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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 : Data.Tree.NTree.Filter
<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: Filter.hs,v 1.6 2006/11/12 14:52:59 hxml Exp $
<a name="line-12"></a>
<a name="line-13"></a>Filter for n-ary tree structure with filter combinators
<a name="line-14"></a>copied and modified from HxXml (<<a href="http://www.cs.york.ac.uk/fp/HaXml/">http://www.cs.york.ac.uk/fp/HaXml/</a>>)
<a name="line-15"></a>
<a name="line-16"></a>Similar but more flexible functions for tree processing are defined in the
<a name="line-17"></a>arrow classes "Control.Arrow.ArrowList", "Control.Arrow.ArrowIf", "Control.Arrow.ArrowTree" and "Control.Arrow.ArrowState".
<a name="line-18"></a>For new applications, especially for XML processing, it's recommended to use the arrow interface
<a name="line-19"></a>"Text.XML.HXT.Arrow" instead of this filter approach as part of the api "Text.XML.HXT.Parser"
<a name="line-20"></a>
<a name="line-21"></a>-}</span>
<a name="line-22"></a>
<a name="line-23"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-24"></a>
<a name="line-25"></a><span class='keyword'>module</span> <span class='conid'>Data</span><span class='varop'>.</span><span class='conid'>Tree</span><span class='varop'>.</span><span class='conid'>NTree</span><span class='varop'>.</span><span class='conid'>Filter</span>
<a name="line-26"></a> <span class='layout'>(</span> <span class='keyword'>module</span> <span class='conid'>Data</span><span class='varop'>.</span><span class='conid'>Tree</span><span class='varop'>.</span><span class='conid'>NTree</span><span class='varop'>.</span><span class='conid'>TypeDefs</span>
<a name="line-27"></a> <span class='layout'>,</span> <span class='conid'>TFilter</span>
<a name="line-28"></a> <span class='layout'>,</span> <span class='conid'>TSFilter</span>
<a name="line-29"></a> <span class='layout'>,</span> <span class='varid'>satisfies</span>
<a name="line-30"></a>
<a name="line-31"></a> <span class='comment'>-- * Filter</span>
<a name="line-32"></a> <span class='layout'>,</span> <span class='varid'>none</span> <span class='comment'>-- simple filter</span>
<a name="line-33"></a> <span class='layout'>,</span> <span class='varid'>this</span>
<a name="line-34"></a>
<a name="line-35"></a> <span class='layout'>,</span> <span class='varid'>isOf</span>
<a name="line-36"></a> <span class='layout'>,</span> <span class='varid'>isOfNode</span> <span class='comment'>-- predicate filter</span>
<a name="line-37"></a>
<a name="line-38"></a> <span class='layout'>,</span> <span class='varid'>mkNTree</span> <span class='comment'>-- contructor filter</span>
<a name="line-39"></a>
<a name="line-40"></a> <span class='layout'>,</span> <span class='varid'>replaceNode</span> <span class='comment'>-- simple editing</span>
<a name="line-41"></a> <span class='layout'>,</span> <span class='varid'>replaceChildren</span>
<a name="line-42"></a>
<a name="line-43"></a> <span class='layout'>,</span> <span class='varid'>modifyNode</span>
<a name="line-44"></a> <span class='layout'>,</span> <span class='varid'>modifyNode0</span>
<a name="line-45"></a> <span class='layout'>,</span> <span class='varid'>modifyChildren</span>
<a name="line-46"></a> <span class='layout'>,</span> <span class='varid'>substChildren</span>
<a name="line-47"></a> <span class='layout'>,</span> <span class='varid'>processChildren</span> <span class='comment'>-- filter combinators</span>
<a name="line-48"></a>
<a name="line-49"></a> <span class='layout'>,</span> <span class='varid'>o</span>
<a name="line-50"></a> <span class='layout'>,</span> <span class='layout'>(</span><span class='varop'>.></span><span class='layout'>)</span>
<a name="line-51"></a> <span class='layout'>,</span> <span class='varid'>seqF</span>
<a name="line-52"></a> <span class='layout'>,</span> <span class='layout'>(</span><span class='varop'>..></span><span class='layout'>)</span>
<a name="line-53"></a> <span class='layout'>,</span> <span class='layout'>(</span><span class='varop'>+++</span><span class='layout'>)</span>
<a name="line-54"></a> <span class='layout'>,</span> <span class='varid'>cat</span>
<a name="line-55"></a>
<a name="line-56"></a> <span class='layout'>,</span> <span class='varid'>orElse</span> <span class='comment'>-- choices</span>
<a name="line-57"></a> <span class='layout'>,</span> <span class='varid'>iff</span> <span class='comment'>-- if then else filter</span>
<a name="line-58"></a> <span class='layout'>,</span> <span class='varid'>choice</span>
<a name="line-59"></a> <span class='layout'>,</span> <span class='conid'>IfThen</span><span class='layout'>(</span><span class='keyglyph'>..</span><span class='layout'>)</span>
<a name="line-60"></a> <span class='layout'>,</span> <span class='varid'>when</span>
<a name="line-61"></a> <span class='layout'>,</span> <span class='varid'>whenNot</span>
<a name="line-62"></a> <span class='layout'>,</span> <span class='varid'>guards</span>
<a name="line-63"></a> <span class='layout'>,</span> <span class='varid'>neg</span> <span class='comment'>-- negation</span>
<a name="line-64"></a> <span class='layout'>,</span> <span class='varid'>containing</span> <span class='comment'>-- previous: with, but with is keyword in haskell extensions</span>
<a name="line-65"></a> <span class='layout'>,</span> <span class='varid'>notContaining</span> <span class='comment'>-- previous: without</span>
<a name="line-66"></a>
<a name="line-67"></a> <span class='layout'>,</span> <span class='layout'>(</span><span class='varop'>/></span><span class='layout'>)</span> <span class='comment'>-- selectors</span>
<a name="line-68"></a> <span class='layout'>,</span> <span class='layout'>(</span><span class='varop'></</span><span class='layout'>)</span>
<a name="line-69"></a> <span class='layout'>,</span> <span class='varid'>deep</span> <span class='comment'>-- recursive search</span>
<a name="line-70"></a> <span class='layout'>,</span> <span class='varid'>deepest</span>
<a name="line-71"></a> <span class='layout'>,</span> <span class='varid'>multi</span>
<a name="line-72"></a> <span class='layout'>,</span> <span class='varid'>processBottomUp</span> <span class='comment'>-- recursive editing</span>
<a name="line-73"></a> <span class='layout'>,</span> <span class='varid'>processBottomUpIfNot</span>
<a name="line-74"></a> <span class='layout'>,</span> <span class='varid'>processTopDown</span>
<a name="line-75"></a> <span class='layout'>,</span> <span class='varid'>processTopDownUntil</span>
<a name="line-76"></a> <span class='layout'>,</span> <span class='varid'>insertChildrenAt</span>
<a name="line-77"></a> <span class='layout'>,</span> <span class='varid'>insertChildrenAfter</span>
<a name="line-78"></a>
<a name="line-79"></a> <span class='comment'>-- * Monadic Filter</span>
<a name="line-80"></a> <span class='layout'>,</span> <span class='varid'>thisM</span> <span class='comment'>-- monadic filter</span>
<a name="line-81"></a> <span class='layout'>,</span> <span class='varid'>noneM</span>
<a name="line-82"></a> <span class='layout'>,</span> <span class='layout'>(</span><span class='varop'>.>></span><span class='layout'>)</span> <span class='comment'>-- monadic composition</span>
<a name="line-83"></a> <span class='layout'>,</span> <span class='varid'>seqM</span> <span class='comment'>-- generalisation of .>></span>
<a name="line-84"></a> <span class='layout'>,</span> <span class='layout'>(</span><span class='varop'>+++>></span><span class='layout'>)</span> <span class='comment'>-- monadic parallel combination, monadic +++</span>
<a name="line-85"></a> <span class='layout'>,</span> <span class='varid'>catM</span> <span class='comment'>-- monadic form of cat</span>
<a name="line-86"></a> <span class='layout'>,</span> <span class='varid'>ifM</span> <span class='comment'>-- monadic if then else</span>
<a name="line-87"></a> <span class='layout'>,</span> <span class='varid'>choiceM</span> <span class='comment'>-- monadic choice</span>
<a name="line-88"></a> <span class='layout'>,</span> <span class='varid'>whenM</span> <span class='comment'>-- special monadic ifs</span>
<a name="line-89"></a> <span class='layout'>,</span> <span class='varid'>whenNotM</span>
<a name="line-90"></a> <span class='layout'>,</span> <span class='varid'>guardsM</span>
<a name="line-91"></a> <span class='layout'>,</span> <span class='varid'>containingM</span>
<a name="line-92"></a> <span class='layout'>,</span> <span class='varid'>processChildrenM</span> <span class='comment'>-- monadic versions of recursive editing</span>
<a name="line-93"></a> <span class='layout'>,</span> <span class='varid'>processTopDownM</span>
<a name="line-94"></a> <span class='layout'>,</span> <span class='varid'>processBottomUpM</span>
<a name="line-95"></a> <span class='layout'>,</span> <span class='varid'>liftMf</span> <span class='comment'>-- lift a normal filter to a monadic filter</span>
<a name="line-96"></a> <span class='layout'>,</span> <span class='layout'>(</span><span class='varop'>$$</span><span class='layout'>)</span> <span class='comment'>-- apply a filter to a list</span>
<a name="line-97"></a> <span class='layout'>,</span> <span class='layout'>(</span><span class='varop'>$$<</span><span class='layout'>)</span> <span class='comment'>-- apply a monad filter to a list</span>
<a name="line-98"></a> <span class='layout'>,</span> <span class='varid'>performAction</span> <span class='comment'>-- run a command within a filter</span>
<a name="line-99"></a> <span class='layout'>)</span>
<a name="line-100"></a>
<a name="line-101"></a><span class='keyword'>where</span>
<a name="line-102"></a>
<a name="line-103"></a>
<a name="line-104"></a><span class='keyword'>import</span> <span class='conid'>Data</span><span class='varop'>.</span><span class='conid'>Tree</span><span class='varop'>.</span><span class='conid'>NTree</span><span class='varop'>.</span><span class='conid'>TypeDefs</span>
<a name="line-105"></a>
<a name="line-106"></a><span class='keyword'>infixl</span> <span class='num'>6</span> <span class='varop'>`containing`</span><span class='layout'>,</span> <span class='varop'>`notContaining`</span><span class='layout'>,</span> <span class='varop'>`containingM`</span>
<a name="line-107"></a><span class='keyword'>infixr</span> <span class='num'>5</span> <span class='varop'>`o`</span><span class='layout'>,</span> <span class='varop'>+++</span><span class='layout'>,</span> <span class='varop'>+++>></span>
<a name="line-108"></a><span class='keyword'>infixl</span> <span class='num'>5</span> <span class='varop'>/></span><span class='layout'>,</span> <span class='varop'></</span><span class='layout'>,</span> <span class='varop'>`orElse`</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-109"></a><span class='keyword'>infixr</span> <span class='num'>4</span> <span class='varop'>`when`</span><span class='layout'>,</span> <span class='varop'>`whenNot`</span><span class='layout'>,</span> <span class='varop'>`guards`</span><span class='layout'>,</span> <span class='varop'>`whenM`</span><span class='layout'>,</span> <span class='varop'>`whenNotM`</span><span class='layout'>,</span> <span class='varop'>`guardsM`</span>
<a name="line-110"></a><span class='keyword'>infixr</span> <span class='num'>3</span> <span class='conop'>:-></span>
<a name="line-111"></a><span class='keyword'>infixr</span> <span class='num'>0</span> <span class='varop'>$$</span><span class='layout'>,</span> <span class='varop'>$$<</span>
<a name="line-112"></a>
<a name="line-113"></a><span class='comment'>-- |</span>
<a name="line-114"></a><span class='comment'>-- tree filter type: a function mapping a tree onto a list of trees</span>
<a name="line-115"></a><span class='comment'>--</span>
<a name="line-116"></a><span class='comment'>-- filter can be used in various ways, as predicates, selectors, transformers, ...</span>
<a name="line-117"></a>
<a name="line-118"></a><a name="TFilter"></a><span class='keyword'>type</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>=</span> <span class='conid'>NTree</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>NTrees</span> <span class='varid'>node</span>
<a name="line-119"></a>
<a name="line-120"></a><span class='comment'>-- |</span>
<a name="line-121"></a><span class='comment'>-- a filter for sequences</span>
<a name="line-122"></a>
<a name="line-123"></a><a name="TSFilter"></a><span class='keyword'>type</span> <span class='conid'>TSFilter</span> <span class='varid'>node</span> <span class='keyglyph'>=</span> <span class='conid'>NTrees</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>NTrees</span> <span class='varid'>node</span>
<a name="line-124"></a>
<a name="line-125"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-126"></a>
<a name="line-127"></a><span class='comment'>-- |</span>
<a name="line-128"></a><span class='comment'>-- satisfies converts a result of a predicate filter into a boolean</span>
<a name="line-129"></a><span class='comment'>--</span>
<a name="line-130"></a><span class='comment'>-- is a shortcut for not . null</span>
<a name="line-131"></a><span class='comment'>--</span>
<a name="line-132"></a><span class='comment'>-- typical use in guards or ifs: @if (satisfies f) t then ... else ... @</span>
<a name="line-133"></a><span class='comment'>--</span>
<a name="line-134"></a><span class='comment'>-- * 1.parameter f : the predicate filter</span>
<a name="line-135"></a><span class='comment'>--</span>
<a name="line-136"></a><span class='comment'>-- - 2.parameter t : the tree to be tested</span>
<a name="line-137"></a><span class='comment'>--</span>
<a name="line-138"></a><span class='comment'>-- - returns : @b = not (null (f t))@</span>
<a name="line-139"></a>
<a name="line-140"></a><a name="satisfies"></a><span class='definition'>satisfies</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></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'>a</span> <span class='keyglyph'>-></span> <span class='conid'>Bool</span>
<a name="line-141"></a><span class='definition'>satisfies</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>not</span> <span class='varop'>.</span> <span class='varid'>null</span> <span class='varop'>.</span> <span class='varid'>f</span>
<a name="line-142"></a>
<a name="line-143"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-144"></a><span class='comment'>--</span>
<a name="line-145"></a><span class='comment'>-- simple filter</span>
<a name="line-146"></a>
<a name="line-147"></a><span class='comment'>-- |</span>
<a name="line-148"></a><span class='comment'>-- the null filter, returns the empty list</span>
<a name="line-149"></a>
<a name="line-150"></a><a name="none"></a><span class='definition'>none</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span>
<a name="line-151"></a><span class='definition'>none</span> <span class='keyword'>_</span> <span class='keyglyph'>=</span> <span class='conid'>[]</span>
<a name="line-152"></a>
<a name="line-153"></a><span class='comment'>-- |</span>
<a name="line-154"></a><span class='comment'>-- the unit filter, returns the single element list containing the argument</span>
<a name="line-155"></a>
<a name="line-156"></a><a name="this"></a><span class='definition'>this</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span>
<a name="line-157"></a><span class='definition'>this</span> <span class='varid'>n</span> <span class='keyglyph'>=</span> <span class='keyglyph'>[</span><span class='varid'>n</span><span class='keyglyph'>]</span>
<a name="line-158"></a>
<a name="line-159"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-160"></a><span class='comment'>--</span>
<a name="line-161"></a><span class='comment'>-- selecting filter</span>
<a name="line-162"></a>
<a name="line-163"></a><span class='comment'>-- |</span>
<a name="line-164"></a><span class='comment'>-- conversion from predicate function to filter</span>
<a name="line-165"></a><span class='comment'>--</span>
<a name="line-166"></a><span class='comment'>-- * 1.parameter p : the predicate for testing the tree</span>
<a name="line-167"></a><span class='comment'>--</span>
<a name="line-168"></a><span class='comment'>-- - returns : 'this' or 'none' depending on the predicate</span>
<a name="line-169"></a>
<a name="line-170"></a><a name="isOf"></a><span class='definition'>isOf</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>Bool</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-171"></a><span class='definition'>isOf</span> <span class='varid'>p</span> <span class='varid'>t</span>
<a name="line-172"></a> <span class='keyglyph'>=</span> <span class='keyword'>if</span> <span class='varid'>p</span> <span class='varid'>t</span> <span class='keyword'>then</span> <span class='keyglyph'>[</span><span class='varid'>t</span><span class='keyglyph'>]</span> <span class='keyword'>else</span> <span class='conid'>[]</span>
<a name="line-173"></a>
<a name="line-174"></a><span class='comment'>-- |</span>
<a name="line-175"></a><span class='comment'>-- select filter, selects trees with node values with a specific property</span>
<a name="line-176"></a><span class='comment'>--</span>
<a name="line-177"></a><span class='comment'>-- * 1.parameter p : the predicate for testing the node value</span>
<a name="line-178"></a><span class='comment'>--</span>
<a name="line-179"></a><span class='comment'>-- - returns : @[]@ or @[t]@ depending on @p t@</span>
<a name="line-180"></a><span class='comment'>--</span>
<a name="line-181"></a><span class='comment'>-- a special case of 'isOf' filter</span>
<a name="line-182"></a>
<a name="line-183"></a><a name="isOfNode"></a><span class='definition'>isOfNode</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>Bool</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-184"></a><span class='definition'>isOfNode</span> <span class='varid'>p</span> <span class='keyglyph'>=</span> <span class='varid'>isOf</span> <span class='layout'>(</span><span class='varid'>p</span> <span class='varop'>.</span> <span class='varid'>getNode</span><span class='layout'>)</span>
<a name="line-185"></a>
<a name="line-186"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-187"></a><span class='comment'>--</span>
<a name="line-188"></a><span class='comment'>-- simple editing filters</span>
<a name="line-189"></a>
<a name="line-190"></a><span class='comment'>-- |</span>
<a name="line-191"></a><span class='comment'>-- filter for substituting an arbitray tree by a constant</span>
<a name="line-192"></a><span class='comment'>--</span>
<a name="line-193"></a><span class='comment'>-- * 1.parameter t : the result tree, the input tree is ignored</span>
<a name="line-194"></a><span class='comment'>--</span>
<a name="line-195"></a><span class='comment'>-- - returns : the filter</span>
<a name="line-196"></a>
<a name="line-197"></a><a name="mkNTree"></a><span class='definition'>mkNTree</span> <span class='keyglyph'>::</span> <span class='conid'>NTree</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-198"></a><span class='definition'>mkNTree</span> <span class='varid'>t</span> <span class='keyglyph'>=</span> <span class='varid'>const</span> <span class='keyglyph'>[</span><span class='varid'>t</span><span class='keyglyph'>]</span>
<a name="line-199"></a>
<a name="line-200"></a><span class='comment'>-- |</span>
<a name="line-201"></a><span class='comment'>-- filter for replacing the node</span>
<a name="line-202"></a><span class='comment'>--</span>
<a name="line-203"></a><span class='comment'>-- * 1.parameter n : the new node</span>
<a name="line-204"></a><span class='comment'>--</span>
<a name="line-205"></a><span class='comment'>-- - returns : the editing filter</span>
<a name="line-206"></a>
<a name="line-207"></a><a name="replaceNode"></a><span class='definition'>replaceNode</span> <span class='keyglyph'>::</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-208"></a><span class='definition'>replaceNode</span> <span class='varid'>n</span> <span class='layout'>(</span><span class='conid'>NTree</span> <span class='keyword'>_</span> <span class='varid'>cs</span><span class='layout'>)</span>
<a name="line-209"></a> <span class='keyglyph'>=</span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>n</span> <span class='varid'>cs</span><span class='keyglyph'>]</span>
<a name="line-210"></a>
<a name="line-211"></a><span class='comment'>-- |</span>
<a name="line-212"></a><span class='comment'>-- filter for replacing the children</span>
<a name="line-213"></a><span class='comment'>--</span>
<a name="line-214"></a><span class='comment'>-- * 1.parameter cs : cs the list of children</span>
<a name="line-215"></a><span class='comment'>--</span>
<a name="line-216"></a><span class='comment'>-- - returns : the filter</span>
<a name="line-217"></a>
<a name="line-218"></a><a name="replaceChildren"></a><span class='definition'>replaceChildren</span> <span class='keyglyph'>::</span> <span class='conid'>NTrees</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-219"></a><span class='definition'>replaceChildren</span> <span class='varid'>cs</span> <span class='layout'>(</span><span class='conid'>NTree</span> <span class='varid'>n</span> <span class='keyword'>_</span><span class='layout'>)</span>
<a name="line-220"></a> <span class='keyglyph'>=</span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>n</span> <span class='varid'>cs</span><span class='keyglyph'>]</span>
<a name="line-221"></a>
<a name="line-222"></a><a name="modifyNode"></a><span class='definition'>modifyNode</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>Maybe</span> <span class='varid'>node</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-223"></a><span class='definition'>modifyNode</span> <span class='varid'>tf</span> <span class='layout'>(</span><span class='conid'>NTree</span> <span class='varid'>n</span> <span class='varid'>cs</span><span class='layout'>)</span>
<a name="line-224"></a> <span class='keyglyph'>=</span> <span class='varid'>maybe</span> <span class='conid'>[]</span> <span class='layout'>(</span><span class='keyglyph'>\</span> <span class='varid'>n'</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>n'</span> <span class='varid'>cs</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='layout'>(</span><span class='varid'>tf</span> <span class='varid'>n</span><span class='layout'>)</span>
<a name="line-225"></a>
<a name="line-226"></a><span class='comment'>-- |</span>
<a name="line-227"></a><span class='comment'>-- filter for editing the node</span>
<a name="line-228"></a><span class='comment'>--</span>
<a name="line-229"></a><span class='comment'>-- * 1.parameter nf : the XNode editing funtion</span>
<a name="line-230"></a><span class='comment'>--</span>
<a name="line-231"></a><span class='comment'>-- - returns : the filter</span>
<a name="line-232"></a>
<a name="line-233"></a><a name="modifyNode0"></a><span class='definition'>modifyNode0</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='varid'>node</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-234"></a><span class='definition'>modifyNode0</span> <span class='varid'>tf</span> <span class='keyglyph'>=</span> <span class='varid'>modifyNode</span> <span class='layout'>(</span><span class='conid'>Just</span> <span class='varop'>.</span> <span class='varid'>tf</span><span class='layout'>)</span>
<a name="line-235"></a>
<a name="line-236"></a><span class='comment'>-- |</span>
<a name="line-237"></a><span class='comment'>-- filter for editing the children</span>
<a name="line-238"></a><span class='comment'>--</span>
<a name="line-239"></a><span class='comment'>-- all children are processed with a filter mapping lists to lists,</span>
<a name="line-240"></a><span class='comment'>-- this enables not only elementwise editing by lifting a normal</span>
<a name="line-241"></a><span class='comment'>-- filter to a list filter with @(f $$)@ (see '($$)') but also manipulation</span>
<a name="line-242"></a><span class='comment'>-- of the order of the elements, e.g. "reverse" is an appropriate childen</span>
<a name="line-243"></a><span class='comment'>-- editing function.</span>
<a name="line-244"></a><span class='comment'>--</span>
<a name="line-245"></a><span class='comment'>-- * 1.parameter csf : the children editing function</span>
<a name="line-246"></a><span class='comment'>--</span>
<a name="line-247"></a><span class='comment'>-- - returns : the filter</span>
<a name="line-248"></a><span class='comment'>--</span>
<a name="line-249"></a><span class='comment'>-- see also : 'processChildren'</span>
<a name="line-250"></a>
<a name="line-251"></a><a name="modifyChildren"></a><span class='definition'>modifyChildren</span> <span class='keyglyph'>::</span> <span class='conid'>TSFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-252"></a><span class='definition'>modifyChildren</span> <span class='varid'>f</span> <span class='comment'>-- (NTree n cs)</span>
<a name="line-253"></a> <span class='comment'>-- = [NTree n (f cs)]</span>
<a name="line-254"></a> <span class='keyglyph'>=</span> <span class='varid'>substChildren</span> <span class='layout'>(</span><span class='varid'>f</span> <span class='varop'>.</span> <span class='varid'>getChildren</span><span class='layout'>)</span>
<a name="line-255"></a>
<a name="line-256"></a><span class='comment'>-- |</span>
<a name="line-257"></a><span class='comment'>-- filter for substituting the children of a tree by</span>
<a name="line-258"></a><span class='comment'>-- a new list of childen computed by applying a filter to the input tree.</span>
<a name="line-259"></a><span class='comment'>-- 'modifyChildren' can be expressed by 'substChildren':</span>
<a name="line-260"></a><span class='comment'>-- @modifyChildren f t@ is equal to @substChildren (f . getChildren)@</span>
<a name="line-261"></a>
<a name="line-262"></a><a name="substChildren"></a><span class='definition'>substChildren</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-263"></a><span class='definition'>substChildren</span> <span class='varid'>f</span> <span class='varid'>t</span><span class='keyglyph'>@</span><span class='layout'>(</span><span class='conid'>NTree</span> <span class='varid'>n</span> <span class='sel'>_cs</span><span class='layout'>)</span>
<a name="line-264"></a> <span class='keyglyph'>=</span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>n</span> <span class='layout'>(</span><span class='varid'>f</span> <span class='varid'>t</span><span class='layout'>)</span><span class='keyglyph'>]</span>
<a name="line-265"></a>
<a name="line-266"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-267"></a><span class='comment'>--</span>
<a name="line-268"></a><span class='comment'>-- combinators (copied from HaXml)</span>
<a name="line-269"></a><span class='comment'>--</span>
<a name="line-270"></a>
<a name="line-271"></a><span class='comment'>-- |</span>
<a name="line-272"></a><span class='comment'>-- sequential composition of filters, usually written in infix notation f2 `o` f1.</span>
<a name="line-273"></a><span class='comment'>--</span>
<a name="line-274"></a><span class='comment'>-- for predicate filter the logical AND</span>
<a name="line-275"></a><span class='comment'>--</span>
<a name="line-276"></a><span class='comment'>-- * 1.parameter f2 : the 2. filter</span>
<a name="line-277"></a><span class='comment'>--</span>
<a name="line-278"></a><span class='comment'>-- - 2.parameter f1 : the 1. filter</span>
<a name="line-279"></a><span class='comment'>--</span>
<a name="line-280"></a><span class='comment'>-- - returns : the fiter applying first f1 to n and then f2 to the result (like function composition)</span>
<a name="line-281"></a>
<a name="line-282"></a><a name="o"></a><span class='definition'>o</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-283"></a><a name="o"></a><span class='definition'>f</span> <span class='varop'>`o`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>concatMap</span> <span class='varid'>f</span> <span class='varop'>.</span> <span class='varid'>g</span>
<a name="line-284"></a>
<a name="line-285"></a><span class='comment'>-- |</span>
<a name="line-286"></a><span class='comment'>-- pronounced \"followed by\", defined as: @f .> g = g \`o\` f@.</span>
<a name="line-287"></a><span class='comment'>--</span>
<a name="line-288"></a><span class='comment'>-- allows filter composition in a more readable way from left to right</span>
<a name="line-289"></a><span class='comment'>--</span>
<a name="line-290"></a><span class='comment'>-- * 1.parameter f1 : the 1. filter</span>
<a name="line-291"></a><span class='comment'>--</span>
<a name="line-292"></a><span class='comment'>-- - 2.parameter f2 : the 2. filter</span>
<a name="line-293"></a><span class='comment'>--</span>
<a name="line-294"></a><span class='comment'>-- - returns : the composition of f1 and f2</span>
<a name="line-295"></a><span class='comment'>--</span>
<a name="line-296"></a><span class='comment'>-- see also : 'o', '(..>)'</span>
<a name="line-297"></a>
<a name="line-298"></a><a name=".>"></a><span class='layout'>(</span><span class='varop'>.></span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</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='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-299"></a><a name="f"></a><span class='definition'>f</span> <span class='varop'>.></span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>g</span> <span class='varop'>`o`</span> <span class='varid'>f</span>
<a name="line-300"></a>
<a name="line-301"></a><span class='comment'>-- |</span>
<a name="line-302"></a><span class='comment'>-- apply a list of filters sequentially with '(.>)', for predicate filters the generalized AND</span>
<a name="line-303"></a><span class='comment'>--</span>
<a name="line-304"></a><span class='comment'>-- see also : '(.>)'</span>
<a name="line-305"></a>
<a name="line-306"></a><a name="seqF"></a><span class='definition'>seqF</span> <span class='keyglyph'>::</span> <span class='keyglyph'>[</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-307"></a><span class='definition'>seqF</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-308"></a>
<a name="line-309"></a><span class='comment'>-- |</span>
<a name="line-310"></a><span class='comment'>-- binary parallel composition, the logical OR for predicate filter</span>
<a name="line-311"></a><span class='comment'>--</span>
<a name="line-312"></a><span class='comment'>-- * 1.parameter f1 : the 1. filter</span>
<a name="line-313"></a><span class='comment'>--</span>
<a name="line-314"></a><span class='comment'>-- - 2.parameter f2 : the 2. filter</span>
<a name="line-315"></a><span class='comment'>--</span>
<a name="line-316"></a><span class='comment'>-- - returns : the filter for applying f1 and f2 both to an argument tree and concatenating the results</span>
<a name="line-317"></a>
<a name="line-318"></a><a name="+++"></a><span class='layout'>(</span><span class='varop'>+++</span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-319"></a><span class='definition'>f</span> <span class='varop'>+++</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='keyglyph'>\</span> <span class='varid'>t</span> <span class='keyglyph'>-></span> <span class='varid'>f</span> <span class='varid'>t</span> <span class='varop'>++</span> <span class='varid'>g</span> <span class='varid'>t</span>
<a name="line-320"></a>
<a name="line-321"></a><span class='comment'>-- |</span>
<a name="line-322"></a><span class='comment'>-- special sequential composition.</span>
<a name="line-323"></a><span class='comment'>--</span>
<a name="line-324"></a><span class='comment'>-- filter f is applied to an argument t.</span>
<a name="line-325"></a><span class='comment'>-- then filter g is applied to all elements of the result list,</span>
<a name="line-326"></a><span class='comment'>-- but the argument t is also passed as extra parameter to g.</span>
<a name="line-327"></a><span class='comment'>--</span>
<a name="line-328"></a><span class='comment'>-- This allows for step by step transformations of a tree</span>
<a name="line-329"></a><span class='comment'>-- with access to the original tree in every</span>
<a name="line-330"></a><span class='comment'>-- transformation step.</span>
<a name="line-331"></a><span class='comment'>--</span>
<a name="line-332"></a><span class='comment'>-- see also : '(.>)', 'o'</span>
<a name="line-333"></a>
<a name="line-334"></a><a name="..>"></a><span class='layout'>(</span><span class='varop'>..></span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>b</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='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>d</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-335"></a><span class='definition'>f</span> <span class='varop'>..></span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='keyglyph'>\</span> <span class='varid'>t</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>g</span> <span class='varid'>t</span> <span class='varop'>`o`</span> <span class='varid'>f</span><span class='layout'>)</span> <span class='varid'>t</span>
<a name="line-336"></a>
<a name="line-337"></a><span class='comment'>-- |</span>
<a name="line-338"></a><span class='comment'>-- apply a list of filters, a \"union\" for lists, for predicate filters the generalized OR</span>
<a name="line-339"></a><span class='comment'>--</span>
<a name="line-340"></a><span class='comment'>-- * 1.parameter fs : the list of filters</span>
<a name="line-341"></a><span class='comment'>--</span>
<a name="line-342"></a><span class='comment'>-- - returns : the composing filter</span>
<a name="line-343"></a>
<a name="line-344"></a><a name="cat"></a><span class='definition'>cat</span> <span class='keyglyph'>::</span> <span class='keyglyph'>[</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-345"></a><span class='definition'>cat</span> <span class='varid'>fs</span> <span class='varid'>t</span>
<a name="line-346"></a> <span class='keyglyph'>=</span> <span class='varid'>concat</span> <span class='keyglyph'>[</span> <span class='varid'>f</span> <span class='varid'>t</span> <span class='keyglyph'>|</span> <span class='varid'>f</span> <span class='keyglyph'><-</span> <span class='varid'>fs</span> <span class='keyglyph'>]</span>
<a name="line-347"></a>
<a name="line-348"></a><span class='comment'>-- |</span>
<a name="line-349"></a><span class='comment'>-- Filter for editing the children of a tree element wise</span>
<a name="line-350"></a><span class='comment'>--</span>
<a name="line-351"></a><span class='comment'>-- * 1.parameter cf : the filter applied to the children</span>
<a name="line-352"></a><span class='comment'>--</span>
<a name="line-353"></a><span class='comment'>-- - returns : the editing filter</span>
<a name="line-354"></a><span class='comment'>--</span>
<a name="line-355"></a><span class='comment'>-- see also : 'modifyChildren'</span>
<a name="line-356"></a>
<a name="line-357"></a><a name="processChildren"></a><span class='definition'>processChildren</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-358"></a><span class='definition'>processChildren</span> <span class='varid'>ft</span> <span class='layout'>(</span><span class='conid'>NTree</span> <span class='varid'>n</span> <span class='varid'>cs</span><span class='layout'>)</span>
<a name="line-359"></a> <span class='keyglyph'>=</span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>n</span> <span class='layout'>(</span><span class='varid'>ft</span> <span class='varop'>$$</span> <span class='varid'>cs</span><span class='layout'>)</span><span class='keyglyph'>]</span>
<a name="line-360"></a>
<a name="line-361"></a><span class='comment'>-- |</span>
<a name="line-362"></a><span class='comment'>-- infix operator for applying a filter to a list of trees</span>
<a name="line-363"></a><span class='comment'>--</span>
<a name="line-364"></a><span class='comment'>-- * 1.parameter f : the filter</span>
<a name="line-365"></a><span class='comment'>--</span>
<a name="line-366"></a><span class='comment'>-- - 2.parameter ts : the list of trees</span>
<a name="line-367"></a><span class='comment'>--</span>
<a name="line-368"></a><span class='comment'>-- - returns : the concatenated list of results</span>
<a name="line-369"></a>
<a name="line-370"></a><a name="$$"></a><span class='layout'>(</span><span class='varop'>$$</span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span>
<a name="line-371"></a><span class='definition'>f</span> <span class='varop'>$$</span> <span class='varid'>l</span>
<a name="line-372"></a> <span class='keyglyph'>=</span> <span class='varid'>concatMap</span> <span class='varid'>f</span> <span class='varid'>l</span>
<a name="line-373"></a>
<a name="line-374"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-375"></a><span class='comment'>--</span>
<a name="line-376"></a><span class='comment'>-- choices</span>
<a name="line-377"></a><span class='comment'>--</span>
<a name="line-378"></a>
<a name="line-379"></a><span class='comment'>-- |</span>
<a name="line-380"></a><span class='comment'>-- directional choice, usually written in infix notation as f `orElse` g</span>
<a name="line-381"></a><span class='comment'>--</span>
<a name="line-382"></a><span class='comment'>-- * 1.parameter f : the 1. filter</span>
<a name="line-383"></a><span class='comment'>--</span>
<a name="line-384"></a><span class='comment'>-- - 2.parameter g : the 2. filter</span>
<a name="line-385"></a><span class='comment'>--</span>
<a name="line-386"></a><span class='comment'>-- - 3.parameter t : the tree</span>
<a name="line-387"></a><span class='comment'>--</span>
<a name="line-388"></a><span class='comment'>-- - returns : the filter, that applies f to t, if the result is not the empty list, the result is found, else g t is the result</span>
<a name="line-389"></a>
<a name="line-390"></a><a name="orElse"></a><span class='definition'>orElse</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-391"></a><a name="orElse"></a><span class='definition'>f</span> <span class='varop'>`orElse`</span> <span class='varid'>g</span>
<a name="line-392"></a> <span class='keyglyph'>=</span> <span class='keyglyph'>\</span> <span class='varid'>t</span><span class='keyglyph'>-></span> <span class='keyword'>let</span>
<a name="line-393"></a> <span class='varid'>res</span> <span class='keyglyph'>=</span> <span class='varid'>f</span> <span class='varid'>t</span>
<a name="line-394"></a> <span class='keyword'>in</span>
<a name="line-395"></a> <span class='keyword'>if</span> <span class='varid'>null</span> <span class='varid'>res</span>
<a name="line-396"></a> <span class='keyword'>then</span> <span class='varid'>g</span> <span class='varid'>t</span>
<a name="line-397"></a> <span class='keyword'>else</span> <span class='varid'>res</span>
<a name="line-398"></a>
<a name="line-399"></a><span class='comment'>-- |</span>
<a name="line-400"></a><span class='comment'>-- if then else lifted to filters</span>
<a name="line-401"></a><span class='comment'>--</span>
<a name="line-402"></a><span class='comment'>-- * 1.parameter p : the predicate filter</span>
<a name="line-403"></a><span class='comment'>--</span>
<a name="line-404"></a><span class='comment'>-- - 2.parameter t : the \"then\" filter</span>
<a name="line-405"></a><span class='comment'>--</span>
<a name="line-406"></a><span class='comment'>-- - 3.parameter e : the \"else\" filter</span>
<a name="line-407"></a><span class='comment'>--</span>
<a name="line-408"></a><span class='comment'>-- - returns : the resulting conditional filter</span>
<a name="line-409"></a>
<a name="line-410"></a><a name="iff"></a><span class='definition'>iff</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</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='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-411"></a><span class='definition'>iff</span> <span class='varid'>p</span> <span class='varid'>f</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='keyglyph'>\</span> <span class='varid'>c</span> <span class='keyglyph'>-></span> <span class='keyword'>if</span> <span class='layout'>(</span><span class='varid'>satisfies</span> <span class='varid'>p</span><span class='layout'>)</span> <span class='varid'>c</span> <span class='keyword'>then</span> <span class='varid'>f</span> <span class='varid'>c</span> <span class='keyword'>else</span> <span class='varid'>g</span> <span class='varid'>c</span>
<a name="line-412"></a>
<a name="line-413"></a><span class='comment'>-- |</span>
<a name="line-414"></a><span class='comment'>-- when the predicate p holds, f is applied, else the identity filter this</span>
<a name="line-415"></a><span class='comment'>--</span>
<a name="line-416"></a><span class='comment'>-- * 1.parameter f : the conditinally applied filter</span>
<a name="line-417"></a><span class='comment'>--</span>
<a name="line-418"></a><span class='comment'>-- - 2.parameter p : the predicate</span>
<a name="line-419"></a><span class='comment'>--</span>
<a name="line-420"></a><span class='comment'>-- - returns : the conditional filter</span>
<a name="line-421"></a><span class='comment'>--</span>
<a name="line-422"></a><span class='comment'>-- see also : 'iff', 'whenNot', 'guards', 'whenM'</span>
<a name="line-423"></a>
<a name="line-424"></a><a name="when"></a><span class='definition'>when</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-425"></a><a name="when"></a><span class='definition'>f</span> <span class='varop'>`when`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>iff</span> <span class='varid'>g</span> <span class='varid'>f</span> <span class='varid'>this</span>
<a name="line-426"></a>
<a name="line-427"></a><span class='comment'>-- |</span>
<a name="line-428"></a><span class='comment'>-- the complementary filter of when</span>
<a name="line-429"></a><span class='comment'>--</span>
<a name="line-430"></a><span class='comment'>-- shortcut for f `when` neg g</span>
<a name="line-431"></a><span class='comment'>--</span>
<a name="line-432"></a><span class='comment'>-- see also : 'iff', 'when', 'whenNotM', 'neg'</span>
<a name="line-433"></a>
<a name="line-434"></a><a name="whenNot"></a><span class='definition'>whenNot</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-435"></a><a name="whenNot"></a><span class='definition'>f</span> <span class='varop'>`whenNot`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>iff</span> <span class='varid'>g</span> <span class='varid'>this</span> <span class='varid'>f</span>
<a name="line-436"></a>
<a name="line-437"></a><span class='comment'>-- |</span>
<a name="line-438"></a><span class='comment'>-- when the predicate p holds, f is applied, else the null filter none</span>
<a name="line-439"></a><span class='comment'>--</span>
<a name="line-440"></a><span class='comment'>-- * 1.parameter p : the predicate filter</span>
<a name="line-441"></a><span class='comment'>--</span>
<a name="line-442"></a><span class='comment'>-- - 2.parameter f : the conditionally applied filter</span>
<a name="line-443"></a><span class='comment'>--</span>
<a name="line-444"></a><span class='comment'>-- - returns : the conditional filter</span>
<a name="line-445"></a><span class='comment'>--</span>
<a name="line-446"></a><span class='comment'>-- see also : 'iff', 'when', 'guardsM'</span>
<a name="line-447"></a>
<a name="line-448"></a><a name="guards"></a><span class='definition'>guards</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-449"></a><a name="guards"></a><span class='definition'>g</span> <span class='varop'>`guards`</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>iff</span> <span class='varid'>g</span> <span class='varid'>f</span> <span class='varid'>none</span>
<a name="line-450"></a>
<a name="line-451"></a>
<a name="line-452"></a><span class='comment'>-- |</span>
<a name="line-453"></a><span class='comment'>-- negation lifted to filters</span>
<a name="line-454"></a><span class='comment'>--</span>
<a name="line-455"></a><span class='comment'>-- * 1.parameter f : the predicate filter</span>
<a name="line-456"></a><span class='comment'>--</span>
<a name="line-457"></a><span class='comment'>-- - returns : the filter, that succeeds, when f failed</span>
<a name="line-458"></a>
<a name="line-459"></a><a name="neg"></a><span class='definition'>neg</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</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='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span>
<a name="line-460"></a><span class='definition'>neg</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>iff</span> <span class='varid'>f</span> <span class='varid'>none</span> <span class='varid'>this</span>
<a name="line-461"></a>
<a name="line-462"></a><span class='comment'>-- |</span>
<a name="line-463"></a><span class='comment'>-- auxiliary datatype for cases within choice filter</span>
<a name="line-464"></a>
<a name="line-465"></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-466"></a>
<a name="line-467"></a><span class='comment'>-- |</span>
<a name="line-468"></a><span class='comment'>-- multiway branch. The list of cases @f :-> g@ is processed sequentially,</span>
<a name="line-469"></a><span class='comment'>-- in the first case for that f holds g is applied, if no case matches, 'none' is</span>
<a name="line-470"></a><span class='comment'>-- applied.</span>
<a name="line-471"></a><span class='comment'>-- This filter can be used like a case expression: @choice [ p1 :-> f1, p2 :-> f2, ... , this :-> defaultFilter]@</span>
<a name="line-472"></a><span class='comment'>--</span>
<a name="line-473"></a><span class='comment'>-- see also : 'iff', 'choiceM'</span>
<a name="line-474"></a>
<a name="line-475"></a><a name="choice"></a><span class='definition'>choice</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='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-476"></a><span class='definition'>choice</span> <span class='conid'>[]</span>
<a name="line-477"></a> <span class='keyglyph'>=</span> <span class='varid'>none</span>
<a name="line-478"></a>
<a name="line-479"></a><span class='definition'>choice</span> <span class='layout'>(</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='conop'>:</span> <span class='varid'>cs</span><span class='layout'>)</span>
<a name="line-480"></a> <span class='keyglyph'>=</span> <span class='varid'>iff</span> <span class='varid'>g</span> <span class='varid'>f</span> <span class='layout'>(</span><span class='varid'>choice</span> <span class='varid'>cs</span><span class='layout'>)</span>
<a name="line-481"></a>
<a name="line-482"></a><span class='comment'>-- |</span>
<a name="line-483"></a><span class='comment'>-- pruning: keep only those results from f for which g holds, usually written in infix notation as f `containing` g</span>
<a name="line-484"></a><span class='comment'>--</span>
<a name="line-485"></a><span class='comment'>-- * 1.parameter f : the processing filter</span>
<a name="line-486"></a><span class='comment'>--</span>
<a name="line-487"></a><span class='comment'>-- - 2.parameter g : the predicate filter</span>
<a name="line-488"></a><span class='comment'>--</span>
<a name="line-489"></a><span class='comment'>-- - 3.parameter t : the tree</span>
<a name="line-490"></a><span class='comment'>--</span>
<a name="line-491"></a><span class='comment'>-- - returns : all trees r from f t, for which g r holds (is not the empty list)</span>
<a name="line-492"></a><span class='comment'>--</span>
<a name="line-493"></a><span class='comment'>-- see also : 'notContaining'</span>
<a name="line-494"></a>
<a name="line-495"></a><a name="containing"></a><span class='definition'>containing</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</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='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span>
<a name="line-496"></a><a name="containing"></a><span class='definition'>f</span> <span class='varop'>`containing`</span> <span class='varid'>g</span>
<a name="line-497"></a> <span class='keyglyph'>=</span> <span class='varid'>filter</span> <span class='layout'>(</span><span class='varid'>satisfies</span> <span class='varid'>g</span><span class='layout'>)</span> <span class='varop'>.</span> <span class='varid'>f</span>
<a name="line-498"></a>
<a name="line-499"></a><span class='comment'>-- |</span>
<a name="line-500"></a><span class='comment'>-- pruning: keep only those results from f for which g does not hold</span>
<a name="line-501"></a><span class='comment'>--</span>
<a name="line-502"></a><span class='comment'>-- see also : 'containing'</span>
<a name="line-503"></a>
<a name="line-504"></a><a name="notContaining"></a><span class='definition'>notContaining</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</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='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span>
<a name="line-505"></a><a name="notContaining"></a><span class='definition'>f</span> <span class='varop'>`notContaining`</span> <span class='varid'>g</span>
<a name="line-506"></a> <span class='keyglyph'>=</span> <span class='varid'>filter</span> <span class='layout'>(</span><span class='varid'>null</span> <span class='varop'>.</span> <span class='varid'>g</span><span class='layout'>)</span> <span class='varop'>.</span> <span class='varid'>f</span>
<a name="line-507"></a>
<a name="line-508"></a><span class='comment'>-- |</span>
<a name="line-509"></a><span class='comment'>-- pruning: monadic version of containing, usually written in infix notation as f `containingM` g</span>
<a name="line-510"></a><span class='comment'>--</span>
<a name="line-511"></a><span class='comment'>-- * 1.parameter f : the monadic processing filter</span>
<a name="line-512"></a><span class='comment'>--</span>
<a name="line-513"></a><span class='comment'>-- - 2.parameter g : the predicate filter</span>
<a name="line-514"></a><span class='comment'>--</span>
<a name="line-515"></a><span class='comment'>-- - 3.parameter t : the tree</span>
<a name="line-516"></a><span class='comment'>--</span>
<a name="line-517"></a><span class='comment'>-- - returns : all trees r from f t, for which g r holds (is not the empty list)</span>
<a name="line-518"></a><span class='comment'>--</span>
<a name="line-519"></a><span class='comment'>-- see also : 'notContaining'</span>
<a name="line-520"></a>
<a name="line-521"></a><a name="containingM"></a><span class='definition'>containingM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</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='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span>
<a name="line-522"></a><a name="containingM"></a><span class='definition'>f</span> <span class='varop'>`containingM`</span> <span class='varid'>g</span>
<a name="line-523"></a> <span class='keyglyph'>=</span> <span class='keyglyph'>\</span> <span class='varid'>t</span> <span class='keyglyph'>-></span> <span class='keyword'>do</span>
<a name="line-524"></a> <span class='varid'>res</span> <span class='keyglyph'><-</span> <span class='varid'>f</span> <span class='varid'>t</span>
<a name="line-525"></a> <span class='varid'>return</span> <span class='varop'>$</span> <span class='varid'>filter</span> <span class='layout'>(</span><span class='varid'>satisfies</span> <span class='varid'>g</span><span class='layout'>)</span> <span class='varid'>res</span>
<a name="line-526"></a>
<a name="line-527"></a><span class='comment'>-- |</span>
<a name="line-528"></a><span class='comment'>-- pronounced \"slash\", meaning g inside f</span>
<a name="line-529"></a>
<a name="line-530"></a><a name="/>"></a><span class='layout'>(</span><span class='varop'>/></span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-531"></a><span class='definition'>f</span> <span class='varop'>/></span> <span class='varid'>g</span>
<a name="line-532"></a> <span class='keyglyph'>=</span> <span class='varid'>g</span> <span class='varop'>`o`</span> <span class='varid'>getChildren</span> <span class='varop'>`o`</span> <span class='varid'>f</span>
<a name="line-533"></a>
<a name="line-534"></a><span class='comment'>-- |</span>
<a name="line-535"></a><span class='comment'>-- pronounced \"outside\" meaning f containing g</span>
<a name="line-536"></a>
<a name="line-537"></a><a name="</"></a><span class='layout'>(</span><span class='varop'></</span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-538"></a><span class='definition'>f</span> <span class='varop'></</span> <span class='varid'>g</span>
<a name="line-539"></a> <span class='keyglyph'>=</span> <span class='varid'>f</span> <span class='varop'>`containing`</span> <span class='layout'>(</span><span class='varid'>g</span> <span class='varop'>`o`</span> <span class='varid'>getChildren</span><span class='layout'>)</span>
<a name="line-540"></a>
<a name="line-541"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-542"></a><span class='comment'>--</span>
<a name="line-543"></a><span class='comment'>-- recursive search filters</span>
<a name="line-544"></a>
<a name="line-545"></a><span class='comment'>-- |</span>
<a name="line-546"></a><span class='comment'>-- top down search.</span>
<a name="line-547"></a><span class='comment'>--</span>
<a name="line-548"></a><span class='comment'>-- search terminates, when filter f succeeds</span>
<a name="line-549"></a><span class='comment'>-- can e.g. be used for finding all outermost tag node of a specific kind</span>
<a name="line-550"></a>
<a name="line-551"></a><a name="deep"></a><span class='definition'>deep</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-552"></a><span class='definition'>deep</span> <span class='varid'>f</span>
<a name="line-553"></a> <span class='keyglyph'>=</span> <span class='varid'>f</span> <span class='varop'>`orElse`</span> <span class='layout'>(</span><span class='varid'>deep</span> <span class='varid'>f</span> <span class='varop'>`o`</span> <span class='varid'>getChildren</span><span class='layout'>)</span>
<a name="line-554"></a>
<a name="line-555"></a><span class='comment'>-- |</span>
<a name="line-556"></a><span class='comment'>-- bottom up search.</span>
<a name="line-557"></a><span class='comment'>--</span>
<a name="line-558"></a><span class='comment'>-- first the children are processed,</span>
<a name="line-559"></a><span class='comment'>-- if this does not succeed, the node itself is processed</span>
<a name="line-560"></a><span class='comment'>-- can e.g. be used for finding all innermost tag nodes of a specific kind</span>
<a name="line-561"></a>
<a name="line-562"></a><a name="deepest"></a><span class='definition'>deepest</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-563"></a><span class='definition'>deepest</span> <span class='varid'>f</span>
<a name="line-564"></a> <span class='keyglyph'>=</span> <span class='layout'>(</span><span class='varid'>getChildren</span> <span class='varop'>.></span> <span class='varid'>deepest</span> <span class='varid'>f</span><span class='layout'>)</span> <span class='varop'>`orElse`</span> <span class='varid'>f</span>
<a name="line-565"></a>
<a name="line-566"></a><span class='comment'>-- |</span>
<a name="line-567"></a><span class='comment'>-- process all nodes of the whole tree.</span>
<a name="line-568"></a><span class='comment'>--</span>
<a name="line-569"></a><span class='comment'>-- can e.g. be used for finding all nodes of a specific kind</span>
<a name="line-570"></a>
<a name="line-571"></a><a name="multi"></a><span class='definition'>multi</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-572"></a><span class='definition'>multi</span> <span class='varid'>f</span>
<a name="line-573"></a> <span class='keyglyph'>=</span> <span class='varid'>f</span> <span class='varop'>+++</span> <span class='layout'>(</span><span class='varid'>getChildren</span> <span class='varop'>.></span> <span class='varid'>multi</span> <span class='varid'>f</span><span class='layout'>)</span>
<a name="line-574"></a>
<a name="line-575"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-576"></a><span class='comment'>--</span>
<a name="line-577"></a><span class='comment'>-- recursive transformation filters</span>
<a name="line-578"></a><span class='comment'>--</span>
<a name="line-579"></a>
<a name="line-580"></a><span class='comment'>-- |</span>
<a name="line-581"></a><span class='comment'>-- bottom up transformation</span>
<a name="line-582"></a><span class='comment'>--</span>
<a name="line-583"></a><span class='comment'>-- * 1.parameter f : the /simple/ transforming filter</span>
<a name="line-584"></a><span class='comment'>--</span>
<a name="line-585"></a><span class='comment'>-- - returns : the filter that applies f to all subtrees and the tree itself in a deepth first left to right manner</span>
<a name="line-586"></a><span class='comment'>--</span>
<a name="line-587"></a><span class='comment'>-- see also : 'processTopDown', 'processBottomUpIfNot'</span>
<a name="line-588"></a>
<a name="line-589"></a><a name="processBottomUp"></a><span class='definition'>processBottomUp</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-590"></a><span class='definition'>processBottomUp</span> <span class='varid'>f</span>
<a name="line-591"></a> <span class='keyglyph'>=</span> <span class='varid'>processChildren</span> <span class='layout'>(</span><span class='varid'>processBottomUp</span> <span class='varid'>f</span><span class='layout'>)</span> <span class='varop'>.></span> <span class='varid'>f</span>
<a name="line-592"></a>
<a name="line-593"></a><span class='comment'>-- |</span>
<a name="line-594"></a><span class='comment'>-- top down transformation</span>
<a name="line-595"></a><span class='comment'>--</span>
<a name="line-596"></a><span class='comment'>-- * 1.parameter f : the /simple/ transforming filter</span>
<a name="line-597"></a><span class='comment'>--</span>
<a name="line-598"></a><span class='comment'>-- - returns : the filter that applies f first to the tree and then recursively to all subtrees of the result</span>
<a name="line-599"></a><span class='comment'>--</span>
<a name="line-600"></a><span class='comment'>-- see also : 'processBottomUp'</span>
<a name="line-601"></a>
<a name="line-602"></a><a name="processTopDown"></a><span class='definition'>processTopDown</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-603"></a><span class='definition'>processTopDown</span> <span class='varid'>f</span>
<a name="line-604"></a> <span class='keyglyph'>=</span> <span class='varid'>f</span> <span class='varop'>.></span> <span class='varid'>processChildren</span> <span class='layout'>(</span><span class='varid'>processTopDown</span> <span class='varid'>f</span><span class='layout'>)</span>
<a name="line-605"></a>
<a name="line-606"></a><span class='comment'>-- |</span>
<a name="line-607"></a><span class='comment'>-- guarded bottom up transformation, stops at subtrees for which a predicate p holds</span>
<a name="line-608"></a><span class='comment'>--</span>
<a name="line-609"></a><span class='comment'>-- * 1.parameter f : the transforming filter</span>
<a name="line-610"></a><span class='comment'>--</span>
<a name="line-611"></a><span class='comment'>-- - 2.parameter p : the predicate filter for the guard</span>
<a name="line-612"></a><span class='comment'>--</span>
<a name="line-613"></a><span class='comment'>-- - returns : the filter for processing all (sub-)trees</span>
<a name="line-614"></a><span class='comment'>--</span>
<a name="line-615"></a><span class='comment'>-- see also : 'processBottomUp'</span>
<a name="line-616"></a>
<a name="line-617"></a><a name="processBottomUpIfNot"></a><span class='definition'>processBottomUpIfNot</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-618"></a><span class='definition'>processBottomUpIfNot</span> <span class='varid'>f</span> <span class='varid'>p</span>
<a name="line-619"></a> <span class='keyglyph'>=</span> <span class='layout'>(</span><span class='varid'>processChildren</span> <span class='layout'>(</span><span class='varid'>processBottomUpIfNot</span> <span class='varid'>f</span> <span class='varid'>p</span><span class='layout'>)</span> <span class='varop'>.></span> <span class='varid'>f</span><span class='layout'>)</span> <span class='varop'>`whenNot`</span> <span class='varid'>p</span>
<a name="line-620"></a>
<a name="line-621"></a><span class='comment'>-- |</span>
<a name="line-622"></a><span class='comment'>-- top down transformation until a node to be transformed is found</span>
<a name="line-623"></a><span class='comment'>--</span>
<a name="line-624"></a><span class='comment'>-- * 1.parameter f : the /simple/ transforming filter</span>
<a name="line-625"></a><span class='comment'>--</span>
<a name="line-626"></a><span class='comment'>-- - returns : the filter that applies f first to the tree and, if the filter does not succeed,</span>
<a name="line-627"></a><span class='comment'>-- recursively to all children of the input tree.</span>
<a name="line-628"></a><span class='comment'>--</span>
<a name="line-629"></a><span class='comment'>-- Example:</span>
<a name="line-630"></a><span class='comment'>--</span>
<a name="line-631"></a><span class='comment'>-- @processTopDownUntil none@</span>
<a name="line-632"></a><span class='comment'>--</span>
<a name="line-633"></a><span class='comment'>-- is the identity filter (maybe a bit more inefficient).</span>
<a name="line-634"></a><span class='comment'>--</span>
<a name="line-635"></a><span class='comment'>-- Example:</span>
<a name="line-636"></a><span class='comment'>--</span>
<a name="line-637"></a><span class='comment'>-- @processTopDownUntil (add1Attr \"border\" \"2\" \`containing\` isTag \"table\")@</span>
<a name="line-638"></a><span class='comment'>--</span>
<a name="line-639"></a><span class='comment'>-- is a filter for adding an attribute border=\"2\" in all top level table tags.</span>
<a name="line-640"></a><span class='comment'>-- The content of table tags will remain unchanged.</span>
<a name="line-641"></a><span class='comment'>--</span>
<a name="line-642"></a><span class='comment'>-- see also : 'processTopDown', 'processBottomUp'</span>
<a name="line-643"></a>
<a name="line-644"></a><a name="processTopDownUntil"></a><span class='definition'>processTopDownUntil</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-645"></a><span class='definition'>processTopDownUntil</span> <span class='varid'>f</span> <span class='varid'>t</span>
<a name="line-646"></a> <span class='keyglyph'>|</span> <span class='varid'>null</span> <span class='varid'>res</span>
<a name="line-647"></a> <span class='keyglyph'>=</span> <span class='varid'>processChildren</span> <span class='layout'>(</span><span class='varid'>processTopDownUntil</span> <span class='varid'>f</span><span class='layout'>)</span> <span class='varid'>t</span>
<a name="line-648"></a> <span class='keyglyph'>|</span> <span class='varid'>otherwise</span>
<a name="line-649"></a> <span class='keyglyph'>=</span> <span class='varid'>res</span>
<a name="line-650"></a> <span class='keyword'>where</span>
<a name="line-651"></a> <span class='varid'>res</span> <span class='keyglyph'>=</span> <span class='varid'>f</span> <span class='varid'>t</span>
<a name="line-652"></a>
<a name="line-653"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-654"></a><span class='comment'>--</span>
<a name="line-655"></a>
<a name="line-656"></a><span class='comment'>-- |</span>
<a name="line-657"></a><span class='comment'>-- insertion of trees into the list of children at a given position</span>
<a name="line-658"></a><span class='comment'>--</span>
<a name="line-659"></a><span class='comment'>-- useful for inserting something into the list of children at a given position</span>
<a name="line-660"></a><span class='comment'>-- the list of children is split with the @splitAt@ function</span>
<a name="line-661"></a><span class='comment'>-- the nodes are inserted between these two sublists.</span>
<a name="line-662"></a><span class='comment'>--</span>
<a name="line-663"></a><span class='comment'>-- examples: @insertChildrenAt 0 ins t@ inserts all elements computed with @ins t@ in front</span>
<a name="line-664"></a><span class='comment'>-- of the childen of @t@, @insertChildrenAt 1 ins t@ behind the first child</span>
<a name="line-665"></a><span class='comment'>--</span>
<a name="line-666"></a><span class='comment'>-- see also: 'insertChildrenAfter'</span>
<a name="line-667"></a>
<a name="line-668"></a>
<a name="line-669"></a><a name="insertChildrenAt"></a><span class='definition'>insertChildrenAt</span> <span class='keyglyph'>::</span> <span class='conid'>Int</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-670"></a><span class='definition'>insertChildrenAt</span> <span class='varid'>i</span> <span class='varid'>ins</span> <span class='varid'>t</span>
<a name="line-671"></a> <span class='keyglyph'>=</span> <span class='varid'>replaceChildren</span> <span class='layout'>(</span><span class='varid'>cl1</span> <span class='varop'>++</span> <span class='varid'>ins</span> <span class='varid'>t</span> <span class='varop'>++</span> <span class='varid'>cl2</span><span class='layout'>)</span> <span class='varid'>t</span>
<a name="line-672"></a> <span class='keyword'>where</span>
<a name="line-673"></a> <span class='layout'>(</span><span class='varid'>cl1</span><span class='layout'>,</span> <span class='varid'>cl2</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='varid'>splitAt</span> <span class='varid'>i</span> <span class='varop'>$</span> <span class='varid'>getChildren</span> <span class='varid'>t</span>
<a name="line-674"></a>
<a name="line-675"></a><span class='comment'>-- |</span>
<a name="line-676"></a><span class='comment'>-- insertion of trees into the list of children after specific elements</span>
<a name="line-677"></a><span class='comment'>--</span>
<a name="line-678"></a><span class='comment'>-- useful for inserting something into the list of children of a node</span>
<a name="line-679"></a><span class='comment'>-- the list of children is split with the @span@ function and the filter p as predicate</span>
<a name="line-680"></a><span class='comment'>-- the nodes are inserted between these two sublists</span>
<a name="line-681"></a><span class='comment'>--</span>
<a name="line-682"></a><span class='comment'>-- examples: @insertChildrenAfter none ins t@ inserts all elements computed with @ins t@ in front</span>
<a name="line-683"></a><span class='comment'>-- of the childen of @t@, @insertChildrenAfter this ins t@ appends the elements to the children</span>
<a name="line-684"></a><span class='comment'>--</span>
<a name="line-685"></a><span class='comment'>-- see also: 'insertChildrenAt'</span>
<a name="line-686"></a>
<a name="line-687"></a><a name="insertChildrenAfter"></a><span class='definition'>insertChildrenAfter</span> <span class='keyglyph'>::</span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='conid'>TFilter</span> <span class='varid'>node</span>
<a name="line-688"></a><span class='definition'>insertChildrenAfter</span> <span class='varid'>p</span> <span class='varid'>ins</span> <span class='varid'>t</span>
<a name="line-689"></a> <span class='keyglyph'>=</span> <span class='varid'>replaceChildren</span> <span class='layout'>(</span><span class='varid'>cl1</span> <span class='varop'>++</span> <span class='varid'>ins</span> <span class='varid'>t</span> <span class='varop'>++</span> <span class='varid'>cl2</span><span class='layout'>)</span> <span class='varid'>t</span>
<a name="line-690"></a> <span class='keyword'>where</span>
<a name="line-691"></a> <span class='layout'>(</span><span class='varid'>cl1</span><span class='layout'>,</span> <span class='varid'>cl2</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='varid'>span</span> <span class='layout'>(</span><span class='varid'>not</span> <span class='varop'>.</span> <span class='varid'>null</span> <span class='varop'>.</span> <span class='varid'>p</span><span class='layout'>)</span> <span class='varop'>$</span> <span class='varid'>getChildren</span> <span class='varid'>t</span>
<a name="line-692"></a>
<a name="line-693"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-694"></a><span class='comment'>--</span>
<a name="line-695"></a><span class='comment'>-- monadic filter</span>
<a name="line-696"></a>
<a name="line-697"></a><span class='comment'>-- |</span>
<a name="line-698"></a><span class='comment'>-- the monadic version of the identity filter this.</span>
<a name="line-699"></a><span class='comment'>--</span>
<a name="line-700"></a><span class='comment'>-- see also : 'this'</span>
<a name="line-701"></a>
<a name="line-702"></a><a name="thisM"></a><span class='definition'>thisM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-703"></a><span class='definition'>thisM</span> <span class='keyglyph'>=</span> <span class='varid'>liftMf</span> <span class='varid'>this</span>
<a name="line-704"></a>
<a name="line-705"></a><span class='comment'>-- |</span>
<a name="line-706"></a><span class='comment'>-- the monadic version of the null filter none.</span>
<a name="line-707"></a><span class='comment'>--</span>
<a name="line-708"></a><span class='comment'>-- see also : 'none'</span>
<a name="line-709"></a>
<a name="line-710"></a><a name="noneM"></a><span class='definition'>noneM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-711"></a><span class='definition'>noneM</span> <span class='keyglyph'>=</span> <span class='varid'>liftMf</span> <span class='varid'>none</span>
<a name="line-712"></a>
<a name="line-713"></a><span class='comment'>-- |</span>
<a name="line-714"></a><span class='comment'>-- sequential composition of monadic filters, monadic version of \".>\".</span>
<a name="line-715"></a><span class='comment'>--</span>
<a name="line-716"></a><span class='comment'>-- * 1.parameter f1 : the 1. monadic filter</span>
<a name="line-717"></a><span class='comment'>--</span>
<a name="line-718"></a><span class='comment'>-- - 2.parameter f2 : the 2. monadic filter</span>
<a name="line-719"></a><span class='comment'>--</span>
<a name="line-720"></a><span class='comment'>-- - returns : the monadic fiter applying first f1 to n and then f2 to the result (like function composition)</span>
<a name="line-721"></a><span class='comment'>--</span>
<a name="line-722"></a><span class='comment'>-- see also : '(.>)'</span>
<a name="line-723"></a>
<a name="line-724"></a><a name=".>>"></a><span class='layout'>(</span><span class='varop'>.>></span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span><span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>b</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span><span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-725"></a><a name="cmd1"></a><span class='definition'>cmd1</span> <span class='varop'>.>></span> <span class='varid'>cmd2</span>
<a name="line-726"></a> <span class='keyglyph'>=</span> <span class='keyglyph'>\</span> <span class='varid'>t</span> <span class='keyglyph'>-></span>
<a name="line-727"></a> <span class='keyword'>do</span>
<a name="line-728"></a> <span class='varid'>r1</span> <span class='keyglyph'><-</span> <span class='varid'>cmd1</span> <span class='varid'>t</span>
<a name="line-729"></a> <span class='varid'>r2</span> <span class='keyglyph'><-</span> <span class='varid'>mapM</span> <span class='varid'>cmd2</span> <span class='varid'>r1</span>
<a name="line-730"></a> <span class='varid'>return</span> <span class='layout'>(</span><span class='varid'>concat</span> <span class='varid'>r2</span><span class='layout'>)</span>
<a name="line-731"></a>
<a name="line-732"></a><span class='comment'>-- |</span>
<a name="line-733"></a><span class='comment'>-- generalized sequential composition of monadic filters</span>
<a name="line-734"></a>
<a name="line-735"></a><a name="seqM"></a><span class='definition'>seqM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='keyglyph'>[</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span><span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span><span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-736"></a><span class='definition'>seqM</span>
<a name="line-737"></a> <span class='keyglyph'>=</span> <span class='varid'>foldr</span> <span class='layout'>(</span><span class='varop'>.>></span><span class='layout'>)</span> <span class='varid'>thisM</span>
<a name="line-738"></a>
<a name="line-739"></a><span class='comment'>-- |</span>
<a name="line-740"></a><span class='comment'>-- binary parallel composition, the logical OR for predicate filter</span>
<a name="line-741"></a><span class='comment'>--</span>
<a name="line-742"></a><span class='comment'>-- * 1.parameter f1 : the 1. filter</span>
<a name="line-743"></a><span class='comment'>--</span>
<a name="line-744"></a><span class='comment'>-- - 2.parameter f2 : the 2. filter</span>
<a name="line-745"></a><span class='comment'>--</span>
<a name="line-746"></a><span class='comment'>-- - returns : the filter for applying f1 and f2 both to an argument tree and concatenating the results</span>
<a name="line-747"></a><span class='comment'>-- see also: 'cat', '+++', 'catM'</span>
<a name="line-748"></a>
<a name="line-749"></a><a name="+++>>"></a><span class='layout'>(</span><span class='varop'>+++>></span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-750"></a><span class='definition'>f</span> <span class='varop'>+++>></span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='keyglyph'>\</span> <span class='varid'>t</span> <span class='keyglyph'>-></span> <span class='keyword'>do</span>
<a name="line-751"></a> <span class='varid'>r1</span> <span class='keyglyph'><-</span> <span class='varid'>f</span> <span class='varid'>t</span>
<a name="line-752"></a> <span class='varid'>r2</span> <span class='keyglyph'><-</span> <span class='varid'>g</span> <span class='varid'>t</span>
<a name="line-753"></a> <span class='varid'>return</span> <span class='layout'>(</span><span class='varid'>r1</span> <span class='varop'>++</span> <span class='varid'>r2</span><span class='layout'>)</span>
<a name="line-754"></a>
<a name="line-755"></a><span class='comment'>-- |</span>
<a name="line-756"></a><span class='comment'>-- apply a list of monadic filters</span>
<a name="line-757"></a><span class='comment'>--</span>
<a name="line-758"></a><span class='comment'>-- * 1.parameter fs : the list of filters</span>
<a name="line-759"></a><span class='comment'>--</span>
<a name="line-760"></a><span class='comment'>-- - returns : the composing filter</span>
<a name="line-761"></a><span class='comment'>-- see also: 'cat', '+++', '+++>>'</span>
<a name="line-762"></a>
<a name="line-763"></a><a name="catM"></a><span class='definition'>catM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='keyglyph'>[</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-764"></a><span class='definition'>catM</span> <span class='varid'>fs</span> <span class='varid'>t</span>
<a name="line-765"></a> <span class='keyglyph'>=</span> <span class='keyword'>do</span>
<a name="line-766"></a> <span class='varid'>res</span> <span class='keyglyph'><-</span> <span class='varid'>sequence</span> <span class='layout'>(</span><span class='varid'>map</span> <span class='layout'>(</span><span class='varop'>$</span> <span class='varid'>t</span><span class='layout'>)</span> <span class='varid'>fs</span><span class='layout'>)</span>
<a name="line-767"></a> <span class='varid'>return</span> <span class='varop'>$</span> <span class='varid'>concat</span> <span class='varid'>res</span>
<a name="line-768"></a>
<a name="line-769"></a><span class='comment'>-- |</span>
<a name="line-770"></a><span class='comment'>-- monadic if-then-else.</span>
<a name="line-771"></a><span class='comment'>--</span>
<a name="line-772"></a><span class='comment'>-- * 1.parameter p : the predicate</span>
<a name="line-773"></a><span class='comment'>--</span>
<a name="line-774"></a><span class='comment'>-- - 2.parameter thenP : the then part: the monadic filter, that is applied if p holds for the input tree</span>
<a name="line-775"></a><span class='comment'>--</span>
<a name="line-776"></a><span class='comment'>-- - 3.parameter elseP : the else part</span>
<a name="line-777"></a><span class='comment'>--</span>
<a name="line-778"></a><span class='comment'>-- - returns : the monadic filter for the conditional</span>
<a name="line-779"></a>
<a name="line-780"></a><a name="ifM"></a><span class='definition'>ifM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-781"></a><span class='definition'>ifM</span> <span class='varid'>p</span> <span class='varid'>thenPart</span> <span class='varid'>elsePart</span>
<a name="line-782"></a> <span class='keyglyph'>=</span> <span class='keyglyph'>\</span> <span class='varid'>t</span> <span class='keyglyph'>-></span>
<a name="line-783"></a> <span class='keyword'>if</span> <span class='layout'>(</span><span class='varid'>satisfies</span> <span class='varid'>p</span><span class='layout'>)</span> <span class='varid'>t</span>
<a name="line-784"></a> <span class='keyword'>then</span> <span class='varid'>thenPart</span> <span class='varid'>t</span>
<a name="line-785"></a> <span class='keyword'>else</span> <span class='varid'>elsePart</span> <span class='varid'>t</span>
<a name="line-786"></a>
<a name="line-787"></a><span class='comment'>-- |</span>
<a name="line-788"></a><span class='comment'>-- monadic version of multiway branch. The list of cases @f :-> g@ is processed sequentially,</span>
<a name="line-789"></a><span class='comment'>-- in the first case for that f holds g is applied, if no case matches, 'noneM' is</span>
<a name="line-790"></a><span class='comment'>-- applied.</span>
<a name="line-791"></a><span class='comment'>-- This filter can be used like a case expression: @choiceM [ p1 :-> f1, p2 :-> f2, ... , thisM :-> defaultFilter]@</span>
<a name="line-792"></a><span class='comment'>--</span>
<a name="line-793"></a><span class='comment'>-- see also : 'choice', 'ifM'</span>
<a name="line-794"></a>
<a name="line-795"></a><a name="choiceM"></a><span class='definition'>choiceM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</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='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-796"></a><span class='definition'>choiceM</span> <span class='conid'>[]</span>
<a name="line-797"></a> <span class='keyglyph'>=</span> <span class='varid'>noneM</span>
<a name="line-798"></a>
<a name="line-799"></a><span class='definition'>choiceM</span> <span class='layout'>(</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='conop'>:</span> <span class='varid'>cs</span><span class='layout'>)</span>
<a name="line-800"></a> <span class='keyglyph'>=</span> <span class='varid'>ifM</span> <span class='varid'>g</span> <span class='varid'>f</span> <span class='layout'>(</span><span class='varid'>choiceM</span> <span class='varid'>cs</span><span class='layout'>)</span>
<a name="line-801"></a>
<a name="line-802"></a>
<a name="line-803"></a><span class='comment'>-- |</span>
<a name="line-804"></a><span class='comment'>-- when the predicate p holds, the monadic filter f is applied, else the identity filter.</span>
<a name="line-805"></a><span class='comment'>--</span>
<a name="line-806"></a><span class='comment'>-- * 1.parameter f : the conditinally applied monadic filter</span>
<a name="line-807"></a><span class='comment'>--</span>
<a name="line-808"></a><span class='comment'>-- - 2.parameter p : the simple predicate</span>
<a name="line-809"></a><span class='comment'>--</span>
<a name="line-810"></a><span class='comment'>-- - returns : the conditional filter</span>
<a name="line-811"></a><span class='comment'>--</span>
<a name="line-812"></a><span class='comment'>-- see also : 'ifM', 'when', 'guardsM', 'whenNotM'</span>
<a name="line-813"></a>
<a name="line-814"></a><a name="whenM"></a><span class='definition'>whenM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-815"></a><a name="whenM"></a><span class='definition'>f</span> <span class='varop'>`whenM`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>ifM</span> <span class='varid'>g</span> <span class='varid'>f</span> <span class='varid'>thisM</span>
<a name="line-816"></a>
<a name="line-817"></a><span class='comment'>-- |</span>
<a name="line-818"></a><span class='comment'>-- the complementary filter of whenM.</span>
<a name="line-819"></a><span class='comment'>--</span>
<a name="line-820"></a><span class='comment'>-- see also : 'ifM', 'whenM', 'whenNot'</span>
<a name="line-821"></a>
<a name="line-822"></a><a name="whenNotM"></a><span class='definition'>whenNotM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-823"></a><a name="whenNotM"></a><span class='definition'>f</span> <span class='varop'>`whenNotM`</span> <span class='varid'>g</span> <span class='keyglyph'>=</span> <span class='varid'>ifM</span> <span class='varid'>g</span> <span class='varid'>thisM</span> <span class='varid'>f</span>
<a name="line-824"></a>
<a name="line-825"></a><span class='comment'>-- |</span>
<a name="line-826"></a><span class='comment'>-- when the predicate p holds, the monadic filter f is applied, else the null filter.</span>
<a name="line-827"></a><span class='comment'>--</span>
<a name="line-828"></a><span class='comment'>-- * 1.parameter p : the simple predicate filter</span>
<a name="line-829"></a><span class='comment'>--</span>
<a name="line-830"></a><span class='comment'>-- - 2.parameter f : the conditionally applied monadic filter</span>
<a name="line-831"></a><span class='comment'>--</span>
<a name="line-832"></a><span class='comment'>-- - returns : the conditional filter</span>
<a name="line-833"></a><span class='comment'>--</span>
<a name="line-834"></a><span class='comment'>-- see also : 'ifM', 'guards', 'whenM'</span>
<a name="line-835"></a>
<a name="line-836"></a><a name="guardsM"></a><span class='definition'>guardsM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>c</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-837"></a><a name="guardsM"></a><span class='definition'>g</span> <span class='varop'>`guardsM`</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>ifM</span> <span class='varid'>g</span> <span class='varid'>f</span> <span class='varid'>noneM</span>
<a name="line-838"></a>
<a name="line-839"></a><span class='comment'>-- |</span>
<a name="line-840"></a><span class='comment'>-- Filter for editing the children of a tree with a monadic filter</span>
<a name="line-841"></a><span class='comment'>--</span>
<a name="line-842"></a><span class='comment'>-- * 1.parameter cf : the monadic filter applied to the children</span>
<a name="line-843"></a><span class='comment'>--</span>
<a name="line-844"></a><span class='comment'>-- - returns : the monadic editing filter</span>
<a name="line-845"></a><span class='comment'>--</span>
<a name="line-846"></a><span class='comment'>-- see also : 'processChildren'</span>
<a name="line-847"></a>
<a name="line-848"></a><a name="processChildrenM"></a><span class='definition'>processChildrenM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='conid'>NTree</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>node</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='conid'>NTree</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>node</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-849"></a><span class='definition'>processChildrenM</span> <span class='varid'>ft</span> <span class='layout'>(</span><span class='conid'>NTree</span> <span class='varid'>n</span> <span class='varid'>cs</span><span class='layout'>)</span>
<a name="line-850"></a> <span class='keyglyph'>=</span> <span class='keyword'>do</span>
<a name="line-851"></a> <span class='varid'>res</span> <span class='keyglyph'><-</span> <span class='varid'>ft</span> <span class='varop'>$$<</span> <span class='varid'>cs</span>
<a name="line-852"></a> <span class='varid'>return</span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>n</span> <span class='varid'>res</span><span class='keyglyph'>]</span>
<a name="line-853"></a>
<a name="line-854"></a><span class='comment'>-- |</span>
<a name="line-855"></a><span class='comment'>-- monadic variant of 'processTopDown'</span>
<a name="line-856"></a>
<a name="line-857"></a><a name="processTopDownM"></a><span class='definition'>processTopDownM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='conid'>NTree</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>node</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='conid'>NTree</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>node</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-858"></a><span class='definition'>processTopDownM</span> <span class='varid'>f</span>
<a name="line-859"></a> <span class='keyglyph'>=</span> <span class='varid'>f</span> <span class='varop'>.>></span> <span class='varid'>processChildrenM</span> <span class='layout'>(</span><span class='varid'>processTopDownM</span> <span class='varid'>f</span><span class='layout'>)</span>
<a name="line-860"></a>
<a name="line-861"></a><span class='comment'>-- |</span>
<a name="line-862"></a><span class='comment'>-- monadic variant of 'processBottomUp'</span>
<a name="line-863"></a>
<a name="line-864"></a><a name="processBottomUpM"></a><span class='definition'>processBottomUpM</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='conid'>NTree</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>node</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='layout'>(</span><span class='conid'>NTree</span> <span class='varid'>node</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='conid'>NTree</span> <span class='varid'>node</span><span class='keyglyph'>]</span><span class='layout'>)</span>
<a name="line-865"></a><span class='definition'>processBottomUpM</span> <span class='varid'>f</span>
<a name="line-866"></a> <span class='keyglyph'>=</span> <span class='varid'>processChildrenM</span> <span class='layout'>(</span><span class='varid'>processBottomUpM</span> <span class='varid'>f</span><span class='layout'>)</span> <span class='varop'>.>></span> <span class='varid'>f</span>
<a name="line-867"></a>
<a name="line-868"></a><span class='comment'>-- |</span>
<a name="line-869"></a><span class='comment'>-- infix operator for applying a monadic filter to a list of trees,</span>
<a name="line-870"></a><span class='comment'>-- typically used in do-notation for processing of intermediate results.</span>
<a name="line-871"></a><span class='comment'>--</span>
<a name="line-872"></a><span class='comment'>-- * 1.parameter f : the monadic filter</span>
<a name="line-873"></a><span class='comment'>--</span>
<a name="line-874"></a><span class='comment'>-- - 2.parameter ts : the list of trees</span>
<a name="line-875"></a><span class='comment'>--</span>
<a name="line-876"></a><span class='comment'>-- - returns : the concatenated list of results</span>
<a name="line-877"></a><span class='comment'>--</span>
<a name="line-878"></a><span class='comment'>-- see also : '($$)'</span>
<a name="line-879"></a>
<a name="line-880"></a><a name="$$<"></a><span class='layout'>(</span><span class='varop'>$$<</span><span class='layout'>)</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span>
<a name="line-881"></a><a name="cmd"></a><span class='definition'>cmd</span> <span class='varop'>$$<</span> <span class='varid'>l</span>
<a name="line-882"></a> <span class='keyglyph'>=</span> <span class='keyword'>do</span>
<a name="line-883"></a> <span class='varid'>r</span> <span class='keyglyph'><-</span> <span class='varid'>mapM</span> <span class='varid'>cmd</span> <span class='varid'>l</span>
<a name="line-884"></a> <span class='varid'>return</span> <span class='layout'>(</span><span class='varid'>concat</span> <span class='varid'>r</span><span class='layout'>)</span>
<a name="line-885"></a>
<a name="line-886"></a><span class='comment'>-- |</span>
<a name="line-887"></a><span class='comment'>-- lift a filter to a monadic filter</span>
<a name="line-888"></a><span class='comment'>--</span>
<a name="line-889"></a><span class='comment'>-- * 1.parameter f : the /simple/ filter</span>
<a name="line-890"></a><span class='comment'>--</span>
<a name="line-891"></a><span class='comment'>-- - returns : the lifted monadic version</span>
<a name="line-892"></a>
<a name="line-893"></a><a name="liftMf"></a><span class='definition'>liftMf</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></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'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>b</span><span class='keyglyph'>]</span>
<a name="line-894"></a><span class='definition'>liftMf</span> <span class='varid'>f</span> <span class='varid'>t</span>
<a name="line-895"></a> <span class='keyglyph'>=</span> <span class='varid'>return</span> <span class='layout'>(</span><span class='varid'>f</span> <span class='varid'>t</span><span class='layout'>)</span>
<a name="line-896"></a>
<a name="line-897"></a><span class='comment'>-- |</span>
<a name="line-898"></a><span class='comment'>-- run an arbitray command on a tree t and return the tree,</span>
<a name="line-899"></a><span class='comment'>-- used for inserting arbitray commands in a filter pipeline</span>
<a name="line-900"></a><span class='comment'>--</span>
<a name="line-901"></a><span class='comment'>-- * 1.parameter cmd : the command</span>
<a name="line-902"></a><span class='comment'>--</span>
<a name="line-903"></a><span class='comment'>-- - 2.parameter t : the argument tree</span>
<a name="line-904"></a><span class='comment'>--</span>
<a name="line-905"></a><span class='comment'>-- - returns : the unchanged tree as a single element list</span>
<a name="line-906"></a>
<a name="line-907"></a><a name="performAction"></a><span class='definition'>performAction</span> <span class='keyglyph'>::</span> <span class='conid'>Monad</span> <span class='varid'>m</span> <span class='keyglyph'>=></span> <span class='layout'>(</span><span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='varid'>b</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>m</span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span>
<a name="line-908"></a><span class='definition'>performAction</span> <span class='varid'>cmd</span> <span class='varid'>t</span>
<a name="line-909"></a> <span class='keyglyph'>=</span> <span class='keyword'>do</span>
<a name="line-910"></a> <span class='varid'>cmd</span> <span class='varid'>t</span>
<a name="line-911"></a> <span class='varid'>return</span> <span class='keyglyph'>[</span><span class='varid'>t</span><span class='keyglyph'>]</span>
<a name="line-912"></a>
<a name="line-913"></a><span class='comment'>-- eof ------------------------------------------------------------</span>
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