Yes, it's possible to extend the method in the linked post to parse trees. Check out monoidal parsing:
http://comonad.com/reader/2009/iteratees-parsec-and-monoid/
This guy figured out how to turn parsers written with Parsec (an excellent collection of parser combinators; truly a pleasure to use) into monoidal parsers that you can use for incremental and/or parallel parsing.