static L scanTree(O root, L<S> fields) {
  new IdentityHashMap out;
  scanTree_impl(root, fields, out);
  ret list(out.keySet());
}

static void scanTree_impl(O root, L<S> fields, IdentityHashMap out) {
  if (root == null) ret;
  if (out.containsKey(root)) ret;
  out.put(root, true);
  for (S field : fields)
    scanTree_impl(getOpt(root, field), fields, out);
}