Ordinary or Special?
Now, on to the differences between ordinary imperatives and special let-imperatives. The first one that CGEL lists is about the contraction of us, which is what Aaron was noticing. CGEL points out that us cannot be contracted in ordinary imperatives, which is exactly what Aaron tried to do when he wrote, “Let’s know when you arrive.” CGEL states further that you can’t contract us in declarative or interrogative sentences, either. You wouldn’t say They didn’t want to let’s join in instead of They didn’t want to let us join in. And you wouldn’t say Will you make’s breakfast? instead of Will you make us breakfast? (Actually, this is an inadvisable question anyway, because the person you’re asking might answer, “Abracadabra! You’re breakfast!”)
Not only can you contract let us if you’re uttering a special let-imperative; usually, you will. The most common place to hear an uncontracted let us is in a religious context, probably in the sentences Let us pray or Let us rejoice. For example, when I checked the Corpus of Contemporary American English, the top two words most associated with uncontracted Let us are rejoice and pray. I also found that with negative suggestions, let us not is more common than you’d expect, although it’s still in the minority compared with let’s not. Interestingly, let us not is especially common with the verb forget. In fact, that one verb flips the usual pattern, so that let us not forget is actually almost three times as common as let’s not forget. If any of you have guesses as to why that’s so, please leave a comment.
The second difference between ordinary imperatives and special let-imperatives has to do with whether you can have an explicit subject. For an ordinary imperative, the subject can be understood, as in the command Be quiet; or it can be explicit, as in No, you be quiet, or All right, everyone be quiet! However, take the sentence Let’s go, and put a you in front of it—You let’s go—and it doesn’t make sense anymore. And I’m laughing as I imagine the classic holiday tune: “Let it snow, no you let it snow, no YOU let it snow!”