Modal Verbs of Obligation

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We can use have to + infinitive, must + infinitive and should + infinitive to express obligation (something you have to do).

have to /
don't have to
strong obligation (possibly from outside)
  • Children have to go to school.
(sometimes 'have got to')
no obligation
  • I don't have to work on Sundays.

  • You don't have to eat anything you don't like.
must / mustn't strong obligation (possibly based on the speaker's opinion)
  • I must study today.
negative obligation
  • You mustn't smoke here.
should / shouldn't mild obligation or advice
  • You should save some money.
mild negative obligation or advice
  • You shouldn't smoke so much.

Be careful about the difference between mustn't and don't have to!
Mustn't means it's not allowed, or it's a bad idea:

Don't have to means you don't need to do something, but it's fine if you want to do it:

had to / didn't have to obligation in the past
  • I had to wear a school uniform when I was a child.
no obligation in the past
  • We didn't have to go to school on Saturdays.
must*changes to 'had to'-
should have + pp / shouldn't have + pp a past action which didn't happen: the advice / regret is too late
  • You should have gone to bed earlier, now you have missed the train.
a past action which didn't happen: the advice / regret is too late
  • You shouldn't have taken that job., it was a bad idea.

* Remember 'must have done' is a modal verb of deduction or speculation, not obligation in the past. For example: Julie must have left. Her coat's not here. See modals of probabilty for more information.