How to override filter in android's ArrayAdapter?

Question

I have an ArrayAdapter wrapped around an ArrayList of custom objects. I'd like to write a custom filter for that adapter so that when I call getListAdapter().getFilter().filter("abc") the list will get filtered by an arbitrary transformation of "abc".

I thought I would just try to override ArrayAdapter.getFilter(), but that requires I re-implement the private ArrayAdapter.ArrayFilter which requires access to a bunch of ArrayAdapter's private instances.

What's the simplest way to do this?