"Thou shalt eat" was an affirmative statement about the future even more certain than "Thou wilt eat". It isn't quite the same as the imperative ("Eat!") though it can be used to give an instruction (compare "Do not kill" with "Thou shalt not kill"). Do you have a suggestion for a better translation that captures this aspect of certainty in the future? Does "(Tu) hás de comer" work?
I'd also be grateful if you could explain why you can't say "Tu comerás"; with or without the pronoun it seems to translate "Thou wilt eat" (and possibly "Thou shalt eat" if there is no alternative). Perhaps you mean it sounds like an imperative if you omit the pronoun.
I was merely trying to address the other comment about DL sentence being archaic - I didn't mean to comment on the imperativeness of it.
If we are talking about archaic ways of speaking, you would use Comerás with no pronoun because that's the way they used to speak eons ago, like Bible-time and the commandments: Thou shalt not kill = Não matarás (it would never be tu não matarás).
Tu comerás is simply future with tu, it's not archaic at all, many people actively speak like this in several different places.
As for the certainty of the sentence... I'm afraid I won't be of much help - I never studied those more old-fashioned forms (neither in English nor in PT).
I know that há de + verb exists and is very old-fashioned - for instance, there this sort of saying that goes A terra há de comer, meaning that, in the end, the earth shall take it/anything/everything. And I have seen it being used with other verbs in period pieces on the TV, for example... But I don't really know much about it comment any further, sorry!
What I can tell you is that Tu vais comer! is exactly what my mom would tell me when I was little and didn't want to eat xD
But at the same time it is fairly common to ask Tu vais comer aquilo/isso? (as in: can I have it if you're not gonna eat it?).
In any case, this is only used on the few places where we still use tu so it is the same as saying Você vai comer - it's not more imperative nor less...
Hope this clarifies things a little! If anything, just ask C:
Thank you very much for your very complete answer. I missed the point that you had simply omitted the pronoun from the "tu" future to give it a more archaic ring (saying it was "absolutely mandatory to omit the pronoun" was the hook that caught my attention).
In much earlier times, "will" and "shall" were much more distinct than they are nowadays and if the Bible had said "Thou wilt not kill" it would probably have sounded a bit more like a suggestion than a command. :-)
The "haver (present) + de + infinitive" form seems to be alive and well in Portugal if not in Brazil. The English name for it is the "emphatic future" as you can read in this snippet from a book on European Portuguese which compares three ways of expressing the future: http://tinyurl.com/emphatic-future
Thanks again for your help.