Changes

In short, an UR-planted PARC has a single PARC as its only attachment, and since this attachment is prevented from being a blank or a paint, the single attachment at its root has to be another sort of structure, that which we call a ''lobe''.

In short, an UR-planted PARC has a single PARC as its only attachment, and since this attachment is prevented from being a blank or a paint, the single attachment at its root has to be another sort of structure, that which we call a ''lobe''.

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 "Node" 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 "Lobe" 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:

1. Node^0         = Node()

 

| 1.

                  = a node with no attachments.

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

 

| <math>=\!</math>

    Node^k_j  C_j = Node(C_1, ..., C_k)

| <math>\operatorname{Node}()</math>

 

                  = a node with the attachments C_1, ..., C_k.

 

2. Lobe^0         = Lobe()

| <math>=\!</math>

 

| a node with no attachments.

                  = a lobe with no accoutrements.

 

    Lobe^k_j  C_j = Lobe(C_1, ..., C_k)

| <math>\operatorname{Node}_{j=1}^k C_j</math>

 

| <math>=\!</math>

                  = a lobe with the accoutrements C_1, ..., C_k.

| <math>\operatorname{Node} (C_1, \ldots, C_k)</math>

| <math>=\!</math>

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

| 2.

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

| <math>=\!</math>

| <math>\operatorname{Lobe}()</math>

| <math>=\!</math>

| a lobe with no accoutrements.

| <math>\operatorname{Lobe}_{j=1}^k C_j</math>

| <math>=\!</math>

| <math>\operatorname{Lobe} (C_1, \ldots, C_k)</math>

| <math>=\!</math>

| a lobe with the accoutrements <math>C_1, \ldots, C_k.</math>

Working from a structural description of the cactus language,

Working from a structural description of the cactus language,

or any suitable formal grammar for !C!(!P!), it is possible to

or any suitable formal grammar for !C!(!P!), it is possible to