On Sat, June 13, 2009 4:28 pm, Lars Hellström wrote: > Here's another question I've encountered while examining how my needs > might be dressed in OM symbols. I think I know the answer already, but > it's still a good starting point for a discussion: This is indeed a good question: see Davenport/Kohlhase in MKM 2009 (early version at http://opus.bath.ac.uk/13079 for one point of view, but there are others, notably the view that the "standard theory" of bing only allows one object for the binding to govern. > Why can binders only take one argument (last child of OMBIND, > which is specified to have exactly three children), when an > application is allowed any number of arguments? > > An elementary case where one might want to do this is that of the > ordinary definite integral > > \int_a^b f(x) \,dx > > which one might expect to encode as something like > > <OMBIND> > <OMS name="naive_integral"/> <!-- role: binder --> > <OMBVAR> <OMV name="x"/> </OMBVAR> > <OMV name="a"/> > <OMV name="b"/> > <OMA> <OMV name="f"/> <OMV name="x"/> </OMA> > </OMBIND> > > were it not for said fact that a binder can (in OM2) only have one > argument, not the three of a, b, and f(x) as needed here. > > There seems to be no technical reason for this restriction, as neither > the XML nor the binary OM encoding need invoke arity to parse a This is correct. Unfortunately (from my pont of view) the abstract description does : see 2.1.3(iv) on page 14. > > If memory serves, relaxations of OMBIND is one (the only?) change to > OM3 that is considered as needed to bring it in line with > Content-MathML3, but I don't know where I might have read that. Perhaps > someone else could elaborate on the current status of that issue? I can't speak on behalf on MathML. > > Now, since previously my informal examples were misunderstood by some, > I suppose I'd better give you my real example this time. My reason to > consider defining a binder in the first place is that I want to encode > Abstract Index Notation expressions > (http://en.wikipedia.org/wiki/Abstract_index_notation), which is an > abstraction of the Einstein notation for tensors -- e.g. I'd better look at this is in more detail before shooting from the hip.
James Davenport Visiting Full Professor, University of Waterloo (and also at the University of Western Ontario) Otherwise: Hebron & Medlock Professor of Information Technology and Chairman, Powerful Computing WP, University of Bath OpenMath Content Dictionary Editor and Programme Chair, OpenMath 2009 IMU Committee on Electronic Information and Communication _______________________________________________ Om mailing list [email protected] http://openmath.org/mailman/listinfo/om
