polyphonic music with tablature

[Art Sulger]

I'm not having much luck printing out polyphonic music on a treble clef with 
guitar tab just below. The following code prints the notes twice on the 
treble clef and nothing on the tab. I've tried several variations of this, 
but so far haven't hit on the right way to do it. Please help.
Thanks,
Art
---------------------------------------------------
%test.ly
\version "2.6.4"
\layout {

}
melody = {
  \time 4/4
  \key c \major
  <<
%  \stemUp
  {
  f'4\1 c'8\2[ c'\2] ~ c'4 f'4\1 |
  f8[ f'\1]~ f'4 s4 s8 f'8\1
  }
  \\
%  \stemDown
  {
  f2\4 a2\3 |
  f2\4 a2\3
  }
  >>
}
\context StaffGroup <<
  \context Staff { \clef "G_8" \melody }
  \context TabStaff { \melody }
>>