I found this: http://www.unix.com/unix-advanced-expert-users/27318-how-see-function-shell.html
which indicates I can use typeset -f to list the functions.
But it also lists the contents of the functions. Is there a
lighter weight way to see what is defined? Is there an
internal array with the function names? Perhaps there is
a conventional idiom out there for asking your program if a
a particular function name is defined?
whence functionname will return 0 or 1 depending on whether a function is defined or not. Of course it will also succeed if a matching programme is found in the PATH, in which case you could test for the presence of "is a function" in the output of whence -v functionname.