As of sentence #3, it looks like a noun can contain cycles. I mean, it can be a cell, and a cell can contain nouns, so that seems like a cycle. Then, in sentence #5, I'm told they don't have cycles. What?
If we used the word "tree" and "leaf" here instead of "noun," would that help? "A tree is a leaf or a cell. A leaf is any unsigned integer. A cell is an ordered pair of trees."
It doesn't strike me that anyone reading this definition, even not knowing what a "tree" and a "leaf" are, would assume that a tree can have cycles. And then, two sentences later, if we say that a tree doesn't have cycles, I'd hope that that would settle the matter.
It's probably a mistake to bring implementation issues (like the fact that you can share a pointer rather than copying a subtree, thus creating a DAG [1]) into a discussion of this level, though. All kinds of people have different kinds of CS backgrounds...