**Update**
I've reimplemented this using `Cell` and `RefCell`, as suggested by @alexcrichton. By taking care with the duration of the borrows, I was able to maintain the recursive allocation feature (now covered by a test) without the use of `Unsafe`, and without breaking the non-aliasing `&mut` invariant.
**Original**
Changes both `Arena` and `TypedArena` to contain an inner struct wrapped in a `Unsafe`, and change field access to go through those instead of transmuting `&self` to `&mut self`.
Part of #13933