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Directory:Jon Awbrey/Papers/Cactus Language (view source)
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, 00:49, 5 January 2009→The Cactus Language : Syntax: move set-up for grammar 2 into the section of the same title
# Given the covering <math>S :> \operatorname{Conc},</math> the covering rule <math>\operatorname{Conc} :> \operatorname{Conc} \cdot S</math> says no more than the covering rule <math>\operatorname{Conc} :> S \cdot S.</math> Consequently, all of the information contained in these two covering rules is already covered by the statement that <math>S :> S \cdot S.</math>
# Given the covering <math>S :> \operatorname{Conc},</math> the covering rule <math>\operatorname{Conc} :> \operatorname{Conc} \cdot S</math> says no more than the covering rule <math>\operatorname{Conc} :> S \cdot S.</math> Consequently, all of the information contained in these two covering rules is already covered by the statement that <math>S :> S \cdot S.</math>
# A grammar rule that invokes a notion of decatenation, deletion, erasure, or any other sort of retrograde production, is frequently considered to be lacking in elegance, and a there is a style of critique for grammars that holds it preferable to avoid these types of operations if it is at all possible to do so. Accordingly, contingent on the prescriptions of the informal rule in question, and pursuing the stylistic dictates that are writ in the realm of its aesthetic regime, it becomes necessary for us to backtrack a little bit, to temporarily withdraw the suggestion of employing these elliptical types of operations, but without, of course, eliding the record of doing so.
# A grammar rule that invokes a notion of decatenation, deletion, erasure, or any other sort of retrograde production, is frequently considered to be lacking in elegance, and a there is a style of critique for grammars that holds it preferable to avoid these types of operations if it is at all possible to do so. Accordingly, contingent on the prescriptions of the informal rule in question, and pursuing the stylistic dictates that are writ in the realm of its aesthetic regime, it becomes necessary for us to backtrack a little bit, to temporarily withdraw the suggestion of employing these elliptical types of operations, but without, of course, eliding the record of doing so.
===Grammar 2===
One way to analyze the surcatenation of any number of sentences is to introduce an auxiliary type of string, not in general a sentence, but a proper component of any sentence that is formed by surcatenation. Doing this brings one to the following definition:
One way to analyze the surcatenation of any number of sentences is to introduce an auxiliary type of string, not in general a sentence, but a proper component of any sentence that is formed by surcatenation. Doing this brings one to the following definition:
Returning to the case of the painted cactus language <math>\mathfrak{L} = \mathfrak{C} (\mathfrak{P}),</math> it is possible to put the currently assembled pieces of a grammar together in the light of the presently adopted canons of style, to arrive a more refined analysis of the fact that the concept of a sentence covers any concatenation of sentences and any surcatenation of sentences, and so to obtain the following form of a grammar:
Returning to the case of the painted cactus language <math>\mathfrak{L} = \mathfrak{C} (\mathfrak{P}),</math> it is possible to put the currently assembled pieces of a grammar together in the light of the presently adopted canons of style, to arrive a more refined analysis of the fact that the concept of a sentence covers any concatenation of sentences and any surcatenation of sentences, and so to obtain the following form of a grammar:
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