trees.java

private static <A> Option<Tree<A>> filterTopDown(Tree<A> tree, Predicate<A> pred)
    {
           if (!pred.test(tree.root()))
           {
              return none();
           }

        Stream<Tree<A>> filteredChildren = tree.subForest().f().map(child -> filterTopDown(child, pred)).filter(x -> x.isSome())
                .map(x -> x.some());
           return some(node(tree.root(), filteredChildren));
    }