Learn English – What are the differences between “I couldn’t pass the exam” & “I couldn’t have passed the exam”

In the past tense, "He was able to..." strongly implies that he did whatever action you describe. The main exception to this is that if the speaker explicitly indicates that the action was not completed, that is understandable to mean simply that he had the ability. For example, "He was able to call home, but chose not to do so," means that he had the ability to call home, but he did not.

In the future tense, to be able to do something means that someone will have the ability to do something, but not necessarily that he will do it. We can't predict the future :)

An infinitive X following to be means to do X at some future time because you are supposed to or scheduled to do X.

I am to go to work tomorrow. (I'm supposed to go to work tomorrow so I plan to do that).

John is to be cleaning and not playing video games. (John is supposed to be playing cleaning. This is likely John's mother telling his friend not to let him play video games.)

Infinitives can take have to specify perfect aspect.

To go to the mountains is something everyone in his family does.

To have gone to the mountains was an important thing to his family. (Implies family or mountains does not exist anymore).

I was to go to work yesterday.

I was to have gone to work yesterday. (Job or need to go doesn't exist anymore).

So the meaning of the second sentence is to have done X at some future time because you were supposed to or scheduled to have done X.

You can't do this:

I am to have gone to work yesterday. (Bad)