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User:Jon Awbrey/SANDBOX (view source)

Revision as of 20:18, 19 January 2009

446 bytes removed , 20:18, 19 January 2009

→‎Grammar Stuff

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==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>

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Parse(Surc^k_j S_j) = Lobe^k_j Parse(S_j).

</pre>

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~~---~~

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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>

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<li>

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For <math>~~\ell~~ > 1,\!</math>

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For <math>k > 1,\!</math>

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<math>\operatorname{Conc}_{j=1}^~~\ell~~ s_j \ = \ \operatorname{~~Conc~~}_{j=1}^{~~\ell - 1~~} s_j ~~\, \cdot \, s_\ell~~.</math></li>

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<math>\operatorname{Parse} (\operatorname{Conc}_{j=1}^k s_j) ~=~ \operatorname{Node}_{j=1}^k \operatorname{Parse} (s_j).</math></li>

</ol>

Jon Awbrey

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