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446 bytes removed ,  20:18, 19 January 2009
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==Grammar Stuff==
 
==Grammar Stuff==
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Working from a structural description of the cactus language, or any suitable formal grammar for <math>\mathfrak{C} (\mathfrak{P}),</math> it is possible to give a recursive definition of the function called <math>\operatorname{Parse}</math> that maps each sentence in <math>\operatorname{PARCE} (\mathfrak{P})</math> to the corresponding graph in <math>\operatorname{PARC} (\mathfrak{P}).</math>  One way to do this proceeds as follows:
      
<pre>
 
<pre>
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         Parse(Surc^k_j S_j)  =  Lobe^k_j Parse(S_j).
 
         Parse(Surc^k_j S_j)  =  Lobe^k_j Parse(S_j).
 
</pre>
 
</pre>
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<ol style="list-style-type:decimal">
 
<ol style="list-style-type:decimal">
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<li>The parse of the concatenation <math>\operatorname{Conc}_{j=1}^k</math> of the sequence of <math>k\!</math> sentences <math>(s_j)_{j=1}^k</math> is defined recursively as follows:</li>
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<li>The parse of the concatenation <math>\operatorname{Conc}_{j=1}^k</math> of the <math>k\!</math> sentences <math>(s_j)_{j=1}^k</math> is defined recursively as follows:</li>
    
<ol style="list-style-type:lower-alpha">
 
<ol style="list-style-type:lower-alpha">
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<li>
 
<li>
<p>For <math>\ell > 1,\!</math></p>
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<p>For <math>k > 1,\!</math></p>
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<p><math>\operatorname{Conc}_{j=1}^\ell s_j \ = \ \operatorname{Conc}_{j=1}^{\ell - 1} s_j \, \cdot \, s_\ell.</math></p></li>
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<p><math>\operatorname{Parse} (\operatorname{Conc}_{j=1}^k s_j) ~=~ \operatorname{Node}_{j=1}^k \operatorname{Parse} (s_j).</math></p></li>
    
</ol>
 
</ol>
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