Models

(PAST) Should (not) have done(V3)

(PAST) Ought (not) to have done(V3)

(PR) Must (must not)

(PR) Have to (don't have to)

(PR) Need to

Needn't

Don't need to

Be supposed to

(PAST) Had to (didn't have to)

(PAST) Need have V3 (nedn't have done(V3))

(PAST) Needed to (didn't need to)

Certainty (90-99%)

(PR) Must, can't, couldn't

(PAST) must, can't, couldn't + have V3

Probability

(PR) Should, ought to

(PAST) should, ought to + have V3

Posibility

(PR) May, could, might

(PAST) may, could, might + have V3

(PR) Can (for present and future situations)

(PR) Could (for unreal)

(PAST) Could (for past situation(real))

(PAST) Could have V3 (for unreal situation)

(PR) May (most polite)

(PR) Could (less polite)

(PR) Can (unpolite)

(PAST) Be allowed to

(PAST) Could (for reported)

(PR) Should

(PR) Ought to

(PR) Had better to do