#t%3AArrowApply"
>ArrowApply</A
> a  <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%3Aapp"
>app</A
> ::  a (a b c, b) c</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
> <A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
> a =&gt; <A HREF="#t%3AArrowMonad"
>ArrowMonad</A
> a b = <A HREF="#v%3AArrowMonad"
>ArrowMonad</A
> (a <A HREF="../ghc-prim/GHC-Unit.html#t%3A%28%29"
>()</A
> b)</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AleftApp"
>leftApp</A
> :: <A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
> a =&gt; a b c -&gt; a (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> b d) (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> c d)</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; <A HREF="#t%3AArrowLoop"
>ArrowLoop</A
> a  <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%3Aloop"
>loop</A
> ::  a (b, d) (c, d) -&gt; a b c</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%3E%3E%3E"
>(&gt;&gt;&gt;)</A
> :: <A HREF="Control-Category.html#t%3ACategory"
>Category</A
> cat =&gt; cat a b -&gt; cat b c -&gt; cat a c</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%3C%3C%3C"
>(&lt;&lt;&lt;)</A
> :: <A HREF="Control-Category.html#t%3ACategory"
>Category</A
> cat =&gt; cat b c -&gt; cat a b -&gt; cat a c</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="1"
><A NAME="1"
>Arrows
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Category.html#t%3ACategory"
>Category</A
> a =&gt; <A NAME="t:Arrow"
><A NAME="t%3AArrow"
></A
></A
><B
>Arrow</B
> a  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
><P
>The basic arrow class.
</P
><P
>Minimal complete definition: <TT
><A HREF="Control-Arrow.html#v%3Aarr"
>arr</A
></TT
> and <TT
><A HREF="Control-Arrow.html#v%3Afirst"
>first</A
></TT
>.
</P
><P
>The other combinators have sensible default definitions,
   which may be overridden for efficiency.
</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:arr"
><A NAME="v%3Aarr"
></A
></A
><B
>arr</B
> ::  (b -&gt; c) -&gt; a b c</TD
></TR
><TR
><TD CLASS="doc"
>Lift a function to an arrow.
</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:first"
><A NAME="v%3Afirst"
></A
></A
><B
>first</B
> ::  a b c -&gt; a (b, d) (c, d)</TD
></TR
><TR
><TD CLASS="doc"
>Send the first component of the input through the argument
   arrow, and copy the rest unchanged to the output.
</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:second"
><A NAME="v%3Asecond"
></A
></A
><B
>second</B
> ::  a b c -&gt; a (d, b) (d, c)</TD
></TR
><TR
><TD CLASS="doc"
><P
>A mirror image of <TT
><A HREF="Control-Arrow.html#v%3Afirst"
>first</A
></TT
>.
</P
><P
>The default definition may be overridden with a more efficient
   version if desired.
</P
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:***"
><A NAME="v%3A%2A%2A%2A"
></A
></A
><B
>(***)</B
> ::  a b c -&gt; a b' c' -&gt; a (b, b') (c, c')</TD
></TR
><TR
><TD CLASS="doc"
><P
>Split the input between the two argument arrows and combine
   their output.  Note that this is in general not a functor.
</P
><P
>The default definition may be overridden with a more efficient
   version if desired.
</P
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:&&&"
><A NAME="v%3A%26%26%26"
></A
></A
><B
>(&amp;&amp;&amp;)</B
> ::  a b c -&gt; a b c' -&gt; a b (c, c')</TD
></TR
><TR
><TD CLASS="doc"
><P
>Fanout: send the input to both argument arrows and combine
   their output.
</P
><P
>The default definition may be overridden with a more efficient
   version if desired.
</P
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Arrow')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Arrow" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> (-&gt;)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:Kleisli"
><A NAME="t%3AKleisli"
></A
></A
><B
>Kleisli</B
> m a b </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>Kleisli arrows of a monad.
</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:Kleisli"
><A NAME="v%3AKleisli"
></A
></A
><B
>Kleisli</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:runKleisli"
><A NAME="v%3ArunKleisli"
></A
></A
><B
>runKleisli</B
> :: a -&gt; m b</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:Kleisli')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Kleisli" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Category.html#t%3ACategory"
>Category</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrowLoop"
>ArrowLoop</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrowChoice"
>ArrowChoice</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad.html#t%3AMonadPlus"
>MonadPlus</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrowPlus"
>ArrowPlus</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad.html#t%3AMonadPlus"
>MonadPlus</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrowZero"
>ArrowZero</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section2"
><A NAME="2"
><A NAME="2"
>Derived combinators
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:returnA"
><A NAME="v%3AreturnA"
></A
></A
><B
>returnA</B
> :: <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; a b b</TD
></TR
><TR
><TD CLASS="doc"
>The identity arrow, which plays the role of <TT
><A HREF="Control-Monad.html#v%3Areturn"
>return</A
></TT
> in arrow notation.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:^>>"
><A NAME="v%3A%5E%3E%3E"
></A
></A
><B
>(^&gt;&gt;)</B
> :: <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; (b -&gt; c) -&gt; a c d -&gt; a b d</TD
></TR
><TR
><TD CLASS="doc"
>Precomposition with a pure function.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:>>^"
><A NAME="v%3A%3E%3E%5E"
></A
></A
><B
>(&gt;&gt;^)</B
> :: <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; a b c -&gt; (c -&gt; d) -&gt; a b d</TD
></TR
><TR
><TD CLASS="doc"
>Postcomposition with a pure function.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section2"
><A NAME="3"
><A NAME="3"
>Right-to-left variants
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:<<^"
><A NAME="v%3A%3C%3C%5E"
></A
></A
><B
>(&lt;&lt;^)</B
> :: <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; a c d -&gt; (b -&gt; c) -&gt; a b d</TD
></TR
><TR
><TD CLASS="doc"
>Precomposition with a pure function (right-to-left variant).
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:^<<"
><A NAME="v%3A%5E%3C%3C"
></A
></A
><B
>(^&lt;&lt;)</B
> :: <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; (c -&gt; d) -&gt; a b c -&gt; a b d</TD
></TR
><TR
><TD CLASS="doc"
>Postcomposition with a pure function (right-to-left variant).
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="4"
><A NAME="4"
>Monoid operations
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; <A NAME="t:ArrowZero"
><A NAME="t%3AArrowZero"
></A
></A
><B
>ArrowZero</B
> a  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><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:zeroArrow"
><A NAME="v%3AzeroArrow"
></A
></A
><B
>zeroArrow</B
> ::  a b c</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:ArrowZero')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:ArrowZero" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Monad.html#t%3AMonadPlus"
>MonadPlus</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrowZero"
>ArrowZero</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Arrow.html#t%3AArrowZero"
>ArrowZero</A
> a =&gt; <A NAME="t:ArrowPlus"
><A NAME="t%3AArrowPlus"
></A
></A
><B
>ArrowPlus</B
> a  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><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:<+>"
><A NAME="v%3A%3C%2B%3E"
></A
></A
><B
>(&lt;+&gt;)</B
> ::  a b c -&gt; a b c -&gt; a b c</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:ArrowPlus')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:ArrowPlus" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Monad.html#t%3AMonadPlus"
>MonadPlus</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrowPlus"
>ArrowPlus</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="5"
><A NAME="5"
>Conditionals
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; <A NAME="t:ArrowChoice"
><A NAME="t%3AArrowChoice"
></A
></A
><B
>ArrowChoice</B
> a  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>Choice, for arrows that support it.  This class underlies the
   <TT
>if</TT
> and <TT
>case</TT
> constructs in arrow notation.
   Any instance must define <TT
><A HREF="Control-Arrow.html#v%3Aleft"
>left</A
></TT
>.  The other combinators have sensible
   default definitions, which may be overridden for efficiency.
</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:left"
><A NAME="v%3Aleft"
></A
></A
><B
>left</B
> ::  a b c -&gt; a (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> b d) (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> c d)</TD
></TR
><TR
><TD CLASS="doc"
>Feed marked inputs through the argument arrow, passing the
   rest through unchanged to the output.
</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:right"
><A NAME="v%3Aright"
></A
></A
><B
>right</B
> ::  a b c -&gt; a (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> d b) (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> d c)</TD
></TR
><TR
><TD CLASS="doc"
><P
>A mirror image of <TT
><A HREF="Control-Arrow.html#v%3Aleft"
>left</A
></TT
>.
</P
><P
>The default definition may be overridden with a more efficient
   version if desired.
</P
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:+++"
><A NAME="v%3A%2B%2B%2B"
></A
></A
><B
>(+++)</B
> ::  a b c -&gt; a b' c' -&gt; a (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> b b') (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> c c')</TD
></TR
><TR
><TD CLASS="doc"
><P
>Split the input between the two argument arrows, retagging
   and merging their outputs.
   Note that this is in general not a functor.
</P
><P
>The default definition may be overridden with a more efficient
   version if desired.
</P
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:|||"
><A NAME="v%3A%7C%7C%7C"
></A
></A
><B
>(|||)</B
> ::  a b d -&gt; a c d -&gt; a (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> b c) d</TD
></TR
><TR
><TD CLASS="doc"
><P
>Fanin: Split the input between the two argument arrows and
   merge their outputs.
</P
><P
>The default definition may be overridden with a more efficient
   version if desired.
</P
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:ArrowChoice')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:ArrowChoice" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Arrow.html#t%3AArrowChoice"
>ArrowChoice</A
> (-&gt;)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrowChoice"
>ArrowChoice</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="6"
><A NAME="6"
>Arrow application
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; <A NAME="t:ArrowApply"
><A NAME="t%3AArrowApply"
></A
></A
><B
>ArrowApply</B
> a  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>Some arrows allow application of arrow inputs to other inputs.
</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:app"
><A NAME="v%3Aapp"
></A
></A
><B
>app</B
> ::  a (a b c, b) c</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:ArrowApply')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:ArrowApply" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
> (-&gt;)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
> <A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
> a =&gt; <A NAME="t:ArrowMonad"
><A NAME="t%3AArrowMonad"
></A
></A
><B
>ArrowMonad</B
> a b </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>The <TT
><A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
></TT
> class is equivalent to <TT
><A HREF="Control-Monad.html#t%3AMonad"
>Monad</A
></TT
>: any monad gives rise
   to a <TT
><A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
></TT
> arrow, and any instance of <TT
><A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
></TT
> defines a monad.
</TD
></TR
><TR
><TD CLASS="section4"
>Constructors</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:ArrowMonad"
><A NAME="v%3AArrowMonad"
></A
></A
><B
>ArrowMonad</B
> (a <A HREF="../ghc-prim/GHC-Unit.html#t%3A%28%29"
>()</A
> b)</TD
><TD CLASS="rdoc"
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:ArrowMonad')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:ArrowMonad" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
> a =&gt; <A HREF="Control-Monad.html#t%3AMonad"
>Monad</A
> (<A HREF="Control-Arrow.html#t%3AArrowMonad"
>ArrowMonad</A
> a)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:leftApp"
><A NAME="v%3AleftApp"
></A
></A
><B
>leftApp</B
> :: <A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
> a =&gt; a b c -&gt; a (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> b d) (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> c d)</TD
></TR
><TR
><TD CLASS="doc"
>Any instance of <TT
><A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
></TT
> can be made into an instance of
   <TT
><A HREF="Control-Arrow.html#t%3AArrowChoice"
>ArrowChoice</A
></TT
> by defining <TT
><A HREF="Control-Arrow.html#v%3Aleft"
>left</A
></TT
> = <TT
><A HREF="Control-Arrow.html#v%3AleftApp"
>leftApp</A
></TT
>.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="7"
><A NAME="7"
>Feedback
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
> <A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; <A NAME="t:ArrowLoop"
><A NAME="t%3AArrowLoop"
></A
></A
><B
>ArrowLoop</B
> a  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>The <TT
><A HREF="Control-Arrow.html#v%3Aloop"
>loop</A
></TT
> operator expresses computations in which an output value is
   fed back as input, even though the computation occurs only once.
   It underlies the <TT
>rec</TT
> value recursion construct in arrow notation.
</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:loop"
><A NAME="v%3Aloop"
></A
></A
><B
>loop</B
> ::  a (b, d) (c, d) -&gt; a b c</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:ArrowLoop')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:ArrowLoop" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Arrow.html#t%3AArrowLoop"
>ArrowLoop</A
> (-&gt;)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Fix.html#t%3AMonadFix"
>MonadFix</A
> m =&gt; <A HREF="Control-Arrow.html#t%3AArrowLoop"
>ArrowLoop</A
> (<A HREF="Control-Arrow.html#t%3AKleisli"
>Kleisli</A
> m)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:>>>"
><A NAME="v%3A%3E%3E%3E"
></A
></A
><B
>(&gt;&gt;&gt;)</B
> :: <A HREF="Control-Category.html#t%3ACategory"
>Category</A
> cat =&gt; cat a b -&gt; cat b c -&gt; cat a c</TD
></TR
><TR
><TD CLASS="doc"
>Left-to-right composition
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:<<<"
><A NAME="v%3A%3C%3C%3C"
></A
></A
><B
>(&lt;&lt;&lt;)</B
> :: <A HREF="Control-Category.html#t%3ACategory"
>Category</A
> cat =&gt; cat b c -&gt; cat a b -&gt; cat a c</TD
></TR
><TR
><TD CLASS="doc"
>Right-to-left composition
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="botbar"
>Produced by <A HREF="http://www.haskell.org/haddock/"
>Haddock</A
> version 2.4.2</TD
></TR
></TABLE
></BODY
></HTML
>