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< a href = "/Scratch/fr/blog/2010-05-24-Trees--Pragmatism-and-Formalism/" onclick = "setLanguage('fr')" > en Français< / a >
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< div id = "titre" >
< h1 >
Trees; Pragmatism and Formalism
< / h1 >
< h2 >
When theory is more efficient than practice
< / h2 >
< / div >
< div class = "flush" > < / div >
< div class = "flush" > < / div >
< div id = "afterheader" >
< div class = "corps" >
< div class = "intro" >
< p > < abbr title = "Too Long; Don't Read" > < span class = "sc" > tl;dr< / span > < / abbr > : < / p >
< ul >
< li > I tried to program a simple filter< / li >
< li > Was blocked 2 days< / li >
< li > Then stopped working like an engineer monkey< / li >
< li > Used a pen and a sheet of paper< / li >
< li > Made some math.< / li >
< 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 >
< / div >
< h2 id = "abstract-longer-than-abbr-titletoo-long-dont-readsctldrscabbr" > Abstract (longer than < abbr title = "Too Long; Don't Read" > < span class = "sc" > tl;dr< / span > < / abbr > )< / h2 >
< 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 >
< blockquote >
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< p > – Just this thing to repair and that should be done.< br / >
– OK, now that should just work.< br / >
– Yeah!!!< br / >
– Oops! I forgotten that…< br / >
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< code > repeat until death< / code > < / p >
< / blockquote >
< 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 >
< 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 >
< / div >
< div class = "corps" >
< h1 class = "first" id = "first-my-experience" > First: my experience< / h1 >
< 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 > < sup id = "fnref:1" > < a href = "#fn:1" rel = "footnote" > 1< / a > < / sup > .
I had to face a problem of the same kind at my job. The problem was simple to the start. Simply transform an < span class = "sc" > xml< / span > from one format to another.< / p >
< p > The source < span class = "sc" > xml< / span > was in the following general format:< / p >
< pre class = "twilight" >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > rubrique< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > contenu< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > tag1< / span > < span class = "MetaTagAll" > > < / span > < / span > value1< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > tag1< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > tag2< / span > < span class = "MetaTagAll" > > < / span > < / span > value2< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > tag2< / span > < span class = "MetaTagAll" > > < / span > < / span >
...
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > contenu< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > enfant< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > rubrique< / span > < span class = "MetaTagAll" > > < / span > < / span >
...
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > rubrique< / span > < span class = "MetaTagAll" > > < / span > < / span >
...
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > rubrique< / span > < span class = "MetaTagAll" > > < / span > < / span >
...
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > rubrique< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > enfant< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > menu< / span > < span class = "MetaTagAll" > > < / span > < / span >
< / pre >
< p > and the destination format was in the following general format:< / p >
< pre class = "twilight" >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > item< / span > < span class = "MetaTagAll" > name< / span > =< span class = "String" > < span class = "String" > " < / span > Menu0< span class = "String" > " < / span > < / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > item< / span > < span class = "MetaTagAll" > name< / span > =< span class = "String" > < span class = "String" > " < / span > menu< span class = "String" > " < / span > < / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > item< / span > < span class = "MetaTagAll" > name< / span > =< span class = "String" > < span class = "String" > " < / span > tag1< span class = "String" > " < / span > < / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span > value1< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > item< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > item< / span > < span class = "MetaTagAll" > name< / span > =< span class = "String" > < span class = "String" > " < / span > tag2< span class = "String" > " < / span > < / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span > value2< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > item< / span > < span class = "MetaTagAll" > > < / span > < / span >
...
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > item< / span > < span class = "MetaTagAll" > name< / span > =< span class = "String" > < span class = "String" > " < / span > menu< span class = "String" > " < / span > < / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span >
...
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span >
...
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > item< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > item< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > value< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > item< / span > < span class = "MetaTagAll" > > < / span > < / span >
< / pre >
< 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 >
< ol >
< li > do not use < span class = "sc" > xslt< / span > < / li >
< li > avoid the use of an < span class = "sc" > xml< / span > parser< / li >
< li > resolve the problem using a simple perl script[^2]< / li >
< / ol >
< 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.
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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 >
< p > What was my behaviour (workflow)?< / p >
< ol >
< li > Think< / li >
< li > Write the program< / li >
< li > Try the program < / li >
< li > Verify the result< / li >
< li > Found a bug< / li >
< li > Resolve the bug< / li >
< li > Go to step 3.< / li >
< / ol >
< 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 >
< blockquote >
< 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 >
< 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 >
< 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 > .
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I took a sheet of paper, a pen and began to draw some trees.< / p >
< 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 alt = "The source tree" src = "/Scratch/en/blog/2010-05-24-Trees--Pragmatism-and-Formalism/graph/The_source_tree.png" / > < / p >
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< p > and< / p >
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< p > < img alt = "The destination tree" src = "/Scratch/en/blog/2010-05-24-Trees--Pragmatism-and-Formalism/graph/The_destination_tree.png" / > < / p >
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< p > Then I made myself the following reflexion:< / p >
< p > Considering Tree Edit Distance, each unitary transformation of tree correspond to a simple search and replace on my < span class = "sc" > xml< / span > source< sup id = "fnref:nb" > < a href = "#fn:nb" rel = "footnote" > 2< / a > < / sup > .
We consider three atomic transformations on trees:< / p >
< ul >
< li > < em > substitution< / em > : renaming a node< / li >
< li > < em > insertion< / em > : adding a node< / li >
< 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 >
< p > If you delete the < code > x< / code > node, you obtain< / p >
< pre class = "twilight" >
a
/
r - b
\
y - c
< / pre >
< p > And look at what it implies when you write it in < span class = "sc" > xml< / span > :< / p >
< pre class = "twilight" >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > r< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > x< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > a< / span > < span class = "MetaTagAll" > > < / span > < / span > value for a< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > a< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > b< / span > < span class = "MetaTagAll" > > < / span > < / span > value for b< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > b< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > x< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > y< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < < / span > < span class = "MetaTagAll" > c< / span > < span class = "MetaTagAll" > > < / span > < / span > value for c< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > c< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > y< / span > < span class = "MetaTagAll" > > < / span > < / span >
< span class = "MetaTagAll" > < span class = "MetaTagAll" > < /< / span > < span class = "MetaTagAll" > r< / span > < span class = "MetaTagAll" > > < / span > < / span >
< / pre >
< p > Then deleting all < code > x< / code > nodes is equivalent to pass the < span class = "sc" > xml< / span > via the following search and replace script:< / p >
< pre class = "twilight" >
< span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "SupportFunction" > s< / span > /< / span > < < span class = "StringRegexpSpecial" > \/< / span > ?x> < / span > < span class = "StringRegexp" > < span class = "StringRegexp" > /< / span > < span class = "StringRegexp" > /< / span > < / span > < span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "Keyword" > g< / span > < / span > < / span >
< / pre >
< p > Therefore, if there exists a one state deterministic transducer which transform my trees ;
I can transform the < span class = "sc" > xml< / span > from one format to another with just a simple list of search and replace directives.< / p >
< h1 id = "solution" > Solution< / h1 >
< p > Transform this tree:< / p >
< pre class = "twilight" >
R - C - tag1
\ \
\ tag2
E -- R - C - tag1
\ \ \
\ \ tag2
\ E ...
R - C - tag1
\ \
\ tag2
E ...
< / pre >
< p > to this tree:< / p >
< pre class = "twilight" >
tag1
/
M - V - M - V - tag2 tag1
\ /
M --- V - tag2
\ \
\ M
\ tag1
\ /
V - tag2
\
M
< / pre >
< p > can be done using the following one state deterministic tree transducer:< / p >
< blockquote >
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< p > C → ε< br / >
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E → M< br / >
R → V < / p >
< / blockquote >
< p > Wich can be traduced by the following simple search and replace directives: < / p >
< pre class = "twilight" >
< span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "SupportFunction" > s< / span > /< / span > C< / span > < span class = "StringRegexp" > < span class = "StringRegexp" > /< / span > < span class = "StringRegexp" > /< / span > < / span > < span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "Keyword" > g< / span > < / span > < / span >
< span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "SupportFunction" > s< / span > /< / span > E< / span > < span class = "StringRegexp" > < span class = "StringRegexp" > /< / span > M< span class = "StringRegexp" > /< / span > < / span > < span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "Keyword" > g< / span > < / span > < / span >
< span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "SupportFunction" > s< / span > /< / span > R< / span > < span class = "StringRegexp" > < span class = "StringRegexp" > /< / span > V< span class = "StringRegexp" > /< / span > < / span > < span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "Keyword" > g< / span > < / span > < / span >
< / pre >
< p > Once adapted to < span class = "sc" > xml< / span > it becomes:< / p >
< pre class = "twilight" >
< span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "SupportFunction" > s< / span > %< / span > < /?contenu> < / span > < span class = "StringRegexp" > < span class = "StringRegexp" > %< / span > < span class = "StringRegexp" > %< / span > < / span > < span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "Keyword" > g< / span > < / span > < / span >
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< span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "SupportFunction" > s< / span > %< / span > < /rubrique> < / span > < span class = "StringRegexp" > < span class = "StringRegexp" > %< / span > < /value> < span class = "StringRegexp" > %< / span > < / span > < span class = "StringRegexp" > < span class = "StringRegexp" > < span class = "Keyword" > g< / span > < / span > < / span >
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< 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 >
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< p > I did a program which generate automatically the weight in a matrix of each edit distance from data.< a href = "#fnref:nb" rev = "footnote" > ↩ < / a > < / p >
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