Modals: Could have, should have, and would have.

Could have

1. [A "could have" B]
   ("You could have burned yourself touching that pan.")
   indicates that B was a possibility for A in the past, although it did not actually happen.
   (Note: "Should have" in this sense could indicate "regret".)
   (Collins Cobuild, 370)
   
   

Should have

1. [A "should have" B]
   ("I should have put a glove on before I touched the pan, then I wouldn't have got burned." (wished), "The pan should have been hotter than it was, I put it on high." (expected)).
   indicates that B did not happen in the past, but that it as a possibility and you wished or expected it to happen.
   (Note: "Should have" in this sense could indicate "regret".)
   (Collins Cobuild, 1539, 3)
   
   
2. [A "should have" B by C]
   ("The pan should have heated up by now.")
   means that in most cases A will probably happen by time C, i.e. at some time in the past before time C.
   (Collins Cobuild, 1539, 4)
   
   
3. [You "should have" B]
   ("You should have seen his face when he touched that pan.")
   emphasizes how "funny, shocking, or impressive" it was when it happened at some time in the past (Note: It's not just a possible event. It actually happened.)
   (Collins Cobuild,1539,11)
   
   

Would have

1. [A "would have" B(a past participle)]
   ("The pan on the upper right burner would have been the hot one, he put the corn in the pan on the lower left burner and it never cooked.")
   indicates not only that something was possible at some time in the past but that you assume or guess it to be so (true) because you have good reason to believe it to be so.
   (Collins Cobuild,1539,4)
   
   
2. [Within A of B, C "would have" D(a past participle)]
   (Within twenty minutes of putting the pan on the burner, it would have come to a boil.)
   indicates that C was not only possible, but also likely to have occurred at a time in the past occurring before A time units had elapsed after event B.
   (Collins Cobuild,1539,17)
   
   
3. [If A, B "would have" C(a past participle)]
   ("If I had known he was going to touch the pan, I would have told him not to touch it.")
   indicates that A was a possible event in the past with a the result or effect C.
   (Note: "Should have" in this sense could indicate "regret".)
   (Collins Cobuild,1539,18)
   
   
4. [A "would have liked"(or "preferred") to B]
   ("I would have liked to have boiled the corn correctly, and I could have done it if I had known where the hot pan was.")
   means that A wanted to do it or have it, but was unable to.
   (Note: "Should have" in this sense could indicate "regret".)
   (Note: This is just a special case of sense #1 using "like".)
   (Collins Cobuild,1539,19)
   
   

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