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.

A rune is a string of blanks and paints concatenated together.  Thus, a typical rune is a string over possibly the empty string.

When there is no risk of confusion, the letter may be used either as a string variable ranging over the set of runes or as a type name for the class of runes.  The latter reading amounts to the recruitment of a new intermediate symbol to form a new grammar for   Thus accords grammatical recognition to any rune forming a part of a sentence in   In situations where the variant usages are likely to be confused the types of strings may be indicated by way of expressions like and

A foil is a string of the form where is a tract, giving a foil the following form.

Thus a foil is nothing other than the surcatenation of a sequence of sentences   In the case where the sequence of sentences is empty and thus where the tract is the empty string, we have the minimal foil

Explicitly marking each foil embodied in a cactus expression is tantamount to recognizing a new intermediate symbol, further articulating the structure of expressions and expanding the grammar for the language   All the same remarks about the versatile uses of intermediate symbols, as string variables and as type names, apply again to the letter

Resources

• Cactus Language • Syntax
• Survey of Animated Logical Graphs
• Survey of Theme One Program

cc: Academia.edu • BlueSky • Laws of Form • Ma^thstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science