[om] OM proposals

[Andreas Strotmann]

Hi all,

I have put up on the web the slides for a presentation I gave in Berlin
the other day, containing some comments on proposals for OpenMath that I
have to fix a couple of problems I think I found.  The URL is

www.cs.fsu.edu/~strotman/slides/slides-omtn1-berlin.ppt

(yes, sorry, it's a Powerpoint presentation.  If anybody could help me
turn that thing into some reasonable file type, I'd be most obliged.)

This presentation triggered quite a discussion off-line, so that it seems
a good idea to open it up to discussion on this list, too.  Besides, it's
a draft for a presentation that I would give at the next OMWS -- which I
do not yet have the necessary funding to go to, and chances are slim I
will be able to change that.

Highlights:

 - proposal to remove the currying rule for OM bind
   (rationale: this can lead to inconsistencies in rare cases)
   - includes reasons why a different potential solution, namely
     allowing only symbols as binders, might not be a good idea

 - proposal to produce a "categorial semantics" for OM objects
   (i.e. a semantics that only covers concepts in the OM standard
   without any reference to any particular OM CD entries.)
   - includes an outline for a Lambek-style example

 - proposal to specify in the standard that any OM object taking
   a unary function as an argument can be used as a binder

 - proposal to specify in the standard that an OM binding construct
   applies the binder to the function which binds the variables
   specified and which has the final argument of the binder as a body

 - ideas for handling type information in OpenMath (responding
   to Michael Kohlhase's challenge to discuss that here).

All of these are inter-related, and I'm afraid I didn't quite manage to
sort them in a nice order for the presentation.

Note that I did not modify these slides in any way yet to account for the
discussion that already took place.

Enjoy ;-)

  Andreas
____________________________________________________________
"The act of defending any of the cardinal virtues has today
all the exhilaration of a vice." -
G.K.Chesterton: A Defense of Humilities, The Defendant, 1901
                           www.chesterton.org/acs/quotes.htm


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