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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.

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>

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>

To express the description of a PARC in terms of its nodes, each node can be specified in the fashion of a functional expression, letting a citation of the generic function name "<math>\operatorname{Node}</math>" be followed by a list of arguments that enumerates the attachments of the node in question, and letting a citation of the generic function name "<math>\operatorname{Lobe}</math>" be followed by a list of arguments that details the accoutrements of the lobe in question.  Thus, one can write expressions of the following forms:

To express the description of a PARC in terms of its nodes, each node can be specified in the fashion of a functional expression, letting a citation of the generic function name "<math>\operatorname{Node}</math>" be followed by a list of arguments that enumerates the attachments of the node in question, and letting a citation of the generic function name "<math>\operatorname{Lobe}</math>" be followed by a list of arguments that details the accoutrements of the lobe in question.  Thus, one can write expressions of the following forms:

{| align="center" cellpadding="8" width="90%"

{| align="center" cellpadding="4" width="90%"

| 1.

| <math>1.\!</math>

| <math>\operatorname{Node}^0</math>

| <math>\operatorname{Node}^0</math>

| <math>=\!</math>

| <math>=\!</math>

| a node with the attachments <math>C_1, \ldots, C_k.</math>

| a node with the attachments <math>C_1, \ldots, C_k.</math>

|-

|-

| 2.

| <math>2.\!</math>

| <math>\operatorname{Lobe}^0</math>

| <math>\operatorname{Lobe}^0</math>

| <math>=\!</math>

| <math>=\!</math>