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, 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:
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| <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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− | ---
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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> | + | <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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| <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> | + | <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> | + | <p><math>\operatorname{Parse} (\operatorname{Conc}_{j=1}^k s_j) ~=~ \operatorname{Node}_{j=1}^k \operatorname{Parse} (s_j).</math></p></li> |
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| </ol> | | </ol> |