• Perfect Modals: Must Have

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• Use the perfect modal form of must to show that you have come to a conclusion* about actions/events in the past.

  
  

  subject + must + have + past participle 

  
  

  -I must have left my notebook on your desk.

  (This shows a conclusion. I think I left my notebook on your desk after I checked all the other places.)

  
  

• You must have seen  them on campus today. She must have waited  for you in the quad for a long time. He must have spoken  to his academic advisor.

• 
  

  *Conclusion: a final decision, often made after a period of thought 

Source : Alison