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

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