It is explained in the essay
http://www.jsoftware.com/jwiki/Essays/Rank

 The recursively-defined verb s boxr y 
 produces the list of such cells.

The purpose of boxr is to produce the list of
such cells.  What are "such cells"?  The
immediately preceding phrase says:

 r cells y computes the array of cells with 
 shape r fr y , each cell individually boxed 
 and shaped s=: r cs y  (r cells y ↔ <"r y) .

And in the model:

 cells =: fr $ cs boxr ,@]

So r cells y makes an array of the boxed cells 
relative to rank r and boxr makes the list of
"such cells" (r (cs boxr ,@]) y ↔ ,<"r y).

boxr just happens to be recursive.  One of its 
requirements is to avoid overt use of rank.

 boxr  =: ]`(<@$ , [ $: */@[}.])@.([EMAIL PROTECTED]@])



----- Original Message -----
From: Raul Miller <[EMAIL PROTECTED]>
Date: Saturday, June 23, 2007 12:08 pm
Subject: Re: [Jgeneral] Let's get explicit about dyadic verb processing

> On 6/23/07, Roger Hui <[EMAIL PROTECTED]> wrote:
> > Your worksheet uses English prose which is difficult
> > to get precise and correct.  What is needed is an
> > expression of the ideas and rules in an executable
> > notation.  I have just the thing:
> > http://www.jsoftware.com/jwiki/Essays/Rank
> 
> What is the purpose of boxr?  More specifically, why is
> its definition recursive?
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