Chomsky’s main idea is that while human language is produced linearly (that is, one word after another), it has a deep structure that is instead hierarchical. The full set of rules governing where different parts of speech can go in this hierarchy is waaaay too long for a Reddit comment (and I doubt I could explain it well since it’s been a few years since I really took syntax).

I believe the highest level in this sentence is a VP (Verb Phrase), although I think one might argue it’s a TP (Tensed Phrase) idk, I’m not a syntactician. A VP can take an internal argument (object, for English verbs), but isn’t required to, and in this case it doesn’t, since sleep is an intransitive verb. Embedded in that VP, as in all VPs, is an external argument, in this case the NP (Noun Phrase) “colorless green ideas”, and a V’ (read as “V bar”). The V’ itself contains the V “sleep” and the AP (Adjunct Phrase) “furiously”.

There’s more analysis to be done on this sentence (going into the NP and its adjuncts), but I’ll spare you. The point I’m trying to make is that rules govern the syntax of languages, but these rules are, under Chomsky’s original proposition, unrelated to semantics. He argued it is entirely possible for a sentence to be syntactically grammatical and semantically meaningless, which I think is well-evidenced by the fact that there are some meaningless sentences that seem like English and some that don’t.

Later linguists working with later models have challenged the strict hierarchy of this theory (called the Minimalist Program), and have also challenged its total separation of syntax and semantics.

The other point I should have made clearer in my first comment is that most people use “grammar rules” differently from how linguists use the term, including, I think, the person I was replying to. Linguists are scientists, and therefore take a descriptive view of language. We model what we observe. If our rules don’t conform to how people actually speak, it is we who are wrong, not the speakers, just like how a physicist’s model of particle behavior must be wrong if it doesn’t accurately product how a particle acts. This disqualifies almost all the grammar rules you learned in school. Things like “you can’t say ‘me and my dad went to the store’” or “you can’t end a sentence with a preposition” are obviously wrong, because people do it all the time. If those actually produced sentences universally judged by our mental grammar to be unacceptable, then people wouldn’t do them. The job of syntacticians is not to impose arbitrary rules like these, but instead to discover the actual, implicitly understood rules governing how all real human beings speak, not just those who have been taught to speak in a certain educated register.