Kip,
You seem to keep wanting to create new data objects when I do not believe
they are necessary.
In J it is perfectly possible to have a sequence and a set having exactly
the same representation. A lot of set theory is concerned with sequences.
They may be sequences of atoms, or sequences of sets. Having set verbs and
sequence verbs operating on these objects is the direction I would go. That
means of course that the order of items in the list of elements may matter.
At an earlier stage in this discussion you suggested that it would be
difficult to sort elements and test identity in sets of sets if the elements
were not in a standard order.
I think the following function will achieve that by sorting into a J sort
order. That provides a standard form to simplify testing. Raul might
provide a tacit form.
sortSet =: 3 : 0
s =. y
for_k. i. >: L. y do. s =. Set L:k s end.
)
The following gives an example of what it does - you need to copy and
execute it to see its results - my mailer seems to really mishandle boxing.
s1 =: 'bdca'
s2 =: powSet s1
s2a =: 0 13 3 6 {s2
s2b =: 1 13 5 2 {s2
s3a =: 2 5 9 13 { powSet s2a
s3b =: 2 5 9 13 { powSet s2b
sc =: |. s1;s2a;<s3a
sd =: |. s1;s2b;<s3b
sc
sortSet sc
sd
sortSet sd
You can get other results by converting sortSet to a dyadic verb and
specifying the levels at which sorting will be done.
Fraser
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