How are new input functions created?

Rick, would it kill you to encourage people and tell them how you think they could do better rather than discouraging them and telling them everything you think they’re doing wrong? Considering mortality and the importance of PCT, you should be working as hard as you can not to be the top expert in PCT when people brighter than either of us are carrying it forward into the future.

I request that you, Ishmael, call me.
I request that you call me Ishmael.

These are homonymous but different verbs. In one, you can substitute telephone; in the other, you can substitute name. What’s going on here is more fundamental than commas and intonation. Also see A grammar of English on mathematical principles, p. 351, for starters, and sections 3.5 and 3.6 of the same work.

The actual structure of language—its grammar in fact—is more or less different from the various descriptions of that structure which have been called grammar, sometimes extremely so, and that includes operator grammar. Confusion of formalisms with that which is formalized is still pretty common. Recent work by Stephen Johnson at Columbia and NYU, showing rules etc. as emergent phenomena, is touched on toward the end of that essay (doi 10.1075/hl.00077.nev). Most of the math you probably won’t find relevant to your interests. Suffice to say, it doesn’t support the notion that grammar is control of program perceptions.