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, 11:55, 20 January 2009→The Cactus Language : Mechanics: mathematical markup
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<pre>
−A "substructure" of a PARC is defined recursively as follows. Starting
−at the root node of the cactus C, any attachment is a substructure of C.
−If a substructure is a blank or a paint, then it constitutes a minimal
−substructure, meaning that no further substructures of C arise from it.
−If a substructure is a lobe, then each one of its accoutrements is also
−a substructure of C, and has to be examined for further substructures.
−The concept of substructure can be used to define varieties of deletion+and erasure operations that respect the structure of the abstract graph.
−For the purposes of this depiction, a blank symbol " " is treated as
−a "white wash". In effect, one is letting m_1 = p_0. In this frame
−1. To "delete" a substructure is to replace it with an empty node,+ in effect, to reduce the whole structure to a trivial point.
−2. To "erase" a substructure is to replace it with a blank symbol,+ in effect, to paint it out of the picture or to overwrite it.+
For ease of reference, Table 13 summarizes the mechanics of these parsing rules.
For ease of reference, Table 13 summarizes the mechanics of these parsing rules.
+
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−A ''substructure'' of a PARC is defined recursively as follows. Starting at the root node of the cactus <math>C,\!</math> any attachment is a substructure of <math>C.\!</math> If a substructure is a blank or a paint, then it constitutes a minimal substructure, meaning that no further substructures of <math>C\!</math> arise from it. If a substructure is a lobe, then each one of its accoutrements is also a substructure of <math>C,\!</math> and has to be examined for further substructures.
−a "primer", in other words, as a "clear paint", a "neutral tint", or
−of discussion, it is useful to make the following distinction:
−The concept of substructure can be used to define varieties of deletion and erasure operations that respect the structure of the abstract graph. For the purposes of this depiction, a blank symbol <math>^{\backprime\backprime} ~ ^{\prime\prime}</math> is treated as a ''primer'', in other words, as a ''clear paint'' or a ''neutral tint". In effect, one is letting <math>m_1 = p_0.\!</math> In this frame of discussion, it is useful to make the following distinction:
−# To ''delete'' a substructure is to replace it with an empty node, in effect, to reduce the whole structure to a trivial point.
−# To ''erase'' a substructure is to replace it with a blank symbol, in effect, to paint it out of the picture or to overwrite it.
+<pre>
A "bare" PARC, loosely referred to as a "bare cactus", is a PARC on the
A "bare" PARC, loosely referred to as a "bare cactus", is a PARC on the
empty palette !P! = {}. In other veins, a bare cactus can be described
empty palette !P! = {}. In other veins, a bare cactus can be described
