Linda wrote:
> ic
> [: , ([: i: 9&o.) j./ [: i: 11&o.
> ic2
> [: , j./&i:/@+.
> f
> [: , [: j./&i:/ +.
> g
> [: j./ [: i: +.
It appears to me that as you move from ic2 to f to g, you are simply
deleting words (the kind that you don't like).
If you go back to the email where ic2 was developed from ic, you'll see that
each of the words in ic2 was introduced deliberately, and none of the words
is superfluous. In fact, it was the very words you arbitrarily deleted
which the email specifically introduced in order to simplify ic to ic2,
without losing functionality. So, if you want to remove those words, you
must do it carefully. In fact, if you take care to do this properly, and
gradually expand the definition of ic2 until it has your preferred,
conjunction-free form, the result will be ic! In effect, you'll end up
working through the ic->ic2 transformation backwards.
You can't have it both ways: the ic2 form is simpler and cleaner, but
requires you to use conjunctions. The ic form is composed solely of verb
trains, but is not as concise, and can't be read left-to-right or executed
right-to-left. That was the point of my original post: that conjunctions
have their benefits, and perhaps it's worth reconsidering your aversion to
them.
Anyway, arbitrarily deleting words you don't like is akin to translating a
sentence from Chinese to English by transliterating the words you know, and
simply ignoring the ones that you don't (or don't have a simple, direct
translation). That won't work.
And, while it is good that you tested your changes along the way, given the
verbs' infinite domain, no amount of tests will ever prove their
correctness. As you discovered, it only takes one counterexample to destroy
the equivalence. You need to bring some theory to the table.
Let me give you an example. If you look at ic, Kip's original:
13 : ',(i: 9 o. y) j./ i: 11 o. y'
[: , ([: i: 9 o. ]) j./ [: i: 11 o. ]
It's quite clear - even just visually - that his j./ has two arguments: one
on the left, and one on the right. Whereas, if you look at your g:
13 :'j./ i:+.y'
[: j./ [: i: +.
it's evident that your j./ only has one argument, on the right. So g can't
be doing the same thing as ic (or, by implication, ic2).
This is the kind of analysis you need to do if you want to simplify J verbs
or phrases. You can't just randomly delete words you don't like. But
moreover, it may be worth your while to reconsider eschewing these words in
the first place. I noticed you picked up on ic2, rather than ic, to use as a
basis for your own approach, even though the former is conjunction-rich and
the latter conjunction-free. And furthermore, while you deleted the / that
followed i:, you retained the / following j. - apparently because you
thought it expressed some concept clearly.
-Dan
PS:
Linda also wrote:
> However, I do not understand how ic and ic2 agree when they don't!
In fact, they do. If you want to understand how, then [1] walks through
that in some detail.
This is despite the observation Raul made earlier:
> I will agree that they do not agree [at rank 1 and higher]
Which was specifically called out in the original email:
> NB. But...
> (ic2 -: ic) 1 2 1j2 0j2
> 0
>
> NB. When we move beyond the original scope of a single,
> NB. scalar input the answers differ. What gives?
> NB. Left as an exercise for the reader.
And in the follow-ups, e.g. from Kip:
> About your closing question, consider
> (ic2"0 -: ic"0) 1 2 1j2 0j2
> 1
>
> Monadic i: has rank 0 and for reasonable behavior
> I think ic and ic2 should be used with rank 0 on vector arguments.
[1] Development of ic2 from ic:
http://www.jsoftware.com/pipermail/programming/2013-January/031131.html
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