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Directory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 17:45, 26 December 2008
, 17:45, 26 December 2008→The Cactus Language : Syntax: markup
The first step is to define two sets of basic operations on strings of <math>\mathfrak{A}^*.</math>
The first step is to define two sets of basic operations on strings of <math>\mathfrak{A}^*.</math>
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| valign="top" | 1.
| The ''concatenation'' of one string <math>s_1\!</math> is just the string <math>s_1.\!</math>
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| The ''concatenation'' of two strings <math>s_1, s_2\!</math> is the string <math>s_1 \cdot s_2.\!</math>
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| The ''concatenation'' of the <math>k\!</math> strings <math>s_j,\!</math> for <math>j = 1 \ldots k,\!</math> is the string of the form <math>s_1 \cdot \ldots \cdot s_k.\!</math>
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| valign="top" | 2.
| The ''surcatenation'' of one string <math>s_1\!</math> is the string <math>^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot s_1 \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math>
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| The ''surcatenation'' of two strings <math>s_1, s_2\!</math> is <math>^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot s_1 \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot s_2 \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math>
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| The ''surcatenation'' of <math>k\!</math> strings <math>s_j,\!</math> for <math>j\!</math> = 1 to <math>k,\!</math> is the string of the form <math>^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot s_1 \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \ldots \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, s_k \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math>
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<pre>
<pre>
These definitions can be made a little more succinct by
These definitions can be made a little more succinct by
defining the following sorts of generic operators on strings:
defining the following sorts of generic operators on strings: