from https://en.wikipedia.org/wiki/Functional_programming
I totally agree that neither iterators nor 2/3s of closures are "functional programming". That's fine, though, because I really enjoy the sane way that it all was done.
If you check out
https://doc.rust-lang.org/std/iter/trait.Iterator.html
and search for `FnMut`, you see that most of the iterator methods are side-effectful. That is cool and fun and very useful, but it isn't functional programming.
Edit. The term you are probably looking for (guessing) is "higher-order programming":