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→‎The Cactus Language : Mechanics: mathematical markup
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</ol></ol>
 
</ol></ol>
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For ease of reference, Table 12 summarizes the mechanics of these parsing rules.
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For ease of reference, Table&nbsp;13 summarizes the mechanics of these parsing rules.
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
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|+ '''Table 13.  Algorithmic Translation Rules'''
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|- style="background:whitesmoke"
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|
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{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:whitesmoke; width:100%"
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| width="33%"    | <math>\text{Sentence in PARCE}\!</math>
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| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
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| width="33%"    | <math>\text{Graph in PARC}\!</math>
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|}
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|-
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|
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{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
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| width="33%"    | <math>\operatorname{Conc}^0</math>
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| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
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| width="33%"    | <math>\operatorname{Node}^0</math>
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|-
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| width="33%"    | <math>\operatorname{Conc}_{j=1}^k s_j</math>
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| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
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| width="33%"    | <math>\operatorname{Node}_{j=1}^k \operatorname{Parse} (s_j)</math>
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|}
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|-
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|
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{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
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| width="33%"    | <math>\operatorname{Surc}^0</math>
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| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
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| width="33%"    | <math>\operatorname{Lobe}^0</math>
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|-
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| width="33%"    | <math>\operatorname{Surc}_{j=1}^k s_j</math>
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| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
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| width="33%"    | <math>\operatorname{Lobe}_{j=1}^k \operatorname{Parse} (s_j)</math>
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|}
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|}
    
<pre>
 
<pre>
−
Table 12.  Algorithmic Translation Rules
  −
o------------------------o---------o------------------------o
  −
|                        |  Parse  |                        |
  −
| Sentence in PARCE      |  -->  | Graph in PARC          |
  −
o------------------------o---------o------------------------o
  −
|                        |        |                        |
  −
| Conc^0                |  -->  | Node^0                |
  −
|                        |        |                        |
  −
| Conc^k_j  S_j          |  -->  | Node^k_j  Parse(S_j)  |
  −
|                        |        |                        |
  −
| Surc^0                |  -->  | Lobe^0                |
  −
|                        |        |                        |
  −
| Surc^k_j  S_j          |  -->  | Lobe^k_j  Parse(S_j)  |
  −
|                        |        |                        |
  −
o------------------------o---------o------------------------o
  −
   
A "substructure" of a PARC is defined recursively as follows.  Starting
 
A "substructure" of a PARC is defined recursively as follows.  Starting
 
at the root node of the cactus C, any attachment is a substructure of C.
 
at the root node of the cactus C, any attachment is a substructure of C.
Jon Awbrey
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