So when using a modal verb in the perfect tense, I've notice two different types of constructions:
1) Ich habe arbeiten müssen.
2) Ich muss gearbeitet haben.
It seems like the first means "I have had to work" and the second one is "I must have worked" but I'm not 100% sure.
Also, can these dual constructions be extended to the other modals? For example, here's a pair of sentences I made up:
1) Ich habe es am Montag machen können.
2) Ich kann es am Montag gemacht haben.
The first is supposed to be "I was able to do it on Monday" and the second one I guess would have to mean something like "I am able to have done it on Monday".
But #2 seems wrong to me somehow, even though it's identical in syntax to the "muss" example above. I almost want to make it subjunctive:
Ich könnte es am Montag gemacht haben.
to say, "I could have done it on Monday", but then I don't know why kann needs to be subjunctive to feel correct when I didn't need it with müssen.
If anyone can help me out with this grammar, I'd very much appreciate it!