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 and its generic part.  For the cactus language one has the following definitions of concatenation as iterated precatenation and surcatenation as iterated subcatenation, respectively.

Transforming the recursive definitions into grammar rules is accomplished by introducing a new pair of intermediate symbols, and corresponding to the operations of the same names but ignoring the inflexions of their individual parameters and   Recognizing the type of a sentence by means of the initial symbol and interpreting and as names for the types of strings generated by concatenation and by surcatenation, respectively, one arrives at the following transformation of the ruling operator definitions into the form of covering grammar rules.

The draft of a grammar reached at this point represents a measure of improvement.  Still, it exhibits a couple of features which are desirable to amend.

• Given the covering the covering rule says no more than the covering rule   Consequently, all the information contained in those two covering rules is already covered by the statement that
• Grammar rules invoking notions of discatenation, deletion, erasure, and other forms of retrograde production may be felt to lack due elegance.  If for the sake of the aesthetic in question one entertains for a moment keeping open the option of adopting that style of critique, it becomes necessary to backtrack a little bit, to experiment with withdrawing all forms of elliptical operators, but without, of course, eliding the record of having considered them.

Resources

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

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