I'm not sure gerunds are defined anywhere. 

But if they were, the phrasing might be "arrays of atomic representations", 
where the "atomic representation" characteristic is the most salient, and 
"array" has the normal meaning (and perhaps the usual question of whether a 
scalar is an array?).  

We often (informally) think of gerunds as vectors, because we compose them with 
` whose product is defined to be vector, and consume them with e.g. @. whose 
(left input) is most useful when vector.  But that's no reason to define 
gerunds as vectors, any more than to define selections as vectors, because we 
compose them with  ,  , and consume them with e.g. { whose (left input) is 
frequently vector. Or saying 'string' is a string but 's' is not.

Of course, in some contexts, 's' is not considered a string.  So perhaps you 
are suggesting that "gerunds are are arrays of atomic representations, where 
the shape of the array has meaning"?  If so,  this is an interesting 
digression, which I'm happy to discuss, but perhaps we should move it to a 
different thread.  

The original question was not concerned with gerunds, and I doubt having the 
atomic representation of  f@g  (vector or scalar) in the corner of the result 
table would be satisfying. What was wanted was the string representation (which 
is produced using 5!:5, which operates on scalars, so shape doesn't have 
meaning to it, and neither does atomic representation).

Anyway, when present the promise of J to newcomers, we need to take care not 
obscure the pitfalls.  The literal Jenie (dJinni?) who delivers exactly what 
was asked for is rarely the hero of folklore.  

-Dan

PS:  If we wish to continue the digression, it might be better to start with 
the links below,  better starting point would be wh 

 Here's a couple places where I've attempted to capture the meaning of "gerund"

Sidebar in NuVoc definition of ` :
http://jsoftware.com/jwiki/Vocabulary/backtick#sidebar.3Agerunds

As a necessary premise in the definition of a modifier utility:
www.jsoftware.com/jwiki/DanBron/Snippets/DOOG#definition

Please excuse typos; composed on a handheld device.

-----Original Message-----
From: Raul Miller <rauldmil...@gmail.com>
Sender: programming-boun...@jsoftware.com
Date: Sat, 18 Feb 2012 11:52:13 
To: Programming forum<programming@jsoftware.com>
Reply-To: Programming forum <programming@jsoftware.com>
Subject: Re: [Jprogramming] Verb display in function tables

Ok...

...except that gerunds are defined as vectors.

Conceptually speaking, if it's a scalar, or a matrix, it's something
different.  It would still be gerund-like, in character (we can
trivially extract gerunds from it), but if we try using such things
with primitives that handle gerunds, we are getting into undocumented
territory.

-- 
Raul

On Sat, Feb 18, 2012 at 11:18 AM, Dan Bron <j...@bron.us> wrote:
> That makes sense.
>
> My personal impression was that the original vector-ness was an 
> (unintentional) side-effect of the method used to remove the trailing atom 
> (select-all-but-last as opposed to select-first).
>
> The proposed scalar should be a transparent replacement for the original 
> vector, whose shape wasn't serving a specific purpose (normally, in J, shape 
> carries meaning, and where it doesn't it is misleading: at best superfluous, 
> but often pernicious).
>
>  -Dan
>
>
> Please excuse typos; composed on a handheld device.
>
> -----Original Message-----
> From: Raul Miller <rauldmil...@gmail.com>
> Sender: programming-boun...@jsoftware.com
> Date: Sat, 18 Feb 2012 10:41:56
> To: Programming forum<programming@jsoftware.com>
> Reply-To: Programming forum <programming@jsoftware.com>
> Subject: Re: [Jprogramming] Verb display in function tables
>
> I often do that myself, but in this case, the original phrase was also
> generating a 1 element vector, so I decided that a 1-element vector
> was an appropriate result.
>
> --
> Raul
>
> On Sat, Feb 18, 2012 at 9:48 AM, Dan Bron <j...@bron.us> wrote:
>> Because in many contexts, a scalar is more convenient than a 1-element 
>> vector, I make a habit of tacking on a   {.  as in   {.u`''  .
>>
>> -Dan
>>
>>
>> On Feb 18, 2012, at 9:32 AM, Raul Miller <rauldmil...@gmail.com> wrote:
>>
>>> I would use u`''
>>>
>>>   avg 1 :'u`'''''
>>> +---+
>>> |avg|
>>> +---+
>>>   avg
>>> |value error: avg
>>>
>>> --
>>> Raul
>>>
>>>
>>> On Fri, Feb 17, 2012 at 1:57 PM, Edward Mokurai Cherlin
>>> <moku...@sugarlabs.org> wrote:
>>>> I had thought that I would not be able to get a program to show the
>>>> definition of a function given its name, but I found a kludge for the
>>>> purpose using tie. Now I would like to know whether somebody has a
>>>> direct solution. My application for this capability is a defined
>>>> adverb for producing function tables.
>>>>
>>>>   t=.1 :(':';'2 2$(>1 0#u`u);y;(,.x);x u/ y')
>>>>   l +t l=.i.5
>>>> ┌─┬─────────┐
>>>> │+│0 1 2 3 4│
>>>> ├─┼─────────┤
>>>> │0│0 1 2 3 4│
>>>> │1│1 2 3 4 5│
>>>> │2│2 3 4 5 6│
>>>> │3│3 4 5 6 7│
>>>> │4│4 5 6 7 8│
>>>> └─┴─────────┘
>>>>
>>>> The question then is whether somebody knows a less ugly way to display
>>>> the value of u in executing this adverb than >1 0#u`u or >0{u`u .
>>>>
>>>> --
>>>> Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin
>>>> Silent Thunder is my name, and Children are my nation.
>>>> The Cosmos is my dwelling place, the Truth my destination.
>>>> http://wiki.sugarlabs.org/go/Replacing_Textbooks
>>>> ----------------------------------------------------------------------
>>>> For information about J forums see http://www.jsoftware.com/forums.htm
>>> ----------------------------------------------------------------------
>>> For information about J forums see http://www.jsoftware.com/forums.htm
>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
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