Author Archives: Jon Awbrey

Grammar 4 If one imposes the distinction between empty and significant types on each non‑terminal symbol in Grammar 2 then the symbols and give rise to the expanded set of non‑terminal symbols leaving the last three to form a new intermediate … Continue reading →

Grammar 3 (concl.) Returning to the cactus language and fixing the parameter for the moment, we have a language of painted and rooted cactus expressions.  It serves the purpose of efficient accounting to divide the language into two sublanguages. The emptily … Continue reading →

Grammar 3 (cont.) In Grammar 3, the first three Rules say a sentence (a string of type ), is either a rune (a string of type ), a foil (a string of type ), or formed by concatenating strings of … Continue reading →

Grammar 3 It is possible to organize the materials of our developing grammar in a more easily graspable fashion by recognizing two recurring types of strings appearing in typical cactus expressions.  In doing so one arrives at the next two definitions. … Continue reading →

Grammar 2 One way to analyze the surcatenation of any number of sentences is to introduce an auxiliary type of string, not itself a sentence but a proper component of any sentence formed by surcatenation.  Doing that brings one to … Continue reading →

Grammar 1 (concl.) Returning to the case of the cactus language, the process of recognizing iterative or recursive types can be illustrated in the following way.  The operative phrases in the simplest form of recursive definition are its initial part … Continue reading →

Grammar 1 (cont.) The degree of intermediate organization in a grammar is measured by the number of its intermediate symbols and the complexity of their mutual interplay within the frame of the grammar’s productions. Grammar 1 has no intermediate symbols at … Continue reading →

Grammar 1 (cont.) In the process of developing a grammar for a language we encounter a number of organizational, pragmatic, and stylistic options whose moment to moment choices decide the ongoing direction of the work in progress and the impacts … Continue reading →

Grammar 1 Grammar 1 is something of a misnomer.  It is nowhere near exemplifying any kind of a standard form and it’s put forth only as a starting point for the initiation of more respectable grammars.  Such as it is, … Continue reading →

A certain degree of flexibility in the use of covering relations is typically allowed in practice.  Where there is little danger of confusion we may allow symbols to stand equivocally either for individual strings or for their types. There is … Continue reading →