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→1.3.10.9. The Cactus Language : Syntax: segment
"blank " = "blank"·" " = "blank"·blank
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A few definitions from formal language theory are required at this point.
A few definitions from formal language theory are required at this point.
A "token" is a particular appearance of a sign.
A "token" is a particular appearance of a sign.
The informal mechanisms that have been illustrated in the immediately preceding
The informal mechanisms that have been illustrated in the immediately preceding
NB. In this transcription, the symbols "-(" and ")-"
NB. In this transcription, the symbols "-(" and ")-"
will serve for the logically significant parentheses.
will serve for the logically significant parentheses.
The discussion that follows is intended to serve a dual purpose,
The discussion that follows is intended to serve a dual purpose,
Surc^k_j z_j = (Surc^(k-1)_j z_j) · ")-"^(-1) · "," · z_k · ")-".
Surc^k_j z_j = (Surc^(k-1)_j z_j) · ")-"^(-1) · "," · z_k · ")-".
The definitions of the foregoing syntactic operations can now be organized in
The definitions of the foregoing syntactic operations can now be organized in
constant functions, whatever sequences of strings z_j
constant functions, whatever sequences of strings z_j
may happen to be listed as their ostensible arguments.
may happen to be listed as their ostensible arguments.
Having defined the basic operations of concatenation and surcatenation
Having defined the basic operations of concatenation and surcatenation
these complementary forms of analysis and synthesis to articulate the
these complementary forms of analysis and synthesis to articulate the
structures of strings and sentences in two directions.
structures of strings and sentences in two directions.
The "painted cactus language" with paints in the
The "painted cactus language" with paints in the
to start with an arbitrary PARCE and then finds a reason to delete or
to start with an arbitrary PARCE and then finds a reason to delete or
to erase all of its paints.
to erase all of its paints.
Only one thing remains to cast this description of the cactus language
Only one thing remains to cast this description of the cactus language
the strings in the disjoint union {"S"} |_| (!Q! |_| !A!)* are known
the strings in the disjoint union {"S"} |_| (!Q! |_| !A!)* are known
as the "sentential forms" of the associated grammar.
as the "sentential forms" of the associated grammar.
In forming a grammar for a language, statements of the form W :> W',
In forming a grammar for a language, statements of the form W :> W',
where any of the symbols "t", "T", "S" can be taken to signify either the
where any of the symbols "t", "T", "S" can be taken to signify either the
tokens or the subtypes of their covering types.
tokens or the subtypes of their covering types.
Employing the notion of a covering relation it becomes possible to
Employing the notion of a covering relation it becomes possible to
how the two features interact with one another, and then I return to address
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 further detail the questions that they engender on their individual bases.
In the process of developing a grammar for a language, it is possible
In the process of developing a grammar for a language, it is possible
expression merely to account for and to recount every increment in the parameter
expression merely to account for and to recount every increment in the parameter
of iteration.
of iteration.
Returning to the case of the cactus language, the process of recognizing an
Returning to the case of the cactus language, the process of recognizing an
T = !e! and S = !e! on the covered side of the rule,
T = !e! and S = !e! on the covered side of the rule,
bears the germinal implication that T :> ",".
bears the germinal implication that T :> ",".
Grammar 2 achieves a portion of its success through a higher degree of
Grammar 2 achieves a portion of its success through a higher degree of
a tract. The last two Rules say that a tract T is either a sentence S or
a tract. The last two Rules say that a tract T is either a sentence S or
else the concatenation of a tract, a comma, and a sentence, in that order.
else the concatenation of a tract, a comma, and a sentence, in that order.
At this point in the succession of grammars for !C!(!P!), the explicit
At this point in the succession of grammars for !C!(!P!), the explicit
Consequences of the distinction between empty expressions and
Consequences of the distinction between empty expressions and
significant expressions are taken up for discussion next time.
significant expressions are taken up for discussion next time.
With the distinction between empty and significant expressions in mind,
With the distinction between empty and significant expressions in mind,
and also to enumerate a larger number of the smallest cases that can
and also to enumerate a larger number of the smallest cases that can
be observed to fall under each significant type.
be observed to fall under each significant type.
With the array of foregoing considerations in mind,
With the array of foregoing considerations in mind,
| |
| |
o-------------------------------------------------o
o-------------------------------------------------o
Finally, it is worth trying to bring together the advantages of these
Finally, it is worth trying to bring together the advantages of these
is a sentence.
is a sentence.
It is fitting to wrap up the foregoing developments by summarizing the
It is fitting to wrap up the foregoing developments by summarizing the
|'Machines, Languages, and Computation',
|'Machines, Languages, and Computation',
| Prentice-Hall, Englewood Cliffs, NJ, 1978.
| Prentice-Hall, Englewood Cliffs, NJ, 1978.
</pre>
=====1.3.10.10. The Cactus Language : Stylistics=====
1.3.10.10. The Cactus Language: Stylistics
<pre>
| As a result, we can hardly conceive of how many possibilities there are for what
| As a result, we can hardly conceive of how many possibilities there are for what
| we call objective reality. Our sharp quills of knowledge are so narrow and so
| we call objective reality. Our sharp quills of knowledge are so narrow and so