The partitioning modifiers (u/ u/\ etc.) can create several pleasing
identities that don't hold for cyclic gerunds.
The key insight is that u"n is a partitioning modifier. It is the
simplest one, the one where partition=cell.
This was not understood when J was defined. u"n is defined to do two
things: partitioning and assigning a rank for combining purposes.
The other partitioning modifiers have rank _ . If u"n had been defined
to have combining rank _, symmetry would be preserved.
And, we wouldn't need @: . u@(v"n) would do what @: does now.
OTOH, we would need a new primitive to assign combining rank, for the
cases where that's needed (especially for names).
It goes without saying that no one is suggesting that these changes
should go into the J language.
Henry Rich
On 12/26/2021 4:54 PM, Raul Miller wrote:
On Sun, Dec 26, 2021 at 2:53 PM Henry Rich <[email protected]> wrote:
You meant to use rank 0.
Ah, I see...
Sadly, this defeats the concept of rank, breaking a simple identity
involving rank and functions:
F=:*:`]"0
(F -: F"F) ,~3
0
That problem would go away if the cyclic mechanism had been deployed
on items within the given rank rather than items selected by the rank.
I wish I had noticed this sooner.
But I guess maybe sometimes there just aren't any good options...
Thanks,
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