Past Negative: may not have been, were not allowed
Future Positive: may
Future Negative: may not
Shall¶
Uses1: Offers, suggestions and advice. We use shall I and shall we to make offers and suggestions, and to ask for advice.
Uses2: Predictions and intentions. We use shall instead of will with I and we in rather formal contexts to make predictions and to talk about intentions or decisions. It is much less common than will.
suggestion: Shall I help you?
promise: I shall never forget where I came from.
predestination: he shall become our next king.
inevitability: I’m afraid Mr. Smith shall become our new director.