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In this Subsection, I discuss the ''mechanics'' of parsing the cactus language into the corresponding class of computational data structures. This provides each sentence of the language with a translation into a computational form that articulates its syntactic structure and prepares it for automated modes of processing and evaluation. For this purpose, it is necessary to describe the target data structures at a fairly high level of abstraction only, ignoring the details of address pointers and record structures and leaving the more operational aspects of implementation to the imagination of prospective programmers. In this way, I can put off to another stage of elaboration and refinement the description of the program that constructs these pointers and operates on these graph-theoretic data structures.
In this Subsection, I discuss the ''mechanics'' of parsing the cactus language into the corresponding class of computational data structures. This provides each sentence of the language with a translation into a computational form that articulates its syntactic structure and prepares it for automated modes of processing and evaluation. For this purpose, it is necessary to describe the target data structures at a fairly high level of abstraction only, ignoring the details of address pointers and record structures and leaving the more operational aspects of implementation to the imagination of prospective programmers. In this way, I can put off to another stage of elaboration and refinement the description of the program that constructs these pointers and operates on these graph-theoretic data structures.
It is conceivable, from a purely graph-theoretical point of view, to have
The structure of a ''painted cactus'', insofar as it presents itself to the visual imagination, can be described as follows. The overall structure, as given by its underlying graph, falls within the species of graph that is commonly known as a ''rooted cactus'', and the only novel feature that it adds to this is that each of its nodes can be ''painted'' with a finite sequence of ''paints'', chosen from a ''palette'' that is given by the parametric set <math>\{ \, ^{\backprime\backprime} \operatorname{~} ^{\prime\prime} \, \} \cup \mathfrak{P} = \{ m_1 \} \cup \{ p_1, \ldots, p_k \}.</math>
a class of cacti that are painted but not rooted, and so it is frequently
necessary, for the sake of precision, to more exactly pinpoint the target
It is conceivable, from a purely graph-theoretical point of view, to have a class of cacti that are painted but not rooted, and so it is frequently necessary, for the sake of precision, to more exactly pinpoint the target species of graphical structure as a ''painted and rooted cactus'' (PARC).
species of graphical structure as a "painted and rooted cactus" (PARC).
A painted cactus, as a rooted graph, has a distinguished "node" that is
A painted cactus, as a rooted graph, has a distinguished node that is called its ''root''. By starting from the root and working recursively, the rest of its structure can be described in the following fashion.
called its "root". By starting from the root and working recursively,
the rest of its structure can be described in the following fashion.
<pre>
Each "node" of a PARC consists of a graphical "point" or "vertex" plus
Each "node" of a PARC consists of a graphical "point" or "vertex" plus
a finite sequence of "attachments", described in relative terms as the
a finite sequence of "attachments", described in relative terms as the