sub visit_preorder {
   my ($cb, node, $depth) = @_;
   $depth ||= 0;
   $cb->($node, $depth);
   visit_preorder($cb, $_, $depth+1) for $node->children();
}

sub visit_postorder {
   my ($cb, $node, $depth) = @_;
   $depth ||= 0;
   visit_postorder($cb, $_, $depth+1) for $node->children();
   $cb->($node, $depth);
}

visit_preorder(sub {
   my ($node, $depth) = @_;
   ...
}, $root);