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Directory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 03:04, 7 January 2009
, 03:04, 7 January 2009→Grammar 5: markup
Grammar 5 is a context-free grammar for the painted cactus language that uses <math>\mathfrak{Q} = \{ \, ^{\backprime\backprime} \, S' \, ^{\prime\prime}, \, ^{\backprime\backprime} \, T \, ^{\prime\prime} \, \},</math> with <math>\mathfrak{K}</math> as listed in the next display.
Grammar 5 is a context-free grammar for the painted cactus language that uses <math>\mathfrak{Q} = \{ \, ^{\backprime\backprime} \, S' \, ^{\prime\prime}, \, ^{\backprime\backprime} \, T \, ^{\prime\prime} \, \},</math> with <math>\mathfrak{K}</math> as listed in the next display.
<pre>
<br>
Finally, it is worth trying to bring together the advantages of these
{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black" width="90%"
diverse styles of grammar, to whatever extent that they are compatible.
| align="left" style="border-left:1px solid black;" width="50%" |
To do this, a prospective grammar must be capable of maintaining a high
<math>\mathfrak{C} (\mathfrak{P}) : \text{Grammar 5}\!</math>
level of intermediate organization, like that arrived at in Grammar 2,
| align="right" style="border-right:1px solid black;" width="50%" |
while respecting the principle of intermediate significance, and thus
<math>\mathfrak{Q} = \{ \, ^{\backprime\backprime} \, S' \, ^{\prime\prime}, \, ^{\backprime\backprime} \, T \, ^{\prime\prime} \, \}</math>
accumulating all the benefits of the context-free format in Grammar 5.
|-
A plausible synthesis of most of these features is given in Grammar 6.
| colspan="2" style="border-top:1px solid black; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black" |
<math>\begin{array}{rcll}
1.
& S
& :>
& \varepsilon
\\
2.
& S
& :>
& S'
\\
3.
& S'
& :>
& m_1
\\
4.
& S'
& :>
& p_j, \, \text{for each} \, j \in J
\\
5.
& S'
& :>
& S' \, \cdot \, S'
\\
6.
& S'
& :>
& ^{\backprime\backprime} \, \operatorname{()} \, ^{\prime\prime}
\\
7.
& S'
& :>
& ^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, T \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}
\\
8.
& T
& :>
& ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime}
\\
9.
& T
& :>
& S'
\\
10.
& T
& :>
& T \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime}
\\
11.
& T
& :>
& T \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, S'
\\
\end{array}</math>
|}
<br>
Finally, it is worth trying to bring together the advantages of these diverse styles of grammar, to whatever extent that they are compatible. To do this, a prospective grammar must be capable of maintaining a high level of intermediate organization, like that arrived at in Grammar 2, while respecting the principle of intermediate significance, and thus accumulating all the benefits of the context-free format in Grammar 5. A plausible synthesis of most of these features is given in Grammar 6.
===Grammar 6===
===Grammar 6===