Changes

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:

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>

<ol style="list-style-type:decimal">

1.  The parse of the concatenation Conc^k of the k sentences S_j,

 

    for j = 1 to k, is defined recursively as follows:

<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>

 

 

 

 

    b.  For k > 0,

<li>The parse of the surcatenation <math>\operatorname{Surc}_{j=1}^k</math> of the <math>k\!</math> sentences <math>(s_j)_{j=1}^k</math> is defined recursively as follows:</li>

        Parse(Conc^k_j S_j)  = Node^k_j Parse(S_j).

<ol style="list-style-type:lower-alpha">

2.  The parse of the surcatenation Surc^k of the k sentences S_j,

<li><math>\operatorname{Parse} (\operatorname{Surc}^0) ~=~ \operatorname{Lobe}^0.</math>

    for j = 1 to k, is defined recursively as follows:

    a.  Parse(Surc^0)        =  Lobe^0.

<p>For <math>k > 0,\!</math></p>

    b. For k > 0,

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

For ease of reference, Table 12 summarizes the mechanics of these parsing rules.

For ease of reference, Table 12 summarizes the mechanics of these parsing rules.

Table 12.  Algorithmic Translation Rules

Table 12.  Algorithmic Translation Rules

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