[om] different representations for a/b and a*b^(-1)

David Carlisle davidc at nag.co.uk
Mon May 20 10:40:18 CEST 2002

> This means that your openmath content is aimed at providing hints
> to the rendering application.
>  So you agree with me.
>  so why do you argue?
Habit, i suppose:-)

> Actually I don't see this as so clear cut. You may wish to encode
> as part of the message, something significant about the choice of divide
> representation.

If you have two related "divide" operators then as I said earlier you
can of course have two different symbols at the openmath level.
However the core CDs don't have two and since your original message
only showed a presentation form I inferred that - and / were the same
operation. Of course infering semantics from presentation is always
suspect, which is rather the point of openmath.

> OK, so OM is not encoding the semantics, but merely the syntax tree.
> Perhaps by reference to some CD, the operators will have some
> associated properties.  So stop claiming that it represents
> math. It is an anotated tree.

Yes, of course the OM object is an annotated tree, and XML being (today)
the syntax of choice for passing round annotated trees, XML is the most
common encoding of openmath. But it could be lisp or tex or pretty much
anything else. But the point is that the annotations _do_ refer to
mathemtical meaning of the symbols. This may be a definition of the
symbol in a foundational logic, or the definition of a symbol in some
textbook in the literature, but either way it seems like mathematics to

> Actually, I think I am still correct.  You are now asserting that
> OM content merely conveys a syntax tree,

It's not the tree that you necessarily use for presentation though.
For example the OM tree for (+ 1 2 3) looks like that expression with head
apply, first child sum and next three children 1 2 3, but typically this
gets rendered as 1 + 2 + 3 which has rather  different tree structure.
So I repeat the OM representation does not give any real hint to desired
presentation, although of course it is true that one can almost always
infer _some_ kind of usable presentation from the tree structure of the

>  My error was in thinking that the OM content
> would represent some kind of canonicalization of content.

OK so we've made some progress.

> The style-sheet MIGHT do it (Any CAS display
> system does it now), but it will not be right in all
> cases.

If (as happens most often in educational scenarios) you need total
control over the presentation form, then you can (and people do) supply
the total presentational form for each expression, in Presentation
MathML, or TeX or as a gif image, whatever.  However even in that case
you might want for other purposes to indicate that all these different
presentational forms refer to the same mathematical operator. linking
them to an OM representation is one way to do this.

> The song might be rendered by your presentation program as

It would, unless the author has marked it up as
<OM cd="american-english" name="tomato"/>
<OM cd="english-english" name="tomato"/>
But even then I doubt that one would really expect a generic system to
really capture jokes and word play. If you were doing this you'd
probably mark up the text as much as possible (to enable
searching/indexing etc) and then link it to a sound file with a real
singer doing the song justice. This is no different from the examples
above,  You always have the option of of explictly giving the
presentation form.


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