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Revision as of 22:51, 30 December 2008
, 22:51, 30 December 2008→The Cactus Language : Syntax: markup
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| || <math>s = s_1 \, \cdot \, ( \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime} \, )^{-1} \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, s_2 \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math>
| || <math>s = s_1 \, \cdot \, ( \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime} \, )^{-1} \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, s_2 \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math>
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| 6. || <math>s\!</math> is the ''surcatenation'' of the <math>k\!</math> strings <math>s_1, \ldots, s_k\!</math> in <math>\mathfrak{L},</math>
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| || if and only if <math>s_j\!</math> is a sentence of <math>\mathfrak{L},</math> for all <math>j = 1 \ldots k,\!</math> and
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| || <math>s \ = \ \operatorname{Surc}_{j=1}^k s_j \ = \ ^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, s_1 \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, \ldots \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, s_k \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math>
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The converses of these decomposition relations are tantamount to the corresponding forms of composition operations, making it possible for these complementary forms of analysis and synthesis to articulate the structures of strings and sentences in two directions.
<pre>
<pre>
The "painted cactus language" with paints in the
The "painted cactus language" with paints in the
set !P! = {p_j : j in J} is the formal language
set !P! = {p_j : j in J} is the formal language
