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, 14:45, 21 January 2009→The Cactus Language : Semantics: mathematical markup
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At this point, there are actually two different dialects, scripts, or modes of presentation for the cactus language that need to be interpreted, in other words, that need to have a semantic function defined on their domains.
At this point, there are actually two different "dialects", "scripts",
or "modes" of presentation for the cactus language that need to be
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interpreted, in other words, that need to have a semantic function
defined on their domains.
<li>There is the literal formal language of strings in <math>\operatorname{PARCE} (\mathfrak{P}),</math> the ''painted and rooted cactus expressions'' that constitute the language <math>\mathfrak{L} = \mathfrak{C} (\mathfrak{P}) \subseteq \mathfrak{A}^* = (\mathfrak{M} \cup \mathfrak{P})^*.</math></li>
<li>There is the figurative formal language of graphs in <math>\operatorname{PARC} (\mathfrak{P}),</math> the ''painted and rooted cacti'' themselves, a parametric family of graphs or a species of computational data structures that is graphically analogous to the language of literal strings.</li>
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<pre>
Of course, these two modalities of formal language, like written and
Of course, these two modalities of formal language, like written and
spoken natural languages, are meant to have compatible interpretations,
spoken natural languages, are meant to have compatible interpretations,
