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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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<pre>+
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+1. The "concatenation" Conc^k of the k strings z_j,+ for j = 1 to k, is defined recursively as follows:
− a. Conc^1_j z_j = z_1.+ b. For k > 1,+ Conc^k_j z_j = (Conc^(k-1)_j z_j) · z_k.+2. The "surcatenation" Surc^k of the k strings z_j,+ for j = 1 to k, is defined recursively as follows:
− a. Surc^1_j z_j = "-(" · z_1 · ")-".+ b. For k > 1,+ Surc^k_j z_j = (Surc^(k-1)_j z_j) · ")-"^(-1) · "," · z_k · ")-".+
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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