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<pre><a name="line-1"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-2"></a>
<a name="line-3"></a><span class='comment'>{- |
<a name="line-4"></a> Module : Control.Arrow.ArrowList
<a name="line-5"></a> Copyright : Copyright (C) 2005 Uwe Schmidt
<a name="line-6"></a> License : MIT
<a name="line-7"></a>
<a name="line-8"></a> Maintainer : Uwe Schmidt (uwe\@fh-wedel.de)
<a name="line-9"></a> Stability : experimental
<a name="line-10"></a> Portability: portable
<a name="line-11"></a> Version : $Id: ArrowList.hs,v 1.11 2006/06/01 12:59:04 hxml Exp $
<a name="line-12"></a>
<a name="line-13"></a>The List Arrow Class
<a name="line-14"></a>
<a name="line-15"></a>This module defines the interface for list arrows.
<a name="line-16"></a>
<a name="line-17"></a>A list arrow is a function, that gives a list of results
<a name="line-18"></a>for a given argument. A single element result represents a normal function.
<a name="line-19"></a>An empty list oven indicates, the function is undefined for the given argument.
<a name="line-20"></a>The empty list may also represent False, none empty lists True.
<a name="line-21"></a>A list with more than one element gives all results for a nondeterministic function.
<a name="line-22"></a>
<a name="line-23"></a>-}</span>
<a name="line-24"></a>
<a name="line-25"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-26"></a>
<a name="line-27"></a><span class='keyword'>module</span> <span class='conid'>Control</span><span class='varop'>.</span><span class='conid'>Arrow</span><span class='varop'>.</span><span class='conid'>ArrowList</span>
<a name="line-28"></a> <span class='layout'>(</span> <span class='conid'>ArrowList</span><span class='layout'>(</span><span class='keyglyph'>..</span><span class='layout'>)</span>
<a name="line-29"></a> <span class='layout'>)</span>
<a name="line-30"></a><span class='keyword'>where</span>
<a name="line-31"></a>
<a name="line-32"></a><span class='keyword'>import</span> <span class='conid'>Control</span><span class='varop'>.</span><span class='conid'>Arrow</span>
<a name="line-33"></a>
<a name="line-34"></a><span class='keyword'>infixl</span> <span class='num'>8</span> <span class='varop'>>>.</span><span class='layout'>,</span> <span class='varop'>>.</span>
<a name="line-35"></a>
<a name="line-36"></a><span class='keyword'>infixl</span> <span class='num'>2</span> <span class='varop'>$<</span><span class='layout'>,</span> <span class='varop'>$<<</span><span class='layout'>,</span> <span class='varop'>$<<<</span><span class='layout'>,</span> <span class='varop'>$<<<<</span>
<a name="line-37"></a><span class='keyword'>infixl</span> <span class='num'>2</span> <span class='varop'>$<$</span>
<a name="line-38"></a>
<a name="line-39"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-40"></a>
<a name="line-41"></a><span class='comment'>-- | The interface for list arrows</span>
<a name="line-42"></a><span class='comment'>--</span>
<a name="line-43"></a><span class='comment'>-- Only 'mkA', 'arr2A', 'isA' '(>>.)' don't have default implementations</span>
<a name="line-44"></a>
<a name="line-45"></a><a name="ArrowList"></a><span class='keyword'>class</span> <span class='layout'>(</span><span class='conid'>Arrow</span> <span class='varid'>a</span><span class='layout'>,</span> <span class='conid'>ArrowPlus</span> <span class='varid'>a</span><span class='layout'>,</span> <span class='conid'>ArrowZero</span> <span class='varid'>a</span><span class='layout'>,</span> <span class='conid'>ArrowApply</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='keyglyph'>=></span> <span class='conid'>ArrowList</span> <span class='varid'>a</span> <span class='keyword'>where</span>
<a name="line-46"></a>
<a name="line-47"></a> <span class='comment'>-- | construction of a 2 argument arrow from a binary function</span>
<a name="line-48"></a> <span class='comment'>-- |</span>
<a name="line-49"></a> <span class='comment'>-- | example: @ a1 &&& a2 >>> arr2 f @</span>
<a name="line-50"></a>
<a name="line-51"></a> <span class='varid'>arr2</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>b1</span> <span class='keyglyph'>-></span> <span class='varid'>b2</span> <span class='keyglyph'>-></span> <span class='varid'>c</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='layout'>(</span><span class='varid'>b1</span><span class='layout'>,</span> <span class='varid'>b2</span><span class='layout'>)</span> <span class='varid'>c</span>
<a name="line-52"></a> <span class='varid'>arr2</span> <span class='keyglyph'>=</span> <span class='varid'>arr</span> <span class='varop'>.</span> <span class='varid'>uncurry</span>
<a name="line-53"></a>
<a name="line-54"></a> <span class='comment'>-- | construction of a 3 argument arrow from a 3-ary function</span>
<a name="line-55"></a> <span class='comment'>-- |</span>
<a name="line-56"></a> <span class='comment'>-- | example: @ a1 &&& a2 &&& a3 >>> arr3 f @</span>
<a name="line-57"></a>
<a name="line-58"></a> <span class='varid'>arr3</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>b1</span> <span class='keyglyph'>-></span> <span class='varid'>b2</span> <span class='keyglyph'>-></span> <span class='varid'>b3</span> <span class='keyglyph'>-></span> <span class='varid'>c</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='layout'>(</span><span class='varid'>b1</span><span class='layout'>,</span> <span class='layout'>(</span><span class='varid'>b2</span><span class='layout'>,</span> <span class='varid'>b3</span><span class='layout'>)</span><span class='layout'>)</span> <span class='varid'>c</span>
<a name="line-59"></a> <span class='varid'>arr3</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>arr</span> <span class='layout'>(</span><span class='keyglyph'>\</span> <span class='keyglyph'>~</span><span class='layout'>(</span><span class='varid'>x1</span><span class='layout'>,</span> <span class='keyglyph'>~</span><span class='layout'>(</span><span class='varid'>x2</span><span class='layout'>,</span> <span class='varid'>x3</span><span class='layout'>)</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>f</span> <span class='varid'>x1</span> <span class='varid'>x2</span> <span class='varid'>x3</span><span class='layout'>)</span>
<a name="line-60"></a>
<a name="line-61"></a> <span class='comment'>-- | construction of a 4 argument arrow from a 4-ary function</span>
<a name="line-62"></a> <span class='comment'>-- |</span>
<a name="line-63"></a> <span class='comment'>-- | example: @ a1 &&& a2 &&& a3 &&& a4 >>> arr4 f @</span>
<a name="line-64"></a>
<a name="line-65"></a> <span class='varid'>arr4</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>b1</span> <span class='keyglyph'>-></span> <span class='varid'>b2</span> <span class='keyglyph'>-></span> <span class='varid'>b3</span> <span class='keyglyph'>-></span> <span class='varid'>b4</span> <span class='keyglyph'>-></span> <span class='varid'>c</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='layout'>(</span><span class='varid'>b1</span><span class='layout'>,</span> <span class='layout'>(</span><span class='varid'>b2</span><span class='layout'>,</span> <span class='layout'>(</span><span class='varid'>b3</span><span class='layout'>,</span> <span class='varid'>b4</span><span class='layout'>)</span><span class='layout'>)</span><span class='layout'>)</span> <span class='varid'>c</span>
<a name="line-66"></a> <span class='varid'>arr4</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>arr</span> <span class='layout'>(</span><span class='keyglyph'>\</span> <span class='keyglyph'>~</span><span class='layout'>(</span><span class='varid'>x1</span><span class='layout'>,</span> <span class='keyglyph'>~</span><span class='layout'>(</span><span class='varid'>x2</span><span class='layout'>,</span> <span class='keyglyph'>~</span><span class='layout'>(</span><span class='varid'>x3</span><span class='layout'>,</span> <span class='varid'>x4</span><span class='layout'>)</span><span class='layout'>)</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>f</span> <span class='varid'>x1</span> <span class='varid'>x2</span> <span class='varid'>x3</span> <span class='varid'>x4</span><span class='layout'>)</span>
<a name="line-67"></a>
<a name="line-68"></a> <span class='comment'>-- | construction of a 2 argument arrow from a singe argument arrow</span>
<a name="line-69"></a>
<a name="line-70"></a> <span class='varid'>arr2A</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>b</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>c</span> <span class='varid'>d</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='layout'>(</span><span class='varid'>b</span><span class='layout'>,</span> <span class='varid'>c</span><span class='layout'>)</span> <span class='varid'>d</span>
<a name="line-71"></a>
<a name="line-72"></a> <span class='comment'>-- | constructor for a list arrow from a function with a list as result</span>
<a name="line-73"></a>
<a name="line-74"></a> <span class='varid'>arrL</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>b</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span>
<a name="line-75"></a>
<a name="line-76"></a> <span class='comment'>-- | constructor for a list arrow with 2 arguments</span>
<a name="line-77"></a>
<a name="line-78"></a> <span class='varid'>arr2L</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>b</span> <span class='keyglyph'>-></span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>d</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='layout'>(</span><span class='varid'>b</span><span class='layout'>,</span> <span class='varid'>c</span><span class='layout'>)</span> <span class='varid'>d</span>
<a name="line-79"></a> <span class='varid'>arr2L</span> <span class='keyglyph'>=</span> <span class='varid'>arrL</span> <span class='varop'>.</span> <span class='varid'>uncurry</span>
<a name="line-80"></a>
<a name="line-81"></a> <span class='comment'>-- | constructor for a const arrow: @ constA = arr . const @</span>
<a name="line-82"></a>
<a name="line-83"></a> <span class='varid'>constA</span> <span class='keyglyph'>::</span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span>
<a name="line-84"></a> <span class='varid'>constA</span> <span class='keyglyph'>=</span> <span class='varid'>arr</span> <span class='varop'>.</span> <span class='varid'>const</span>
<a name="line-85"></a>
<a name="line-86"></a> <span class='comment'>-- | constructor for a const arrow: @ constL = arrL . const @</span>
<a name="line-87"></a>
<a name="line-88"></a> <span class='varid'>constL</span> <span class='keyglyph'>::</span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span>
<a name="line-89"></a> <span class='varid'>constL</span> <span class='keyglyph'>=</span> <span class='varid'>arrL</span> <span class='varop'>.</span> <span class='varid'>const</span>
<a name="line-90"></a>
<a name="line-91"></a> <span class='comment'>-- | builds an arrow from a predicate.</span>
<a name="line-92"></a> <span class='comment'>-- If the predicate holds, the single list containing the input is returned, else the empty list</span>
<a name="line-93"></a>
<a name="line-94"></a> <span class='varid'>isA</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>b</span> <span class='keyglyph'>-></span> <span class='conid'>Bool</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>b</span>
<a name="line-95"></a>
<a name="line-96"></a> <span class='comment'>-- | combinator for converting the result of a list arrow into another list</span>
<a name="line-97"></a> <span class='comment'>--</span>
<a name="line-98"></a> <span class='comment'>-- example: @ foo >>. reverse @ reverses the the result of foo</span>
<a name="line-99"></a> <span class='comment'>--</span>
<a name="line-100"></a> <span class='comment'>-- example: @ foo >>. take 1 @ constructs a deterministic version of foo by deleting all further results</span>
<a name="line-101"></a>
<a name="line-102"></a> <span class='layout'>(</span><span class='varop'>>>.</span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>d</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span>
<a name="line-103"></a>
<a name="line-104"></a> <span class='comment'>-- | combinator for converting the result of an arrow into a single element result</span>
<a name="line-105"></a>
<a name="line-106"></a> <span class='layout'>(</span><span class='varop'>>.</span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='varid'>d</span> <span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span>
<a name="line-107"></a> <span class='varid'>af</span> <span class='varop'>>.</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>af</span> <span class='varop'>>>.</span> <span class='layout'>(</span><span class='layout'>(</span><span class='conop'>:</span><span class='conid'>[]</span><span class='layout'>)</span> <span class='varop'>.</span> <span class='varid'>f</span><span class='layout'>)</span>
<a name="line-108"></a>
<a name="line-109"></a> <span class='comment'>-- | combinator for converting an arrow into a determinstic version with all results collected in a single element list</span>
<a name="line-110"></a> <span class='comment'>--</span>
<a name="line-111"></a> <span class='comment'>-- @ listA af = af >>. (:[]) @</span>
<a name="line-112"></a> <span class='comment'>--</span>
<a name="line-113"></a> <span class='comment'>-- this is useful when the list of results computed by an arrow must be manipulated (e.g. sorted)</span>
<a name="line-114"></a> <span class='comment'>--</span>
<a name="line-115"></a> <span class='comment'>-- example for sorting the results of a filter</span>
<a name="line-116"></a> <span class='comment'>--</span>
<a name="line-117"></a> <span class='comment'>-- > collectAndSort :: a b c -> a b c</span>
<a name="line-118"></a> <span class='comment'>-- ></span>
<a name="line-119"></a> <span class='comment'>-- > collectAndSort collect = listA collect >>> arrL sort</span>
<a name="line-120"></a>
<a name="line-121"></a> <span class='varid'>listA</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span>
<a name="line-122"></a> <span class='varid'>listA</span> <span class='varid'>af</span> <span class='keyglyph'>=</span> <span class='varid'>af</span> <span class='varop'>>>.</span> <span class='layout'>(</span><span class='conop'>:</span><span class='conid'>[]</span><span class='layout'>)</span>
<a name="line-123"></a>
<a name="line-124"></a> <span class='comment'>-- | the inverse of 'listA'</span>
<a name="line-125"></a> <span class='comment'>--</span>
<a name="line-126"></a> <span class='comment'>-- @ listA af >>> unlistA = af @</span>
<a name="line-127"></a> <span class='comment'>--</span>
<a name="line-128"></a> <span class='comment'>-- unlistA is defined as @ arrL id @</span>
<a name="line-129"></a>
<a name="line-130"></a> <span class='varid'>unlistA</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span> <span class='varid'>b</span>
<a name="line-131"></a> <span class='varid'>unlistA</span> <span class='keyglyph'>=</span> <span class='varid'>arrL</span> <span class='varid'>id</span>
<a name="line-132"></a>
<a name="line-133"></a> <span class='comment'>-- | the identity arrow, alias for returnA</span>
<a name="line-134"></a>
<a name="line-135"></a> <span class='varid'>this</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>b</span>
<a name="line-136"></a> <span class='varid'>this</span> <span class='keyglyph'>=</span> <span class='varid'>returnA</span>
<a name="line-137"></a>
<a name="line-138"></a> <span class='comment'>-- | the zero arrow, alias for zeroArrow</span>
<a name="line-139"></a>
<a name="line-140"></a> <span class='varid'>none</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span>
<a name="line-141"></a> <span class='varid'>none</span> <span class='keyglyph'>=</span> <span class='varid'>zeroArrow</span>
<a name="line-142"></a>
<a name="line-143"></a> <span class='comment'>-- | converts an arrow, that may fail, into an arrow that always succeeds</span>
<a name="line-144"></a> <span class='comment'>--</span>
<a name="line-145"></a> <span class='comment'>-- example: @ withDefault none \"abc\" @ is equivalent to @ constA \"abc\" @</span>
<a name="line-146"></a>
<a name="line-147"></a> <span class='varid'>withDefault</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span>
<a name="line-148"></a> <span class='varid'>withDefault</span> <span class='varid'>a</span> <span class='varid'>d</span> <span class='keyglyph'>=</span> <span class='varid'>a</span> <span class='varop'>>>.</span> <span class='keyglyph'>\</span> <span class='varid'>x</span> <span class='keyglyph'>-></span> <span class='keyword'>if</span> <span class='varid'>null</span> <span class='varid'>x</span> <span class='keyword'>then</span> <span class='keyglyph'>[</span><span class='varid'>d</span><span class='keyglyph'>]</span> <span class='keyword'>else</span> <span class='varid'>x</span>
<a name="line-149"></a>
<a name="line-150"></a> <span class='comment'>-- | makes a list arrow deterministic, the number of results is at most 1</span>
<a name="line-151"></a> <span class='comment'>--</span>
<a name="line-152"></a> <span class='comment'>-- definition</span>
<a name="line-153"></a> <span class='comment'>--</span>
<a name="line-154"></a> <span class='comment'>-- > single f = f >>. take 1</span>
<a name="line-155"></a> <span class='comment'>--</span>
<a name="line-156"></a> <span class='comment'>-- examples with strings:</span>
<a name="line-157"></a> <span class='comment'>--</span>
<a name="line-158"></a> <span class='comment'>-- > runLA ( single none ) "x" == []</span>
<a name="line-159"></a> <span class='comment'>-- > runLA ( single this ) "x" == ["x"]</span>
<a name="line-160"></a> <span class='comment'>-- > runLA ( single</span>
<a name="line-161"></a> <span class='comment'>-- > (constA "y"</span>
<a name="line-162"></a> <span class='comment'>-- > <+> this ) ) "x" == ["y"]</span>
<a name="line-163"></a>
<a name="line-164"></a> <span class='varid'>single</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span>
<a name="line-165"></a> <span class='varid'>single</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>f</span> <span class='varop'>>>.</span> <span class='varid'>take</span> <span class='num'>1</span>
<a name="line-166"></a>
<a name="line-167"></a> <span class='comment'>-- | compute an arrow from the input and apply the arrow to this input</span>
<a name="line-168"></a> <span class='comment'>--</span>
<a name="line-169"></a> <span class='comment'>-- definition: @ (f &&& this) >>> app @</span>
<a name="line-170"></a> <span class='comment'>--</span>
<a name="line-171"></a> <span class='comment'>-- in a point free style, there is no way to use an argument in 2 places,</span>
<a name="line-172"></a> <span class='comment'>-- this is a combinator for simulating this. first the argument is used to compute an arrow,</span>
<a name="line-173"></a> <span class='comment'>-- then this new arrow is applied to the input</span>
<a name="line-174"></a> <span class='comment'>--</span>
<a name="line-175"></a> <span class='comment'>-- applyA coresponds to: @ apply f x = let g = f x in g x @</span>
<a name="line-176"></a> <span class='comment'>--</span>
<a name="line-177"></a> <span class='comment'>-- see also: '$<', '$<<', '$<<<', '$<<<<', '$<$'</span>
<a name="line-178"></a>
<a name="line-179"></a> <span class='varid'>applyA</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span>
<a name="line-180"></a> <span class='varid'>applyA</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='layout'>(</span><span class='varid'>f</span> <span class='varop'>&&&</span> <span class='varid'>this</span><span class='layout'>)</span> <span class='varop'>>>></span> <span class='varid'>app</span>
<a name="line-181"></a>
<a name="line-182"></a> <span class='comment'>-- | compute the parameter for an arrow with extra parameters from the input</span>
<a name="line-183"></a> <span class='comment'>-- and apply the arrow for all parameter values to the input</span>
<a name="line-184"></a> <span class='comment'>--</span>
<a name="line-185"></a> <span class='comment'>-- a kind of \"function call\" for arrows, useful for joining arrows</span>
<a name="line-186"></a> <span class='comment'>--</span>
<a name="line-187"></a> <span class='comment'>-- > infixl 2 ($<)</span>
<a name="line-188"></a> <span class='comment'>--</span>
<a name="line-189"></a> <span class='comment'>-- definition:</span>
<a name="line-190"></a> <span class='comment'>--</span>
<a name="line-191"></a> <span class='comment'>-- > g $< f = applyA (f >>> arr g)</span>
<a name="line-192"></a> <span class='comment'>--</span>
<a name="line-193"></a> <span class='comment'>-- if @f@ fails, the whole arrow fails, e.g. @ g \$\< none == none @</span>
<a name="line-194"></a> <span class='comment'>--</span>
<a name="line-195"></a> <span class='comment'>-- if @f@ computes n values and @g@ is deterministic, the whole arrow computes n values</span>
<a name="line-196"></a> <span class='comment'>--</span>
<a name="line-197"></a> <span class='comment'>-- examples with simple list arrows with strings</span>
<a name="line-198"></a> <span class='comment'>--</span>
<a name="line-199"></a> <span class='comment'>-- > prefixString :: String -> a String String</span>
<a name="line-200"></a> <span class='comment'>-- > prefixString s = arr (s++)</span>
<a name="line-201"></a> <span class='comment'>-- ></span>
<a name="line-202"></a> <span class='comment'>-- > runLA ( prefixString $< none ) "x" == []</span>
<a name="line-203"></a> <span class='comment'>-- > runLA ( prefixString $< constA "y" ) "x" == ["yx"]</span>
<a name="line-204"></a> <span class='comment'>-- > runLA ( prefixString $< this ) "x" == ["xx"]</span>
<a name="line-205"></a> <span class='comment'>-- > runLA ( prefixString $< constA "y"</span>
<a name="line-206"></a> <span class='comment'>-- > <+> constA "z" ) "x" == ["yx","zx"]</span>
<a name="line-207"></a> <span class='comment'>-- > runLA ( prefixString $< constA "y"</span>
<a name="line-208"></a> <span class='comment'>-- > <+> this</span>
<a name="line-209"></a> <span class='comment'>-- > <+> constA "z" ) "x" == ["yx","xx","zx"]</span>
<a name="line-210"></a> <span class='comment'>--</span>
<a name="line-211"></a> <span class='comment'>-- see also: 'applyA', '$<<', '$<<<', '$<<<<', '$<$'</span>
<a name="line-212"></a>
<a name="line-213"></a> <span class='layout'>(</span><span class='varop'>$<</span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span>
<a name="line-214"></a> <span class='varid'>g</span> <span class='varop'>$<</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>applyA</span> <span class='layout'>(</span><span class='varid'>f</span> <span class='varop'>>>></span> <span class='varid'>arr</span> <span class='varid'>g</span><span class='layout'>)</span>
<a name="line-215"></a>
<a name="line-216"></a> <span class='comment'>-- | binary version of '$<'</span>
<a name="line-217"></a> <span class='comment'>--</span>
<a name="line-218"></a> <span class='comment'>-- example with simple list arrows with strings</span>
<a name="line-219"></a> <span class='comment'>--</span>
<a name="line-220"></a> <span class='comment'>-- > infixString :: String -> String -> a String String</span>
<a name="line-221"></a> <span class='comment'>-- > infixString s1 s2</span>
<a name="line-222"></a> <span class='comment'>-- > = arr (\ s -> s1 ++ s ++ s2)</span>
<a name="line-223"></a> <span class='comment'>-- ></span>
<a name="line-224"></a> <span class='comment'>-- > runLA ( infixString $<< constA "y" &&& constA "z" ) "x" = ["yxz"]</span>
<a name="line-225"></a> <span class='comment'>-- > runLA ( infixString $<< this &&& this ) "x" = ["xxx"]</span>
<a name="line-226"></a> <span class='comment'>-- > runLA ( infixString $<< constA "y"</span>
<a name="line-227"></a> <span class='comment'>-- > &&& (constA "z" <+> this) ) "x" = ["yxz", "yxx"]</span>
<a name="line-228"></a>
<a name="line-229"></a> <span class='layout'>(</span><span class='varop'>$<<</span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>c1</span> <span class='keyglyph'>-></span> <span class='varid'>c2</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='layout'>(</span><span class='varid'>c1</span><span class='layout'>,</span> <span class='varid'>c2</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span>
<a name="line-230"></a> <span class='varid'>f</span> <span class='varop'>$<<</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>applyA</span> <span class='layout'>(</span><span class='varid'>g</span> <span class='varop'>>>></span> <span class='varid'>arr2</span> <span class='varid'>f</span><span class='layout'>)</span>
<a name="line-231"></a>
<a name="line-232"></a> <span class='comment'>-- | version of '$<' for arrows with 3 extra parameters</span>
<a name="line-233"></a> <span class='comment'>--</span>
<a name="line-234"></a> <span class='comment'>-- typical usage</span>
<a name="line-235"></a> <span class='comment'>--</span>
<a name="line-236"></a> <span class='comment'>-- > f $<<< g1 &&& g2 &&& g3</span>
<a name="line-237"></a>
<a name="line-238"></a> <span class='layout'>(</span><span class='varop'>$<<<</span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>c1</span> <span class='keyglyph'>-></span> <span class='varid'>c2</span> <span class='keyglyph'>-></span> <span class='varid'>c3</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='layout'>(</span><span class='varid'>c1</span><span class='layout'>,</span> <span class='layout'>(</span><span class='varid'>c2</span><span class='layout'>,</span> <span class='varid'>c3</span><span class='layout'>)</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span>
<a name="line-239"></a> <span class='varid'>f</span> <span class='varop'>$<<<</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>applyA</span> <span class='layout'>(</span><span class='varid'>g</span> <span class='varop'>>>></span> <span class='varid'>arr3</span> <span class='varid'>f</span><span class='layout'>)</span>
<a name="line-240"></a>
<a name="line-241"></a> <span class='comment'>-- | version of '$<' for arrows with 4 extra parameters</span>
<a name="line-242"></a> <span class='comment'>--</span>
<a name="line-243"></a> <span class='comment'>-- typical usage</span>
<a name="line-244"></a> <span class='comment'>--</span>
<a name="line-245"></a> <span class='comment'>-- > f $<<<< g1 &&& g2 &&& g3 &&& g4</span>
<a name="line-246"></a>
<a name="line-247"></a> <span class='layout'>(</span><span class='varop'>$<<<<</span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>c1</span> <span class='keyglyph'>-></span> <span class='varid'>c2</span> <span class='keyglyph'>-></span> <span class='varid'>c3</span> <span class='keyglyph'>-></span> <span class='varid'>c4</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='layout'>(</span><span class='varid'>c1</span><span class='layout'>,</span> <span class='layout'>(</span><span class='varid'>c2</span><span class='layout'>,</span> <span class='layout'>(</span><span class='varid'>c3</span><span class='layout'>,</span> <span class='varid'>c4</span><span class='layout'>)</span><span class='layout'>)</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span>
<a name="line-248"></a> <span class='varid'>f</span> <span class='varop'>$<<<<</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>applyA</span> <span class='layout'>(</span><span class='varid'>g</span> <span class='varop'>>>></span> <span class='varid'>arr4</span> <span class='varid'>f</span><span class='layout'>)</span>
<a name="line-249"></a>
<a name="line-250"></a> <span class='comment'>-- | compute the parameter for an arrow @f@ with an extra parameter by an arrow @g@</span>
<a name="line-251"></a> <span class='comment'>-- and apply all the results from @g@ sequentially to the input</span>
<a name="line-252"></a> <span class='comment'>--</span>
<a name="line-253"></a> <span class='comment'>-- > infixl 2 ($<$)</span>
<a name="line-254"></a> <span class='comment'>--</span>
<a name="line-255"></a> <span class='comment'>-- typical usage:</span>
<a name="line-256"></a> <span class='comment'>--</span>
<a name="line-257"></a> <span class='comment'>-- > g :: a b c</span>
<a name="line-258"></a> <span class='comment'>-- > g = ...</span>
<a name="line-259"></a> <span class='comment'>-- ></span>
<a name="line-260"></a> <span class='comment'>-- > f :: c -> a b b</span>
<a name="line-261"></a> <span class='comment'>-- > f x = ... x ...</span>
<a name="line-262"></a> <span class='comment'>-- ></span>
<a name="line-263"></a> <span class='comment'>-- > f $<$ g</span>
<a name="line-264"></a> <span class='comment'>--</span>
<a name="line-265"></a> <span class='comment'>-- @f@ computes the extra parameters for @g@ from the input of type @b@ and @g@ is applied with this</span>
<a name="line-266"></a> <span class='comment'>-- parameter to the input. This allows programming in a point wise style in @g@, which becomes</span>
<a name="line-267"></a> <span class='comment'>-- neccessary, when a value is needed more than once.</span>
<a name="line-268"></a> <span class='comment'>--</span>
<a name="line-269"></a> <span class='comment'>-- this combinator is useful, when transforming a single value (document) step by step,</span>
<a name="line-270"></a> <span class='comment'>-- with @g@ for collecting the data for all steps, and @f@ for transforming the input step by step</span>
<a name="line-271"></a> <span class='comment'>--</span>
<a name="line-272"></a> <span class='comment'>-- if @g@ is deterministic (computes exactly one result),</span>
<a name="line-273"></a> <span class='comment'>-- @ g $\<$ f == g $\< f @ holds</span>
<a name="line-274"></a> <span class='comment'>--</span>
<a name="line-275"></a> <span class='comment'>-- if @g@ fails, @ f $<$ g == this @</span>
<a name="line-276"></a> <span class='comment'>--</span>
<a name="line-277"></a> <span class='comment'>-- if @g@ computes more than one result, @f@ is applied sequentially to the input for every result from @g@</span>
<a name="line-278"></a> <span class='comment'>--</span>
<a name="line-279"></a> <span class='comment'>-- examples with simple list arrows with strings</span>
<a name="line-280"></a> <span class='comment'>--</span>
<a name="line-281"></a> <span class='comment'>-- > prefixString :: String -> a String String</span>
<a name="line-282"></a> <span class='comment'>-- > prefixString s = arr (s++)</span>
<a name="line-283"></a> <span class='comment'>-- ></span>
<a name="line-284"></a> <span class='comment'>-- > runLA ( prefixString $<$ none ) "x" == ["x"]</span>
<a name="line-285"></a> <span class='comment'>-- > runLA ( prefixString $<$ constA "y" ) "x" == ["yx"]</span>
<a name="line-286"></a> <span class='comment'>-- > runLA ( prefixString $<$ constA "y" <+> constA "z" ) "x" == ["zyx"]</span>
<a name="line-287"></a> <span class='comment'>-- > runLA ( prefixString $<$ constA "y" <+> this</span>
<a name="line-288"></a> <span class='comment'>-- > <+> constA "z" ) "x" == ["zxyx"]</span>
<a name="line-289"></a> <span class='comment'>--</span>
<a name="line-290"></a> <span class='comment'>-- example with two extra parameter</span>
<a name="line-291"></a> <span class='comment'>--</span>
<a name="line-292"></a> <span class='comment'>-- > g1 :: a b c1</span>
<a name="line-293"></a> <span class='comment'>-- > g2 :: a b c2</span>
<a name="line-294"></a> <span class='comment'>-- ></span>
<a name="line-295"></a> <span class='comment'>-- > f :: (c1, c2) -> a b b</span>
<a name="line-296"></a> <span class='comment'>-- > f (x1, x2) = ... x1 ... x2 ... </span>
<a name="line-297"></a> <span class='comment'>-- ></span>
<a name="line-298"></a> <span class='comment'>-- > f $<$ g1 &&& g2</span>
<a name="line-299"></a> <span class='comment'>--</span>
<a name="line-300"></a> <span class='comment'>-- see also: 'applyA', '$<'</span>
<a name="line-301"></a>
<a name="line-302"></a> <span class='layout'>(</span><span class='varop'>$<$</span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>b</span><span class='layout'>)</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>b</span>
<a name="line-303"></a> <span class='varid'>g</span> <span class='varop'>$<$</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>applyA</span> <span class='layout'>(</span><span class='varid'>listA</span> <span class='layout'>(</span><span class='varid'>f</span> <span class='varop'>>>></span> <span class='varid'>arr</span> <span class='varid'>g</span><span class='layout'>)</span> <span class='varop'>>>></span> <span class='varid'>arr</span> <span class='varid'>seqA</span><span class='layout'>)</span>
<a name="line-304"></a>
<a name="line-305"></a> <span class='comment'>-- | merge the result pairs of an arrow with type @a a1 (b1, b2)@</span>
<a name="line-306"></a> <span class='comment'>-- by combining the tuple components with the @op@ arrow</span>
<a name="line-307"></a> <span class='comment'>--</span>
<a name="line-308"></a> <span class='comment'>-- examples with simple list arrows working on strings and XmlTrees</span>
<a name="line-309"></a> <span class='comment'>--</span>
<a name="line-310"></a> <span class='comment'>-- > a1 :: a String (XmlTree, XmlTree)</span>
<a name="line-311"></a> <span class='comment'>-- > a1 = selem "foo" [this >>> mkText]</span>
<a name="line-312"></a> <span class='comment'>-- > &&&</span>
<a name="line-313"></a> <span class='comment'>-- > selem "bar" [arr (++"0") >>> mkText]</span>
<a name="line-314"></a> <span class='comment'>-- > </span>
<a name="line-315"></a> <span class='comment'>-- > runLA (a1 >>> mergeA (<+>) >>> xshow this) "42" == ["<foo>42</foo>","<bar>420</bar>"]</span>
<a name="line-316"></a> <span class='comment'>-- > runLA (a1 >>> mergeA (+=) >>> xshow this) "42" == ["<foo>42<bar>420</bar></foo>"]</span>
<a name="line-317"></a> <span class='comment'>--</span>
<a name="line-318"></a> <span class='comment'>-- see also: 'applyA', '$<' and '+=' in class 'Text.XML.HXT.Arrow.ArrowXml'</span>
<a name="line-319"></a>
<a name="line-320"></a> <span class='varid'>mergeA</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='layout'>(</span><span class='varid'>a1</span><span class='layout'>,</span> <span class='varid'>b1</span><span class='layout'>)</span> <span class='varid'>a1</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='layout'>(</span><span class='varid'>a1</span><span class='layout'>,</span> <span class='varid'>b1</span><span class='layout'>)</span> <span class='varid'>b1</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='layout'>(</span><span class='varid'>a1</span><span class='layout'>,</span> <span class='varid'>b1</span><span class='layout'>)</span> <span class='varid'>c</span><span class='layout'>)</span> <span class='keyglyph'>-></span>
<a name="line-321"></a> <span class='varid'>a</span> <span class='layout'>(</span><span class='varid'>a1</span><span class='layout'>,</span> <span class='varid'>b1</span><span class='layout'>)</span> <span class='varid'>c</span>
<a name="line-322"></a> <span class='varid'>mergeA</span> <span class='varid'>op</span> <span class='keyglyph'>=</span> <span class='layout'>(</span><span class='keyglyph'>\</span> <span class='varid'>x</span> <span class='keyglyph'>-></span> <span class='varid'>arr</span> <span class='varid'>fst</span> <span class='varop'>`op`</span> <span class='varid'>constA</span> <span class='layout'>(</span><span class='varid'>snd</span> <span class='varid'>x</span><span class='layout'>)</span><span class='layout'>)</span> <span class='varop'>$<</span> <span class='varid'>this</span>
<a name="line-323"></a>
<a name="line-324"></a> <span class='comment'>-- | useful only for arrows with side effects: perform applies an arrow to the input</span>
<a name="line-325"></a> <span class='comment'>-- ignores the result and returns the input</span>
<a name="line-326"></a> <span class='comment'>--</span>
<a name="line-327"></a> <span class='comment'>-- example: @ ... >>> perform someTraceArrow >>> ... @</span>
<a name="line-328"></a>
<a name="line-329"></a> <span class='varid'>perform</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>b</span>
<a name="line-330"></a> <span class='varid'>perform</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>listA</span> <span class='varid'>f</span> <span class='varop'>&&&</span> <span class='varid'>this</span> <span class='varop'>>>></span> <span class='varid'>arr</span> <span class='varid'>snd</span>
<a name="line-331"></a>
<a name="line-332"></a> <span class='comment'>-- | generalization of arrow combinator '<+>'</span>
<a name="line-333"></a> <span class='comment'>--</span>
<a name="line-334"></a> <span class='comment'>-- definition: @ catA = foldl (<+>) none @</span>
<a name="line-335"></a>
<a name="line-336"></a> <span class='varid'>catA</span> <span class='keyglyph'>::</span> <span class='keyglyph'>[</span><span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span>
<a name="line-337"></a> <span class='varid'>catA</span> <span class='keyglyph'>=</span> <span class='varid'>foldl</span> <span class='layout'>(</span><span class='varop'><+></span><span class='layout'>)</span> <span class='varid'>none</span>
<a name="line-338"></a>
<a name="line-339"></a> <span class='comment'>-- | generalization of arrow combinator '>>>'</span>
<a name="line-340"></a> <span class='comment'>--</span>
<a name="line-341"></a> <span class='comment'>-- definition: @ seqA = foldl (>>>) this @</span>
<a name="line-342"></a>
<a name="line-343"></a> <span class='varid'>seqA</span> <span class='keyglyph'>::</span> <span class='keyglyph'>[</span><span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>b</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>b</span>
<a name="line-344"></a> <span class='varid'>seqA</span> <span class='keyglyph'>=</span> <span class='varid'>foldl</span> <span class='layout'>(</span><span class='varop'>>>></span><span class='layout'>)</span> <span class='varid'>this</span>
<a name="line-345"></a>
<a name="line-346"></a><span class='comment'>-- ------------------------------------------------------------</span>
</pre></body>
</html>