Hi,
I'm writing a total functional language as well. I think that garbage collection is still useful however, as it can collect garbage as the program runs, not just at the end.
I would say that just because your memory use is deterministic, doesn't mean you don't get garbage. Garbage is just memory that isn't needed any more.
for example, in
let
a = f(x)
b = g(y)
in
a + b