I know that "tap" means "would have". Where does this construction come from? Is it a combination of "ta + ap" or something else? Thank you!

It can be te ap or ta ap

te + ap = past continuous forms

1.
Li t'ap mache byen vit pou l pa ta rate bis la.
He was walking quickly so that he would not miss the bus.

2.
Nou t'ap tann ou.
We were waiting for you.

3. 
M t'ap panse pou m anile kont lan.
I was thinking to cancel the account.


Ta + ap =  conditional statements

4.
Ou t'ap fache avè'm si m pa't pote manje a pou ou.
You would have been mad at me If I didn't bring you the food.

5.
Si w pa't wo konsa, m t'ap fese w atè.
If you weren't that tall, I would have thrown you to the ground.


Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words