run a complete -F function inside HERE document?

[Britton Kerin]

I'd like to be able to generate completion candidates inside a HERE
document.  Unfortunately this doesn't work:

$ complete -r cat
$ complete -F myfunc cat
$ cat <<END_CAT_INPUT
foo[TAB here should fire myfunc but doesn't]
END_CAT_INPUT

Is there any way to get completion to fire in this context?

Britton