Must (Past Obligation Interrogative) "Must you have eaten all the food?" [closed]

Is the question "Must you have eaten all the food" correct when used in the past obligatory sense?

The best examples I can find are quite ambiguous.

"Must He have been less than perfectly kind to one of His creatures? I do not think it can reasonably be argued that in such a case God must have wronged one of His creatures." -Kopelman, ‎L.M. and Moskop, J.C.; Ethics and Mental Retardation, 1984 [pg. 130]

If you change the question to read as follows it seems to share a similar intent:

"Did He have to be less than perfectly kind to one of His creatures? I do not think it can reasonably be argued that in such a case God must have wronged one of His creatures."

I am looking for solid references or consensus as to why "much" can't be used in the past deontic sense.

Solution 1:

Must is a modal auxiliary verb, and like all such, has many restrictions and irregularities.
For one thing, must can't be used to refer to past deontic (obligation) senses. At all.
For another, must with a human subject and active predicate is usually interpreted as deontic.

• He must be there tomorrow.
  (= he is obliged to be there tomorrow;
    ≠ he is almost certain to be there tomorrow)
• *He must be there yesterday.

Must have is always epistemic (logical conclusion), rather than deontic.

• He must have been there yesterday.
  (= he was almost certainly there yesterday;
    ≠ he was obliged to be there yesterday)

If you need to refer to a past obligation, you use the modal paraphrase have to;
it has a past tense, an infinitive, and a participle, where must doesn't,
so it can swing either way in the past or the present.

• He has to be there tomorrow.
  (= he is almost certain to be there tomorrow;
    = he is obliged to be there tomorrow)

• He had to be there yesterday.
  (= he was almost certainly there yesterday;
    = he was obliged to be there yesterday)