I am a simple user, you are not only the architect, but also the implementor. 
Most of all I consider J as a mathematical  tool, that's the way I use it 
anyhow, and in mathematics I would immediately define u&.(w`v) as I did. 
What's more, I would extend &, &: en &:. accordingly. 
Just to have a complete and (IMO) elegant language. 

But, as a Dutch poet once wrote (and google translated): "but between dream and 
deed, laws stand in the way, and practical objections."
After all, there is a workaround.


R.E. Boss


-----Original Message-----
From: Programming <[email protected]> On Behalf Of Henry 
Rich
Sent: woensdag 17 november 2021 16:35
To: [email protected]
Subject: Re: [Jprogramming] x u&.(w`v) y

Here's an argument against:

The dual [x] u&.v y says 'apply u, but with a different point of view. First 
transform [x and] y, then apply u, then transform the result back to the 
original point of view.'

The semidual x u&(a:`v) y says 'u&.v, but the point-of-view business applies 
only to y'.  x goes through unchanged.

What you propose puts x and y in different spaces to begin with; presumably w 
and v transform them to a common point of view, but then the result is 
transformed back by  applying BOTH inverses.  I don't see an application for 
this, or an easy verbal description of it.

Henry Rich

On 11/17/2021 10:18 AM, R.E. Boss wrote:
>     *&.(>:`<:)/ i.2 3
> |domain error
> |   *    &.(>:`<:)/i.2 3
>
>     *&.(a:`<:)/ i.2 3
> 1 4 9
>     *&.(a:`<:)&.(>:`a:)/ i.2 3
> 2 6 12
>
> so why not define
> x u&.(w`v) y
>   as
> x u&.(w`a:)&.(a:`v) y
> ?
>
>
> R.E. Boss
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm


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