[R] Molecule-like Notation for Arrays -- anyone interested?

[Hans Ehrbar]

At the APL conference in Berlin on July 24 I am giving a
talk about about a molecule-like notation for arrays for
which some prototype code is available in R.  It is a
graphical notation for arrays of higher rank which makes the
structure of arrays and their various concatenations
intuitively apparent, and which, in my judgment, would make
an excellent interface for array programming languages.  I
originally developed it for teaching, but when I tried to
firm it up mathematically it became clear that there are a
number of fundamental issues involved which I do not have
the time to work through.  Therefore my talk contains the
invitations for others to take this line of research over.
I would like to extent this invitation to this community
here as well.  I think it would be a nice dissertation in
math, perhaps for someone who is interested in category
theory, and I also think an implementation of this would be
an interesting addition for R/S, but of course I am biased.
I apologize for offering up my unfinished business for
others to continue; I am doing it here in the hope that the
work I did put in will somehow benefit the free software
movement.  My talk is available at
http://www.econ.utah.edu/ehrbar/arca.pdf (2.3 Kbytes).

Here is the abstract as it appears at the conference web site
http://stat.cs.tu-berlin.de/APL-Berlin-2000/index.htm :
A graph-theoretical notation for array concatenation
represents arrays as bubbles with arms sticking out, each
arm with a specified number of ``fingers.'' Bubbles with one
arm are vectors, with two arms matrices, etc.  Arrays can
only hold hands, i.e., ``contract'' along a given pair of
arms, if the arms have the same number of fingers.  There are
three array concatenations: outer product, contraction, and
direct sum.  Special arrays are the unit vectors and the
diagonal array, which is the branching point of several
arms.  Outer products and contractions are independent of the
order in which they are performed and distributive with
respect to the direct sum.  Examples are given where this
notation clarifies mathematical proofs.

Hans Ehrbar

-- 
Hans G. Ehrbar   http://www.econ.utah.edu/ehrbar   ehrbar at econ.utah.edu
Economics Department, University of Utah     (801) 581 7797 (my office)
1645 Campus Center Dr., Rm 308               (801) 581 7481 (econ office)
Salt Lake City    UT 84112-9300              (801) 585 5649 (FAX)

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