completion for function arguments?

[TJ Luoma <luomat@xxxxxxxxx>]

Let me start by saying that I don't understand completion at all, so
this may be a) simple or b) impossible or c) have to be done a
completely different way.

I have a function called 'jump' which I will include below.

The function takes one (1) argument from a specific list of arguments.
I have defined these arguments as part of the function, although they
don't have to be defined that way if there's another way of doing it
that would work better for completion.

Here's what the function looks like now, and then I'll continue my
question below:

## Begin
JDIR="$HOME/Library/Mobile
Documents/2HCKV38EEC~com~p5sys~jump~servers/Documents/Servers"

for ARGS in "$@"
do
     case "$ARGS" in
          m1|macbook)

                    'Computer - m1 - 6F333BF4-CF2B-4E98-8281-A79667878D40.jump'
          ;;

          imac)

                    FILE='Computer - iMac -
4D391A42-B26E-460E-BDDD-88C9CCA882CF.jump'
          ;;

          tyrion)

                    FILE='Computer - Tyrion -
2709D3BB-41BE-4410-8606-6B4DEB92F104.jump'
          ;;

          mba|macbookair|air)

                    FILE='Computer - MBA -
4690FEF3-F057-4529-998A-9349F616C1FE.jump'
          ;;


          mini|mmcolo|macminicolo)

                    FILE='Computer - MacMiniColo -
13033BED-C6CA-4A5E-970E-47D7869EE09E.jump'
          ;;

          *)
                    echo "     [jump]: Fatal Error! Don't know what to
do with arg: $1"
                    return 1
          ;;

     esac

done # for args

if [[ -f "$JDIR/$FILE" ]]
then

     open -a 'Jump Desktop' "$JDIR/$FILE"

else

     echo "[jump] No file found at '$JDIR/$FILE'."
     return 1
fi

# End

As you can see, these files are obscurely named in an obscure folder
on my Mac, but I _could_ create links to all of them with the
preferred names, such as

~/jump/m1
~/jump/mini
~/jump/mba
~/jump/tyrion
~/jump/imac

and then all the function would need to do is open the file that
matches the argument.

I'd like to be able to type "jump [tab]" and have all of the options
appear (m1, mini, mba, tyrion, imac) or type "jump m[tab]" and have
just the ones that start with 'm' appear, etc. I think that's all
fairly standard completion stuff.

Any help would be appreciated.

Also, anyone has or knows of a "beginners' step-by-step guide to
understanding completion" please let me know.

Thanks, as always!

TjL