Dan Bron wrote (inter alia) :
> ... this would be like implementing an array (sequence)
> as a set ...
This struck a bell with me because I have recently published
an essay describing an advanced calculator, which I called
a formulator, in which items of a sequence could be sets
(eprints.utas.edu.au/9474, and I've submitted a follow-up
essay to Vector).
The formulator is a subset of J with modifications. One
major restriction, in the spirit of calculators for general
use, is in not allowing arrays, but I added the idea of sets
as items both to enrich the formulator and to add a kind
of extra dimension to what otherwise only has one.
But, thinking back, enforcing the truth about calculations
that yield more than one answer for an item, for example,
the square root, was perhaps the strongest motivation
(the essay's title is "Truth and breadth, clarity and depth
in algebra").
However, there's a lot of other aspects to the idea. It's
a way of marking empty slots in a sequence. My notation
enclosed sets in parentheses, so () is an empty set.
If brackets were used to enclose intervals (and these would
be valid within a set as well as an item) then it would give
an alternative and arguably more meaningful representation
for complete indeterminacy. Maybe.
In any case, allowing sets as items would allow calculations
to be done in one expression that would otherwise need to
be done in a boringly repetitive way.
Neville Holmes, P.O. Box 2412, Bakery Hill 3354, Victoria
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