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Past modals come in two forms. The first type is the easiest and usually requires only a simple word change:
I can drive.
I could drive when I was 16.
I have to go to California.
I had to go to California.
Lenny will pay tomorrow.
Lenny said he would pay tomorrow.
(future reported from the past)
Past modals with have
Some past modals can be formed by using have + the past participle of the main verb immediately after the modal. (should have, could have, would have, etc.)
However, since modals express possibility, intention, obligation, etc., they do not always indicate a definite tense. Therefore, when using past modals with have, special meanings need to be considered.
I should go to the funeral.
I should have gone to the funeral.
Lex might take Karen to the airport.
Lex might have taken Karen to the airport.
Lex could have taken Karen to the airport.
Lex would have taken Karen to the airport.
Otis didn't come to work yesterday.
He had to take care of his children.
His children must have been sick.
(I feel an obligation to go--later.)
(I didn't go. Now I regret it.)
(It's a future possibility.)
(He may be on his way there now.)
(Most likely he didn't.)
(He didn't. He had an excuse.)
(conjecture about the past)
See also :
Grammar : Common Modal Usage
Textbook Recommendation : Touchy Situations, Chapter 19
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