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Directory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 03:40, 27 December 2008
, 03:40, 27 December 2008→The Cactus Language : Syntax: markup
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(NB. I will need to figure out what I meant by the following definitions.)
These definitions can be made a little more succinct by
defining the following sorts of generic operators on strings:
These definitions can be made a little more succinct by defining the following sorts of generic operators on strings:
<ol style="list-style-type:decimal">
<li>The ''concatenation'' <math>\operatorname{Conc}^k</math> of the <math>k\!</math> strings <math>s_j, j = 1 \ldots k,\!</math> is defined recursively as follows:</li>
<ol style="list-style-type:lower-alpha">
<li><math>\operatorname{Conc}^1_j s_j \ = \ s_1.</math></li>
<li><p>For <math>k > 1,\!</math></p>
<p><math>\operatorname{Conc}^k_j s_j \ = \ (\operatorname{Conc}^{k-1}_j s_j) \cdot s_k.</math></p></li>
</ol>
<li>The ''surcatenation'' <math>\operatorname{Surc}^k</math> of the <math>k\!</math> strings <math>s_j, j = 1 \ldots k,\!</math> is defined recursively as follows:</li>
<ol style="list-style-type:lower-alpha">
<li><math>\operatorname{Surc}^1_j s_j \ = \ ^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot s_1 \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math></li>
<li><p>For <math>k > 1,\!</math></p>
<p><math>\operatorname{Surc}^k_j s_j \ = \ (\operatorname{Surc}^{k-1}_j s_j) \cdot \, (^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime})^{-1} \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot s_k \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math></p></li>
</ol></ol>
<pre>
The definitions of these syntactic operations can now be organized in a slightly
The definitions of these syntactic operations can now be organized in a slightly
better fashion, for both conceptual and computational purposes, by making a few
better fashion, for both conceptual and computational purposes, by making a few