Obligation

Obligation

Modal verbs of obligation : must, have to, should and ought to
 
There are two types of  modal verbs of obligation ;

•   those that primarily express a firm obligation or necessity - must and have to
•   those that express a recommendation or moral obligation - should and ought to

Firm obligation, etc. - must and have to  
The verb must only exists in the simple present and present perfect forms.
While the present form can express obligation, necessity, certainty or strong probability, the present perfect forms only express a strongly felt opinion or supposition.

All persons	Present	Present perfect
Affirmative	must	must have
Negative	must not, mustn't	must not have, mustn't have

If other tenses are required, the speaker or writer must use forms of the synonymous modal verb "have to" .  This modal auxiliary has all normal tenses, including progressive or continuous forms; these are not common, but need to be used in some cases.
 

Principal tenses	Present	Present perfect	Past	Future
Affirmative:	has to, have to	has had to have had to	had to	will have to
Negative;	does not have to, do not have to , doesn't have to don't have to	has not had to have not had to	did not have to didn't have to *	will not have to won't have to
Progressive or continuous	am having to is having to, are having to	has been having to have been having to	was having to were having to	will be having to

* The form "had not to" is sometimes used, but it is generally considered to be archaic.

Got to : 

• In spoken English, and in the present form only, have to is often substantiated by the word got;
• For example an alternative to I have to is I've got to.
• For more on this, study: get and got

Examples of must and have to being used to express :
a. Firm obligation or necessity
b. Certainty  or strong probability.
c. Must have only :  supposition

a1) You must see a doctor at once !
a2)  I have to be at school tomorrow at 8 a.m. I have an exam !
a21) I've got to be at school tomorrow at .....
a3)  You mustn't touch that plate, it's too hot.
a4)  I had to see a doctor, because I felt very sick.
a5)  I had to break the window ! I lost my key !
a6)  The manager isn't here, he's had to go to Paris on urgent business.
a7)  Tomorrow the President will have to open Parliament.
a8)  She's having to move because she can't stand the noise.
a9)  I'm having to take out this detonator very slowly, to avoid an explosion.
a10)  Oh you're so kind!  You didn't have to do it as well as that !

b1)  He must be over eighty, he was born in 1930.
b2)  If my brother's not in London, he has to be in New York.
b3)  I've got all the right answers, I must be one of the winners !
b4)  If I remember correctly, it has to be here.

c1)  I can't find my laptop, I must have left it in the train.
c2)  If they're out, they mustn't have heard the news.

Attention ! 
Take care to distinguish correctly between  "had to" and "must have"

They had to go to London
   = They were obliged to go to London
They must have gone to London. 
   = In my opinion, they have certainly gone to London.

Source: damaruta.com from linguapress.com