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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.ArrowIf
<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: ArrowIf.hs,v 1.8 2006/05/04 14:17:53 hxml Exp $
<a name="line-12"></a>
<a name="line-13"></a>Conditionals for List Arrows
<a name="line-14"></a>
<a name="line-15"></a>This module defines conditional combinators for list arrows.
<a name="line-16"></a>
<a name="line-17"></a>The empty list as result represents False, none empty lists True.
<a name="line-18"></a>
<a name="line-19"></a>-}</span>
<a name="line-20"></a>
<a name="line-21"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-22"></a>
<a name="line-23"></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'>ArrowIf</span>
<a name="line-24"></a> <span class='layout'>(</span> <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'>ArrowIf</span>
<a name="line-25"></a> <span class='layout'>)</span>
<a name="line-26"></a><span class='keyword'>where</span>
<a name="line-27"></a>
<a name="line-28"></a><span class='keyword'>import</span> <span class='conid'>Control</span><span class='varop'>.</span><span class='conid'>Arrow</span>
<a name="line-29"></a><span class='keyword'>import</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-30"></a>
<a name="line-31"></a><span class='keyword'>import</span> <span class='conid'>Data</span><span class='varop'>.</span><span class='conid'>List</span>
<a name="line-32"></a> <span class='layout'>(</span> <span class='varid'>partition</span> <span class='layout'>)</span>
<a name="line-33"></a>
<a name="line-34"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-35"></a>
<a name="line-36"></a><span class='comment'>-- | The interface for arrows as conditionals.</span>
<a name="line-37"></a><span class='comment'>--</span>
<a name="line-38"></a><span class='comment'>-- Requires list arrows because False is represented as empty list, True as none empty lists.</span>
<a name="line-39"></a><span class='comment'>--</span>
<a name="line-40"></a><span class='comment'>-- Only 'ifA' and 'orElse' don't have default implementations</span>
<a name="line-41"></a>
<a name="line-42"></a><a name="ArrowIf"></a><span class='keyword'>class</span> <span class='conid'>ArrowList</span> <span class='varid'>a</span> <span class='keyglyph'>=></span> <span class='conid'>ArrowIf</span> <span class='varid'>a</span> <span class='keyword'>where</span>
<a name="line-43"></a>
<a name="line-44"></a> <span class='comment'>-- | if lifted to arrows</span>
<a name="line-45"></a>
<a name="line-46"></a> <span class='varid'>ifA</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> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span>
<a name="line-47"></a>
<a name="line-48"></a> <span class='comment'>-- | shortcut: @ ifP p = ifA (isA p) @</span>
<a name="line-49"></a>
<a name="line-50"></a> <span class='varid'>ifP</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'>d</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span>
<a name="line-51"></a> <span class='varid'>ifP</span> <span class='varid'>p</span> <span class='keyglyph'>=</span> <span class='varid'>ifA</span> <span class='layout'>(</span><span class='varid'>isA</span> <span class='varid'>p</span><span class='layout'>)</span>
<a name="line-52"></a>
<a name="line-53"></a> <span class='comment'>-- | negation: @ neg f = ifA f none this @</span>
<a name="line-54"></a>
<a name="line-55"></a> <span class='varid'>neg</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-56"></a> <span class='varid'>neg</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>ifA</span> <span class='varid'>f</span> <span class='varid'>none</span> <span class='varid'>this</span>
<a name="line-57"></a>
<a name="line-58"></a> <span class='comment'>-- | @ f \`when\` g @ : when the predicate g holds, f is applied, else the identity filter this</span>
<a name="line-59"></a>
<a name="line-60"></a> <span class='varid'>when</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='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-61"></a> <span class='varid'>f</span> <span class='varop'>`when`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>ifA</span> <span class='varid'>g</span> <span class='varid'>f</span> <span class='varid'>this</span>
<a name="line-62"></a>
<a name="line-63"></a> <span class='comment'>-- | shortcut: @ f \`whenP\` p = f \`when\` (isA p) @</span>
<a name="line-64"></a>
<a name="line-65"></a> <span class='varid'>whenP</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='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-66"></a> <span class='varid'>f</span> <span class='varop'>`whenP`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>ifP</span> <span class='varid'>g</span> <span class='varid'>f</span> <span class='varid'>this</span>
<a name="line-67"></a>
<a name="line-68"></a> <span class='comment'>-- | @ f \`whenNot\` g @ : when the predicate g does not hold, f is applied, else the identity filter this</span>
<a name="line-69"></a>
<a name="line-70"></a> <span class='varid'>whenNot</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='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-71"></a> <span class='varid'>f</span> <span class='varop'>`whenNot`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>ifA</span> <span class='varid'>g</span> <span class='varid'>this</span> <span class='varid'>f</span>
<a name="line-72"></a>
<a name="line-73"></a> <span class='comment'>-- | like 'whenP'</span>
<a name="line-74"></a>
<a name="line-75"></a> <span class='varid'>whenNotP</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='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-76"></a> <span class='varid'>f</span> <span class='varop'>`whenNotP`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>ifP</span> <span class='varid'>g</span> <span class='varid'>this</span> <span class='varid'>f</span>
<a name="line-77"></a>
<a name="line-78"></a> <span class='comment'>-- | @ g \`guards\` f @ : when the predicate g holds, f is applied, else none</span>
<a name="line-79"></a>
<a name="line-80"></a> <span class='varid'>guards</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> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span>
<a name="line-81"></a> <span class='varid'>f</span> <span class='varop'>`guards`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>ifA</span> <span class='varid'>f</span> <span class='varid'>g</span> <span class='varid'>none</span>
<a name="line-82"></a>
<a name="line-83"></a> <span class='comment'>-- | like 'whenP'</span>
<a name="line-84"></a>
<a name="line-85"></a> <span class='varid'>guardsP</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'>d</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span>
<a name="line-86"></a> <span class='varid'>f</span> <span class='varop'>`guardsP`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>ifP</span> <span class='varid'>f</span> <span class='varid'>g</span> <span class='varid'>none</span>
<a name="line-87"></a>
<a name="line-88"></a> <span class='comment'>-- | shortcut for @ f `guards` this @</span>
<a name="line-89"></a>
<a name="line-90"></a> <span class='varid'>filterA</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-91"></a> <span class='varid'>filterA</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>ifA</span> <span class='varid'>f</span> <span class='varid'>this</span> <span class='varid'>none</span>
<a name="line-92"></a>
<a name="line-93"></a> <span class='comment'>-- | @ f \`containing\` g @ : keep only those results from f for which g holds</span>
<a name="line-94"></a> <span class='comment'>--</span>
<a name="line-95"></a> <span class='comment'>-- definition: @ f \`containing\` g = f >>> g \`guards\` this @</span>
<a name="line-96"></a>
<a name="line-97"></a> <span class='varid'>containing</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'>c</span> <span class='varid'>d</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span>
<a name="line-98"></a> <span class='varid'>f</span> <span class='varop'>`containing`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>f</span> <span class='varop'>>>></span> <span class='varid'>g</span> <span class='varop'>`guards`</span> <span class='varid'>this</span>
<a name="line-99"></a>
<a name="line-100"></a> <span class='comment'>-- | @ f \`notContaining\` g @ : keep only those results from f for which g does not hold</span>
<a name="line-101"></a> <span class='comment'>--</span>
<a name="line-102"></a> <span class='comment'>-- definition: @ f \`notContaining\` g = f >>> ifA g none this @</span>
<a name="line-103"></a>
<a name="line-104"></a> <span class='varid'>notContaining</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'>c</span> <span class='varid'>d</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span>
<a name="line-105"></a> <span class='varid'>f</span> <span class='varop'>`notContaining`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>f</span> <span class='varop'>>>></span> <span class='varid'>ifA</span> <span class='varid'>g</span> <span class='varid'>none</span> <span class='varid'>this</span>
<a name="line-106"></a>
<a name="line-107"></a> <span class='comment'>-- | @ f \`orElse\` g @ : directional choice: if f succeeds, the result of f is the result, else g is applied</span>
<a name="line-108"></a> <span class='varid'>orElse</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> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>c</span>
<a name="line-109"></a>
<a name="line-110"></a> <span class='comment'>-- | generalisation of 'orElse' for multi way branches like in case expressions.</span>
<a name="line-111"></a> <span class='comment'>--</span>
<a name="line-112"></a> <span class='comment'>-- An auxiliary data type 'IfThen' with an infix constructor ':->' is used for writing multi way branches</span>
<a name="line-113"></a> <span class='comment'>--</span>
<a name="line-114"></a> <span class='comment'>-- example: @ choiceA [ p1 :-> e1, p2 :-> e2, this :-> default ] @</span>
<a name="line-115"></a> <span class='varid'>choiceA</span> <span class='keyglyph'>::</span> <span class='keyglyph'>[</span><span class='conid'>IfThen</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='layout'>(</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='keyglyph'>-></span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='varid'>d</span>
<a name="line-116"></a> <span class='varid'>choiceA</span> <span class='keyglyph'>=</span> <span class='varid'>foldr</span> <span class='varid'>ifA'</span> <span class='varid'>none</span>
<a name="line-117"></a> <span class='keyword'>where</span>
<a name="line-118"></a> <span class='varid'>ifA'</span> <span class='layout'>(</span><span class='varid'>g</span> <span class='conop'>:-></span> <span class='varid'>f</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='varid'>ifA</span> <span class='varid'>g</span> <span class='varid'>f</span>
<a name="line-119"></a>
<a name="line-120"></a>
<a name="line-121"></a> <span class='comment'>-- | tag a value with Left or Right, if arrow has success, input is tagged with Left, else with Right</span>
<a name="line-122"></a> <span class='varid'>tagA</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='layout'>(</span><span class='conid'>Either</span> <span class='varid'>b</span> <span class='varid'>b</span><span class='layout'>)</span>
<a name="line-123"></a> <span class='varid'>tagA</span> <span class='varid'>p</span> <span class='keyglyph'>=</span> <span class='varid'>ifA</span> <span class='varid'>p</span> <span class='layout'>(</span><span class='varid'>arr</span> <span class='conid'>Left</span><span class='layout'>)</span> <span class='layout'>(</span><span class='varid'>arr</span> <span class='conid'>Right</span><span class='layout'>)</span>
<a name="line-124"></a>
<a name="line-125"></a>
<a name="line-126"></a> <span class='comment'>-- | split a list value with an arrow and returns a pair of lists.</span>
<a name="line-127"></a> <span class='comment'>-- This is the arrow version of 'span'. The arrow is deterministic.</span>
<a name="line-128"></a> <span class='comment'>--</span>
<a name="line-129"></a> <span class='comment'>-- example: @ runLA (spanA (isA (\/= \'-\'))) \"abc-def\" @ gives @ [(\"abc\",\"-def\")] @ as result</span>
<a name="line-130"></a>
<a name="line-131"></a> <span class='varid'>spanA</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='varid'>a</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span> <span class='layout'>(</span><span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>,</span><span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-132"></a> <span class='varid'>spanA</span> <span class='varid'>p</span> <span class='keyglyph'>=</span> <span class='varid'>ifA</span> <span class='layout'>(</span> <span class='varid'>arrL</span> <span class='layout'>(</span><span class='varid'>take</span> <span class='num'>1</span><span class='layout'>)</span> <span class='varop'>>>></span> <span class='varid'>p</span> <span class='layout'>)</span>
<a name="line-133"></a> <span class='layout'>(</span> <span class='varid'>arr</span> <span class='varid'>head</span> <span class='varop'>&&&</span> <span class='layout'>(</span><span class='varid'>arr</span> <span class='varid'>tail</span> <span class='varop'>>>></span> <span class='varid'>spanA</span> <span class='varid'>p</span><span class='layout'>)</span>
<a name="line-134"></a> <span class='varop'>>>></span>
<a name="line-135"></a> <span class='varid'>arr</span> <span class='layout'>(</span><span class='keyglyph'>\</span> <span class='keyglyph'>~</span><span class='layout'>(</span><span class='varid'>x</span><span class='layout'>,</span> <span class='keyglyph'>~</span><span class='layout'>(</span><span class='varid'>xs</span><span class='layout'>,</span><span class='varid'>ys</span><span class='layout'>)</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>x</span> <span class='conop'>:</span> <span class='varid'>xs</span><span class='layout'>,</span> <span class='varid'>ys</span><span class='layout'>)</span><span class='layout'>)</span>
<a name="line-136"></a> <span class='layout'>)</span>
<a name="line-137"></a> <span class='layout'>(</span> <span class='varid'>arr</span> <span class='layout'>(</span><span class='keyglyph'>\</span> <span class='varid'>l</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='conid'>[]</span><span class='layout'>,</span><span class='varid'>l</span><span class='layout'>)</span><span class='layout'>)</span> <span class='layout'>)</span>
<a name="line-138"></a>
<a name="line-139"></a> <span class='comment'>-- | partition a list of values into a pair of lists</span>
<a name="line-140"></a> <span class='comment'>--</span>
<a name="line-141"></a> <span class='comment'>-- This is the arrow Version of 'Data.List.partition'</span>
<a name="line-142"></a>
<a name="line-143"></a> <span class='varid'>partitionA</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='varid'>a</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span> <span class='layout'>(</span><span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>,</span><span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-144"></a> <span class='varid'>partitionA</span> <span class='varid'>p</span> <span class='keyglyph'>=</span> <span class='varid'>listA</span> <span class='layout'>(</span> <span class='varid'>arrL</span> <span class='varid'>id</span> <span class='varop'>>>></span> <span class='varid'>tagA</span> <span class='varid'>p</span> <span class='layout'>)</span>
<a name="line-145"></a> <span class='varop'>>>^</span>
<a name="line-146"></a> <span class='layout'>(</span> <span class='layout'>(</span><span class='keyglyph'>\</span> <span class='keyglyph'>~</span><span class='layout'>(</span><span class='varid'>l1</span><span class='layout'>,</span> <span class='varid'>l2</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>unTag</span> <span class='varid'>l1</span><span class='layout'>,</span> <span class='varid'>unTag</span> <span class='varid'>l2</span><span class='layout'>)</span> <span class='layout'>)</span> <span class='varop'>.</span> <span class='varid'>partition</span> <span class='layout'>(</span><span class='varid'>isLeft</span><span class='layout'>)</span> <span class='layout'>)</span>
<a name="line-147"></a> <span class='keyword'>where</span>
<a name="line-148"></a> <span class='varid'>isLeft</span> <span class='layout'>(</span><span class='conid'>Left</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>True</span>
<a name="line-149"></a> <span class='varid'>isLeft</span> <span class='keyword'>_</span> <span class='keyglyph'>=</span> <span class='conid'>False</span>
<a name="line-150"></a> <span class='varid'>unTag</span> <span class='keyglyph'>=</span> <span class='varid'>map</span> <span class='layout'>(</span><span class='varid'>either</span> <span class='varid'>id</span> <span class='varid'>id</span><span class='layout'>)</span>
<a name="line-151"></a>
<a name="line-152"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-153"></a>
<a name="line-154"></a><span class='comment'>-- | an auxiliary data type for 'choiceA'</span>
<a name="line-155"></a>
<a name="line-156"></a><a name="IfThen"></a><span class='keyword'>data</span> <span class='conid'>IfThen</span> <span class='varid'>a</span> <span class='varid'>b</span> <span class='keyglyph'>=</span> <span class='varid'>a</span> <span class='conop'>:-></span> <span class='varid'>b</span>
<a name="line-157"></a>
<a name="line-158"></a><span class='comment'>-- ------------------------------------------------------------</span>
</pre></body>
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