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Directory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 19:00, 5 January 2009
, 19:00, 5 January 2009→The Cactus Language : Syntax: reformat grammar boxes
{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black" width="90%"
{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black" width="90%"
| align="left" style="border-left:1px solid black;" width="33%" |
| align="left" style="border-left:1px solid black;" width="50%" |
<math>\mathfrak{C} (\mathfrak{P})</math>
<math>\mathfrak{C} (\mathfrak{P}) : \text{Grammar 1}\!</math>
| align="right" style="border-right:1px solid black;" width="50%" |
| align="right" style="border-right:1px solid black;" width="33%" |
<math>\mathfrak{Q} = \emptyset</math>
<math>\mathfrak{Q} = \emptyset</math>
|-
|-
| colspan="3" style="border-top:1px solid black; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black" |
| 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}{llll}
<math>\begin{array}{llll}
1.
1.
{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black" width="90%"
{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black" width="90%"
| align="left" style="border-left:1px solid black;" width="33%" |
| align="left" style="border-left:1px solid black;" width="50%" |
<math>\mathfrak{C} (\mathfrak{P})</math>
<math>\mathfrak{C} (\mathfrak{P}) : \text{Grammar 2}\!</math>
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<math>\mathfrak{Q} = \{ \, ^{\backprime\backprime} T ^{\prime\prime} \, \}</math>
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<math>\mathfrak{Q} = \{ ^{\backprime\backprime} \operatorname{T} ^{\prime\prime} \}</math>
|-
|-
| colspan="3" style="border-top:1px solid black; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black" |
| 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}{llll}
<math>\begin{array}{llll}
1.
1.
& S
& S
& :>
& :>
& p_j, \, \text{for each} \, j \in J
& p_j, \, \text{for each}\ j \in J
\\
\\
4.
4.
===Grammar 3===
===Grammar 3===
<br>
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| align="left" style="border-left:1px solid black;" width="50%" |
<math>\mathfrak{C} (\mathfrak{P}) : \text{Grammar 3}\!</math>
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<math>\mathfrak{Q} = \{ \, ^{\backprime\backprime} F ^{\prime\prime}, \, ^{\backprime\backprime} R ^{\prime\prime}, \, ^{\backprime\backprime} T ^{\prime\prime} \, \}</math>
|-
| 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}{llll}
1.
& S
& :>
& R
\\
2.
& S
& :>
& F
\\
3.
& S
& :>
& S \, \cdot \, S
\\
4.
& R
& :>
& \varepsilon
\\
5.
& R
& :>
& m_1
\\
6.
& R
& :>
& p_j, \, \text{for each}\ j \in J
\\
7.
& R
& :>
& R \, \cdot \, R
\\
8.
& F
& :>
& ^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, T \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}
\\
9.
& T
& :>
& S
\\
10.
& T
& :>
& T \, \cdot \, ^{\backprime\backprime} \operatorname{,} ^{\prime\prime} \, \cdot \, S
\\
\end{array}</math>
|}
<br>
<pre>
<pre>
In Grammar 3, the first three Rules say that a sentence (a string of type S),
In Grammar 3, the first three Rules say that a sentence (a string of type S),
is a rune (a string of type R), a foil (a string of type F), or an arbitrary
is a rune (a string of type R), a foil (a string of type F), or an arbitrary