Why "Sleep well" after sleep?

I heard protagonists say "Sleep well?" after sleep in a movie and got curious; why is it "Sleep well", not "Slept well"? Shouldn't it be "Slept well"? Since they are not about to sleep, but already have slept. Is Did you removed from "Did you sleep well"?

Solution 1:

Is Did you removed from "Did you sleep well"?

Yes, exactly. The speaker's intonation ought to convey the intention that this is a question rather than an imperative. One would also say "Sleep well" before someone goes to sleep, but in that case the intonation would be different.

Solution 2:

Yes, it's an elision. We could perfectly well ask, "slept well?" instead but don't always.