Changes

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 ''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.

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:

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 ''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.

# 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.

A ''bare PARC'', loosely referred to as a ''bare cactus'', is a PARC on the empty palette <math>\mathfrak{P} = \varnothing.</math> In other veins, a bare cactus can be described in several different ways, depending on how the form arises in practice.

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

in several different ways, depending on how the form arises in practice.

<ol style="list-style-type:decimal">

    the bare cactus language !C!^0 = PARCE^0.

2.  To express it more in its own terms, a bare PARC can be defined

<li>Leaning on the definition of a bare PARCE, a bare PARC can be described as the kind of a parse graph that results from parsing a bare cactus expression, in other words, as the kind of a graph that issues from the requirements of processing a sentence of the bare cactus language <math>\mathfrak{C}^0 = \operatorname{PARCE}^0.</math></li>

    by tracing the recursive definition of a generic PARC, but then

    by detaching an independent form of description from the source

    of that analogy. The method is sufficiently sketched as follows:

    a.  A "bare PARC" is a PARC whose attachments

<li>To express it more in its own terms, a bare PARC can be defined by tracing the recursive definition of a generic PARC, but then by detaching an independent form of description from the source of that analogy. The method is sufficiently sketched as follows:</li>

        are limited to blanks and "bare lobes".

    b.  A "bare lobe" is a lobe whose accoutrements

<ol style="list-style-type:lower-latin">

3. In practice, a bare cactus is usually encountered in the process

    of analyzing or handling an arbitrary PARC, the circumstances of

 

    which frequently call for deleting or erasing all of its paints.

<li>A ''bare lobe'' is a lobe whose accoutrements are limited to bare PARC's.</li>

    In particular, this generally makes it easier to observe the

 

    various properties of its underlying graphical structure.

</pre>

 

<li>In practice, a bare cactus is usually encountered in the process of analyzing or handling an arbitrary PARC, the circumstances of which frequently call for deleting or erasing all of its paints. In particular, this generally makes it easier to observe the various properties of its underlying graphical structure.</li>

 

</ol>

==The Cactus Language : Semantics==

==The Cactus Language : Semantics==