what was the function of the Roman cavalry?

[Theodosius the Great]

I think the Carthaginian cavalry at Cannae fought on foot when they closed the encirclement.... The lack of stability would maybe explain why the cavalry got off their horses at Cannae

Actually, the "Carthaginian" cavalry that closed the encirclement at Cannae were in fact Spanish cavalry who were known for dismounting and joining their infantrymen in emergencies and they were famous for also having TWO riders per horse. (Although, I don't know if this was the case at Cannae.)

~Theo