Changes

</ol>

</ol>

This appears to be just about the most concise description of the cactus language <math>\mathfrak{C} (\mathfrak{P})</math> that one can imagine, but there are a couple of problems that are commonly felt to afflict this style of presentation and to make it less than completely acceptable.  Briefly stated, these problems turn on the following properties of the presentation:

This appears to be just about the most concise description

of the cactus language !C!(!P!) that one can imagine, but

there exist a couple of problems that are commonly felt

to afflict this style of presentation and to make it

less than completely acceptable.  Briefly stated,

these problems turn on the following properties

of the presentation:

1.  The invocation of the kleene star operation

# The invocation of the kleene star operation is not reduced to a manifestly finitary form.

    is not reduced to a manifestly finitary form.

# The type <math>S\!</math> that indicates a sentence is allowed to cover not only itself but also the empty string.

2.  The type of a sentence S is allowed to cover

I will discuss these issues at first in general, and especially in regard to how the two features interact with one another, and then I return to address in further detail the questions that they engender on their individual bases.

    not only itself but also the empty string.

I will discuss these issues at first in general, and especially in regard to

In the process of developing a grammar for a language, it is possible to notice a number of organizational, pragmatic, and stylistic questions, whose moment to moment answers appear to decide the ongoing direction of the grammar that develops and the impact of whose considerations work in tandem to determine, or at least to influence, the sort of grammar that turns out.  The issues that I can see arising at this point I can give the following prospective names, putting off the discussion of their natures and the treatment of their details to the points in the development of the present example where they evolve their full import.

how the two features interact with one another, and then I return to address

in further detail the questions that they engender on their individual bases.

In the process of developing a grammar for a language, it is possible

# The ''degree of intermediate organization'' in a grammar.

to notice a number of organizational, pragmatic, and stylistic questions,

# The ''distinction between empty and significant strings'', and thus the ''distinction between empty and significant types of strings''.

whose moment to moment answers appear to decide the ongoing direction of the

# The ''principle of intermediate significance''.  This is a constraint on the grammar that arises from considering the interaction of the first two issues.

grammar that develops and the impact of whose considerations work in tandem

to determine, or at least to influence, the sort of grammar that turns out.

The issues that I can see arising at this point I can give the following

prospective names, putting off the discussion of their natures and the

treatment of their details to the points in the development of the

present example where they evolve their full import.

In responding to these issues, it is advisable at first to proceed in a stepwise fashion, all the better to accommodate the chances of pursuing a series of parallel developments in the grammar, to allow for the possibility of reversing many steps in its development, indeed, to take into account the near certain necessity of having to revisit, to revise, and to reverse many decisions about how to proceed toward an optimal description or a satisfactory grammar for the language. Doing all this means exploring the effects of various alterations and innovations as independently from each other as possible.

 

 

 

In responding to these issues, it is advisable at first to proceed in

a stepwise fashion, all the better thereby to accommodate the chances

of pursuing a series of parallel developments in the grammar, to allow

for the possibility of reversing many steps in its development, indeed,

to take into account the near certain necessity of having to revisit,

to revise, and to reverse many decisions about how to proceed toward

an optimal description or a satisfactory grammar for the language.

Doing all this means exploring the effects of various alterations

and innovations as independently from each other as possible.

The degree of intermediate organization in a grammar is measured by how many

The degree of intermediate organization in a grammar is measured by how many

intermediate symbols it has and by how they interact with each other by means

intermediate symbols it has and by how they interact with each other by means