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Revision as of 11:55, 20 January 2009

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→‎The Cactus Language : Mechanics: mathematical markup
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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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<pre>
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A "substructure" of a PARC is defined recursively as follows.  Starting
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at the root node of the cactus C, any attachment is a substructure of C.
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If a substructure is a blank or a paint, then it constitutes a minimal
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substructure, meaning that no further substructures of C arise from it.
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If a substructure is a lobe, then each one of its accoutrements is also
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a substructure of C, and has to be examined for further substructures.
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The concept of substructure can be used to define varieties of deletion
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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.
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and erasure operations that respect the structure of the abstract graph.
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For the purposes of this depiction, a blank symbol " " is treated as
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a "primer", in other words, as a "clear paint", a "neutral tint", or
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a "white wash".  In effect, one is letting m_1 = p_0.  In this frame
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of discussion, it is useful to make the following distinction:
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1.  To "delete" a substructure is to replace it with an empty node,
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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:
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    in effect, to reduce the whole structure to a trivial point.
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2. To "erase" a substructure is to replace it with a blank symbol,
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# To ''delete'' a substructure is to replace it with an empty node, in effect, to reduce the whole structure to a trivial point.
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    in effect, to paint it out of the picture or to overwrite it.
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# 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.
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<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
Jon Awbrey
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