high-level overview of where we are

Dear Math-ERB Friends:

I thought it might be useful to send my high-level understanding of where
our committee is heading.  The picture I paint below is based largely on
discussions from the last few weekly conference calls.  The fact that these
calls have been so poorly attended provided further motivation for sending
this message.

During the last few conference calls we discussed two possible entry points
into the HTML math environment - the first being our HTML math notation
(i.e. the specification that Bruce is developing) and the second being a
HTML display-oriented markup that is directly derivable from our display
list format.  I believe Neil was thinking of this display-oriented HTML
format as being logically equivalent to the display list - one might think
of the display list as being a "compiled" version of the other.

A primary motivation for the second format is that it would be easier (and
therefore cheaper) for publishers to convert legacy data into a
display-oriented markup.  Providing a display-only entry point might
therefore help to facilitate more widespread acceptance of HTML math across
the electronic publishing community.  Uphill translation of legacy data to
the fuller HTML math notation would also be possible for those who choose
that route.

Please forgive the crudeness of the ASCII-based display below, but I think
this fairly accurately conveys my understanding of where we are heading.
If people find this useful I'd be quite willing to put this on the Web
site as a GIF that I maintain, but I wanted to send it via email in this
format first to be sure everyone read it.  ;-)


                                   ---------------           -------------
                                   |    HTML     | (i.e.,    |  "DAVE'S" |
                         /  -  -  >|    MATH     | Bruce's   |  NOTATION |
                                   |  NOTATION   | spec)     -------------
                       /           ---------------                 |
                                             |                     |
                     /                (Bruce)|                     |(Dave?)
                                             |      MACROS?        |
                   /                         |                     |
                                             V                     V
                 /                      ------------         --------------
                 Uphill                 |EXPRESSION|         |  OpenMath  |
               /Translation             |   TREE   |         | EXPRESSION |
               Possible                 ------------         |    TREE    |
             /                         /         |           --------------
                                      /(Bruce)   |
           /                         /(Dave?)    |
                                    /            |
         /                         V             V
------------------            ---------   ------------------   -------------
|    HTML MATH   |    1:1     |DISPLAY|   |   TEMPLATE     |   |  OpenMath |
|DISPLAY-ORIENTED|<-mapping ->|  LIST |   |   MATCHING     |   |  DISPLAY  |
|    NOTATION    |            ---------   |(ADDS SEMANTICS)|   |    LIST   |
------------------                |       ------------------   -------------
               \                  |              |
                \                 V              V
         (Robert)\           ----------   ----------------------
                  \--------->|   WEB  |   |VOICE SYNTHESIZER   |
                             |RENDERER|   |SYMBOLIC MANIPULATOR|
                             ----------   |ETC.                |


A few observations and questions:

- If I'm reading the recent mail correctly, we seem to have two competing
  schemes for the spec for the full HTML math notation (Bruce's spec and
  Dave's spec).  This seems like wasted and duplicated effort, but maybe
  I'm misunderstanding or not following things accurately.

- There has also been some notion of using the OpenMath specs for the
  expression tree and/or display list formats.  I assume that would make
  Bruce's work more difficult, since I believe the expression tree and
  display list formats he's currently working with are based to some
  extent on Mathematica models.

- I'm not sure how and where to integrate macros into this picture.
  Do the macros simply expand into HTML math "primitives" in the expression
  tree, or is some of the macro context passed along to the expression tree
  to be used as "hints" for the template matching?

- Do we need both the "HTML math display-oriented notation" and the
  "display list" formats?  I'm guessing yes, since I think we probably
  wouldn't want to translate from the expression tree into the more verbose
  HTML display-oriented notation.

- If we maintain both, then Robert, I assume the work you're doing on the
  parser from the display format could be fairly easily adapted for use
  with the display list format.  Yes?

Comments are most welcome.