(0$0) u y and x u (0$0) ARE defined, but it's not
what you think.

For the atomic verbs (of which + is one), the 
shape of the result is the shape of the argument
with greater rank.  When one argument is an atom,
that is, has rank 0, the smallest possible rank,
then the shape of the result is necessarily the
shape of the other argument.  



----- Original Message -----
From: Pascal Jasmin <[EMAIL PROTECTED]>
Date: Sunday, October 22, 2006 7:59 am
Subject: [Jprogramming] Dyads and identity function

> At the bottom of this essay, there is discussion about identity 
> functions and how they interact with the / adverb.
> http://www.jsoftware.com/jwiki/PascalJasmin/nil_and_empty_in_J
> 
> 
>   +/ (i.0) , i.0
> 0
>   */ (i.0) , i.0
> 1
>    (+/ (i.0) , i.0) -: +/ i.0
> 1
> 
> if u/ 0$0 is defined, then so should (0$0) u y or x u 0$0 or (0$0) 
> u 0$0.
> the equivalent definitions are: (u/ (0$0)) u y  and x u u/ 0$0 and 
> (u/ 0$0) u u/ 0$0
> 
> currently x + empty returns empty:
>   $ 3 + i.0
> 0
>   +/ 3
> 3
> 
> which doesn't make sense if an identity function has been defined 
> for +


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