Rules

If I had a regular grammar, I could just use a finite state automata for rules.
However, NL is widely agreed to be at least context free.
So, I needed some mechanism to store phrases.
Following Fillmore (68) I used case frames.
A simple phrase had features (like determiners and adjectives), that were in essence regular.
Complex phrases (e.g. a verb phrase with an actor and an object) needed variable binding .
We also needed some process to manage several frames, and to reuse them for the next sentence.
However, given those frames, rules were implemented by the activity of various CAs.
If a simple NP was being constructed (the state said it was), and an adjective was the input, the adjective feature was marked.
If a simple NP was being constructed, and a noun was the input, the noun was made the head, and the simple NP was finished.
If an NP was active, and a VP was active (both instances), we could use the VP -> NP active VP rule.
Linguistically, we made use of X-bar theory to separate simple and complex phrases.