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<a href="../../../../Scratch/fr/blog/2010-05-24-Trees--Pragmatism-and-Formalism/">French</a>
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<h1>Trees; Pragmatism and Formalism</h1>
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<h2>When theory is more efficient than practice</h2>
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<p><span class="sc"><abbr title="Too long; didn't read">tl;dr</abbr>: </span>:</p>
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<ul>
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<li>I tried to program a simple filter</li>
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<li>Was blocked 2 days</li>
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<li>Then stopped working like an engineer monkey</li>
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<li>Used a pen and a sheet of paper</li>
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<li>Made some math.</li>
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<li>Crushed the problem in 10 minutes</li>
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<li>Conclusion: The pragmatism shouldn’t mean “never use theory”.</li>
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</ul>
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<h2 id="abstract-longer-than-tldr">Abstract (longer than <span class="sc"><abbr title="Too long; didn't read">tl;dr</abbr>: </span>)</h2>
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<p>For my job, I needed to resolve a problem. It first seems not too hard. Then I started working directly on my program. I entered in the <em>infernal</em>: <em>try & repair loop</em>. Each step was like:</p>
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<blockquote>
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<p>– Just this thing to repair and that should be done.<br />
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– OK, now that should just work.<br />
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– Yeah!!!<br />
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– Oops! I forgotten that…<br />
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<code>repeat until death</code></p>
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</blockquote>
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<p>After two days of this <a href="http://fr.wikipedia.org/wiki/Sisyphe">Sisyphus</a> work, I finally just stopped to rethink the problem. I took a pen, a sheet of paper. I simplified the problem, reminded what I learned during my Ph.D. about trees. Finally, the problem was crushed in less than 20 minutes.</p>
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<p>I believe the important lesson is to remember that the most efficient methodology to resolve this <em>pragmatic</em> problem was the <em>theoretical</em> one. And therefore, argues opposing science, theory to pragmatism and efficiency are fallacies.</p>
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<hr />
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<h1 id="first-my-experience">First: my experience</h1>
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<p>Apparently 90% of programmer are unable to program a binary search without bug. The algorithm is well known and easy to understand. However it is difficult to program it without any flaw. I participated to <a href="http://reprog.wordpress.com/2010/04/19/are-you-one-of-the-10-percent/">this contest</a>. And you can see the <a href="http://reprog.wordpress.com/2010/04/21/binary-search-redux-part-1/">results here</a><a href="#fn1" class="footnote-ref" id="fnref1"><sup>1</sup></a>. I had to face a problem of the same kind at my job. The problem was simple to the start. Simply transform an <sc>xml</sc> from one format to another.</p>
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<p>The source <sc>xml</sc> was in the following general format:</p>
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<div class="sourceCode" id="cb1"><pre class="sourceCode xml"><code class="sourceCode xml"><a class="sourceLine" id="cb1-1" title="1"><span class="kw"><rubrique></span></a>
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<a class="sourceLine" id="cb1-2" title="2"> <span class="kw"><contenu></span></a>
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<a class="sourceLine" id="cb1-3" title="3"> <span class="kw"><tag1></span>value1<span class="kw"></tag1></span></a>
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<a class="sourceLine" id="cb1-4" title="4"> <span class="kw"><tag2></span>value2<span class="kw"></tag2></span></a>
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<a class="sourceLine" id="cb1-5" title="5"> ...</a>
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<a class="sourceLine" id="cb1-6" title="6"> <span class="kw"></contenu></span></a>
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<a class="sourceLine" id="cb1-7" title="7"> <span class="kw"><enfant></span></a>
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<a class="sourceLine" id="cb1-8" title="8"> <span class="kw"><rubrique></span></a>
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<a class="sourceLine" id="cb1-9" title="9"> ...</a>
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||
<a class="sourceLine" id="cb1-10" title="10"> <span class="kw"></rubrique></span></a>
|
||
<a class="sourceLine" id="cb1-11" title="11"> ...</a>
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||
<a class="sourceLine" id="cb1-12" title="12"> <span class="kw"><rubrique></span></a>
|
||
<a class="sourceLine" id="cb1-13" title="13"> ...</a>
|
||
<a class="sourceLine" id="cb1-14" title="14"> <span class="kw"></rubrique></span></a>
|
||
<a class="sourceLine" id="cb1-15" title="15"> <span class="kw"></enfant></span></a>
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<a class="sourceLine" id="cb1-16" title="16"><span class="kw"></menu></span></a></code></pre></div>
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<p>and the destination format was in the following general format:</p>
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<div class="sourceCode" id="cb2"><pre class="sourceCode xml"><code class="sourceCode xml"><a class="sourceLine" id="cb2-1" title="1"><span class="kw"><item</span><span class="ot"> name=</span><span class="st">"Menu0"</span><span class="kw">></span></a>
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<a class="sourceLine" id="cb2-2" title="2"> <span class="kw"><value></span></a>
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<a class="sourceLine" id="cb2-3" title="3"> <span class="kw"><item</span><span class="ot"> name=</span><span class="st">"menu"</span><span class="kw">></span></a>
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<a class="sourceLine" id="cb2-4" title="4"> <span class="kw"><value></span></a>
|
||
<a class="sourceLine" id="cb2-5" title="5"> <span class="kw"><item</span><span class="ot"> name=</span><span class="st">"tag1"</span><span class="kw">></span></a>
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||
<a class="sourceLine" id="cb2-6" title="6"> <span class="kw"><value></span>value1<span class="kw"></value></span></a>
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<a class="sourceLine" id="cb2-7" title="7"> <span class="kw"></item></span></a>
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<a class="sourceLine" id="cb2-8" title="8"> <span class="kw"><item</span><span class="ot"> name=</span><span class="st">"tag2"</span><span class="kw">></span></a>
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||
<a class="sourceLine" id="cb2-9" title="9"> <span class="kw"><value></span>value2<span class="kw"></value></span></a>
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||
<a class="sourceLine" id="cb2-10" title="10"> <span class="kw"></item></span></a>
|
||
<a class="sourceLine" id="cb2-11" title="11"> ...</a>
|
||
<a class="sourceLine" id="cb2-12" title="12"> <span class="kw"><item</span><span class="ot"> name=</span><span class="st">"menu"</span><span class="kw">></span></a>
|
||
<a class="sourceLine" id="cb2-13" title="13"> <span class="kw"><value></span></a>
|
||
<a class="sourceLine" id="cb2-14" title="14"> ...</a>
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||
<a class="sourceLine" id="cb2-15" title="15"> <span class="kw"></value></span></a>
|
||
<a class="sourceLine" id="cb2-16" title="16"> <span class="kw"><value></span></a>
|
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<a class="sourceLine" id="cb2-17" title="17"> ...</a>
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||
<a class="sourceLine" id="cb2-18" title="18"> <span class="kw"></value></span></a>
|
||
<a class="sourceLine" id="cb2-19" title="19"> <span class="kw"></item></span></a>
|
||
<a class="sourceLine" id="cb2-20" title="20"> <span class="kw"></value></span></a>
|
||
<a class="sourceLine" id="cb2-21" title="21"> <span class="kw"></item></span></a>
|
||
<a class="sourceLine" id="cb2-22" title="22"> <span class="kw"></value></span></a>
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<a class="sourceLine" id="cb2-23" title="23"><span class="kw"></item></span></a></code></pre></div>
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<p>At first sight I believed it will be easy. I was so certain it will be easy that I fixed to myself the following rules:</p>
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<ol type="1">
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<li>do not use <sc>xslt</sc></li>
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<li>avoid the use of an <sc>xml</sc> parser</li>
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<li>resolve the problem using a simple perl script[^2]</li>
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</ol>
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<p>You can try if you want. If you attack the problem directly opening an editor, I assure you, it will certainly be not so simple. I can tell that, because it’s what I’ve done. And I must say I lost almost a complete day at work trying to resolve this. There was also, many small problems around that make me lose more than two days for this problem.</p>
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<p>Why after two days did I was unable to resolve this problem which seems so simple?</p>
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<p>What was my behaviour (workflow)?</p>
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<ol type="1">
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<li>Think</li>
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<li>Write the program</li>
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<li>Try the program</li>
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<li>Verify the result</li>
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<li>Found a bug</li>
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<li>Resolve the bug</li>
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<li>Go to step 3.</li>
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</ol>
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<p>This was a <em>standard</em> workflow for computer engineer. The flaw came from the first step. I thought about how to resolve the problem but with the eyes of a <em>pragmatic engineer</em>. I was saying:</p>
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<blockquote>
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<p>That should be a simple perl search and replace program.<br />
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Let’s begin to write code</p>
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</blockquote>
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<p>This is the second sentence that was plainly wrong. I started in the wrong direction. And the workflow did not work from this entry point.</p>
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<h2 id="think">Think</h2>
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<p>After some times, I just stopped to work. Tell myself <em>“it is enough, now, I must finish it!”</em>. I took a sheet of paper, a pen and began to draw some trees.</p>
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<p>I began by make by removing most of the verbosity. I first renamed <code><item name="Menu"></code> by simpler name <code>M</code> for example. I obtained something like:</p>
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<p><img src="code/The_source_tree.png" alt="The source tree" /></p>
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<p>and</p>
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<p><img src="code/The_destination_tree.png" alt="The destination tree" /></p>
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<p>Then I made myself the following reflexion:</p>
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<p>Considering Tree Edit Distance, each unitary transformation of tree correspond to a simple search and replace on my <sc>xml</sc> source<a href="#fn2" class="footnote-ref" id="fnref2"><sup>2</sup></a>. We consider three atomic transformations on trees:</p>
|
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<ul>
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<li><em>substitution</em>: renaming a node</li>
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<li><em>insertion</em>: adding a node</li>
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||
<li><em>deletion</em>: remove a node</li>
|
||
</ul>
|
||
<p>One of the particularity of atomic transformations on trees, is ; if you remove a node, all children of this node, became children of its father.</p>
|
||
<p>An example:</p>
|
||
<pre class="twilight">
|
||
r - x - a
|
||
\ \
|
||
\ b
|
||
y - c
|
||
</pre>
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<p>If you delete the <code>x</code> node, you obtain</p>
|
||
<pre class="twilight">
|
||
a
|
||
/
|
||
r - b
|
||
\
|
||
y - c
|
||
</pre>
|
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<p>And look at what it implies when you write it in <sc>xml</sc>:</p>
|
||
<div class="sourceCode" id="cb3"><pre class="sourceCode xml"><code class="sourceCode xml"><a class="sourceLine" id="cb3-1" title="1"><span class="kw"><r></span></a>
|
||
<a class="sourceLine" id="cb3-2" title="2"> <span class="kw"><x></span></a>
|
||
<a class="sourceLine" id="cb3-3" title="3"> <span class="kw"><a></span>value for a<span class="kw"></a></span></a>
|
||
<a class="sourceLine" id="cb3-4" title="4"> <span class="kw"><b></span>value for b<span class="kw"></b></span></a>
|
||
<a class="sourceLine" id="cb3-5" title="5"> <span class="kw"></x></span></a>
|
||
<a class="sourceLine" id="cb3-6" title="6"> <span class="kw"><y></span></a>
|
||
<a class="sourceLine" id="cb3-7" title="7"> <span class="kw"><c></span>value for c<span class="kw"></c></span></a>
|
||
<a class="sourceLine" id="cb3-8" title="8"> <span class="kw"></y></span></a>
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<a class="sourceLine" id="cb3-9" title="9"><span class="kw"></r></span></a></code></pre></div>
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<p>Then deleting all <code>x</code> nodes is equivalent to pass the <sc>xml</sc> via the following search and replace script:</p>
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<div class="sourceCode" id="cb4"><pre class="sourceCode perl"><code class="sourceCode perl"><a class="sourceLine" id="cb4-1" title="1"><span class="kw">s/</span><span class="ot"><\/</span><span class="ch">?</span><span class="ot">x></span><span class="kw">//g</span></a></code></pre></div>
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<p>Therefore, if there exists a one state deterministic transducer which transform my trees ; I can transform the <sc>xml</sc> from one format to another with just a simple list of search and replace directives.</p>
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<h1 id="solution">Solution</h1>
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<p>Transform this tree:</p>
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<pre class="twilight">
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R - C - tag1
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\ \
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\ tag2
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E -- R - C - tag1
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\ \ \
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\ \ tag2
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\ E ...
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R - C - tag1
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\ \
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\ tag2
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E ...
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</pre>
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<p>to this tree:</p>
|
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<pre class="twilight">
|
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tag1
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/
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||
M - V - M - V - tag2 tag1
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\ /
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M --- V - tag2
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\ \
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\ M
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\ tag1
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\ /
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V - tag2
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\
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M
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</pre>
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<p>can be done using the following one state deterministic tree transducer:</p>
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<blockquote>
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<p>C -> ε<br />
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E -> M<br />
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R -> V</p>
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</blockquote>
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<p>Wich can be traduced by the following simple search and replace directives:</p>
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<div class="sourceCode" id="cb5"><pre class="sourceCode perl"><code class="sourceCode perl"><a class="sourceLine" id="cb5-1" title="1"><span class="kw">s/</span><span class="ot">C</span><span class="kw">//g</span></a>
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<a class="sourceLine" id="cb5-2" title="2"><span class="kw">s/</span><span class="ot">E</span><span class="kw">/</span><span class="st">M</span><span class="kw">/g</span></a>
|
||
<a class="sourceLine" id="cb5-3" title="3"><span class="kw">s/</span><span class="ot">R</span><span class="kw">/</span><span class="st">V</span><span class="kw">/g</span></a></code></pre></div>
|
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<p>Once adapted to <sc>xml</sc> it becomes:</p>
|
||
<div class="sourceCode" id="cb6"><pre class="sourceCode perl"><code class="sourceCode perl"><a class="sourceLine" id="cb6-1" title="1"><span class="kw">s%</span><span class="ot"></</span><span class="ch">?</span><span class="ot">contenu></span><span class="kw">%%g</span></a>
|
||
<a class="sourceLine" id="cb6-2" title="2"><span class="kw">s%</span><span class="ot"><enfant></span><span class="kw">%</span><span class="st"><item name="menu"></span><span class="kw">%g</span></a>
|
||
<a class="sourceLine" id="cb6-3" title="3"><span class="kw">s%</span><span class="ot"></enfant></span><span class="kw">%</span><span class="st"></item></span><span class="kw">%g</span></a>
|
||
<a class="sourceLine" id="cb6-4" title="4"><span class="kw">s%</span><span class="ot"><rubrique></span><span class="kw">%</span><span class="st"><value></span><span class="kw">%g</span></a>
|
||
<a class="sourceLine" id="cb6-5" title="5"><span class="kw">s%</span><span class="ot"></rubrique></span><span class="kw">%</span><span class="st"></value></span><span class="kw">%g</span></a></code></pre></div>
|
||
<p>That is all.</p>
|
||
<h1 id="conclusion">Conclusion</h1>
|
||
<p>It should seems a bit paradoxal, but sometimes the most efficient approach to a pragmatic problem is to use the theoretical methodology.</p>
|
||
<section class="footnotes">
|
||
<hr />
|
||
<ol>
|
||
<li id="fn1"><p>Hopefully I am in the 10% who had given a bug free implementation.<a href="#fnref1" class="footnote-back">↩</a></p></li>
|
||
<li id="fn2"><p>I did a program which generate automatically the weight in a matrix of each edit distance from data.<a href="#fnref2" class="footnote-back">↩</a></p></li>
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