The Rambam (Laws of Sukkah and Lulav, 4:7) writes:
A sukkah that does not possess a roof is invalid
This is from a halachic perspective. However, I was wondering what the deeper meaning behind the roof of the sukkah is. A obvious reason would be that we are under Hashem's protection, but is there more to it and to the greenery we place on top of the schach? Why do we put leaves on top of it....
What's the reasoning behind all this? Especially since Rav Hirsch is quoted in saying that a roof, "with its ability to shut out the heavenly influences of rain and sun, symbolizes man's imagined independence from G-d".