A small forest:
5!:4 <'ic'
-- [:
+- ,
│ -- [:
│ +- i:
--+ ------+ -- 9
│ │ L- & -+- o.
│ │
│ +- / --- j.
L----+
│ -- [:
│ +- i:
L-----+ -- 11
L- & -+- o.
5!:4 <'ic2'
-- [:
+- ,
--+ -- / --- j.
│ -- / --- & -+- i:
L- @ -+- +.
5!:4 <'ic4'
-- [:
+- ,
│ -- [:
--+ │ -- i:
│ │ -- @ -+- [
│ │ │
L----+ +- / --- j.
+- / ---+
│ │ -- i:
│ L- @ -+- ]
L- +.
5!:4 <'f'
-- [:
+- ,
│ -- [:
│ │ -- [:
--+ │ ------+- i:
│ │ │ L- [
│ │ │
L----+- / ---+- / --- j.
│ │
│ │ -- [:
│ L-----+- i:
│ L- ]
L- +.
Linda
-----Original Message-----
From: programming-boun...@forums.jsoftware.com
[mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Linda Alvord
Sent: Wednesday, January 23, 2013 2:48 AM
To: programm...@jsoftware.com
Subject: Re: [Jprogramming] [Jprogrammingou Hermitian from triangular
This wasn't easy, but I'm finally peaceful! Thanks to all for your prodding
and coaching.
ic=:[: , ([: i: 9&o.) j./ ([: i: 11&o.)
ic2=:[: ,j./&i:/@+.
ic4=:[: , [: (i:@[ j./ i:@])/ +. NB. Kip
f=: 13 :',([:(([:i:[)j./[:i:])/+.)y'
ic
[: , ([: i: 9&o.) j./ [: i: 11&o.
ic2
[: , j./&i:/@+.
ic4
[: , [: (i:@[ j./ i:@])/ +.
f
[: , [: (([: i: [) j./ [: i: ])/ +.
ic 1j2
_1j_2 _1j_1 _1 _1j1 _1j2 0j_2 0j_1 0 0j1 0j2 1j_2 1j_1 1 1j1 1j2
ic2 1j2
_1j_2 _1j_1 _1 _1j1 _1j2 0j_2 0j_1 0 0j1 0j2 1j_2 1j_1 1 1j1 1j2
ic4 1j2
_1j_2 _1j_1 _1 _1j1 _1j2 0j_2 0j_1 0 0j1 0j2 1j_2 1j_1 1 1j1 1j2
f 1j2
_1j_2 _1j_1 _1 _1j1 _1j2 0j_2 0j_1 0 0j1 0j2 1j_2 1j_1 1 1j1 1j2
Linda
Sent: Tuesday, January 22, 2013 1:56 AM
To: programm...@jsoftware.com
Subject: Re: [Jprogramming] [Jprogrammingou Hermitian from triangular
Linda, here I remove conjunctions @ and & from ic2, leading to ic4 not ic.
Two new @'s creep in but they would be easy to remove!
9!:3 [ 6 NB. fully parenthesized display
ic2
[: , ((((j./)&i:)/)@+.)
ic4 =: [: , [: ((j./)&i:)/ +. NB. remove @
ic4 =: [: , [: (i:@[ j./ i:@])/ +. NB. remove &
ic4 1j2
_1j_2 _1j_1 _1 _1j1 _1j2 0j_2 0j_1 0 0j1 0j2 1j_2 1j_1 1 1j1 1j2
Kip
Sent from my iPad
On Jan 21, 2013, at 9:49 PM, "Linda Alvord" <lindaalv...@verizon.net> wrote:
> It would be most helpful if you would give a sequence of legitimate
> substitutions which can be made in an orderly fashion to work "backwards"
> from ic2 to ic . If you could then go from ic to an explicit
> definition that would be great.
>
> I start with an explicit definition to write statements that work on
> real data. Later it is possible to simplify. When I can't understand
> a terse expression, I need to "work backwards" to make it
> understandable. I try to use definitions for @ and @. and & as
> that makes right to left execution more clear. It is obvious from
> this example that it becomes Important to include rank somehow.
>
> Thanks in advance if you can do this.
>
> Linda
>
> : Monday, January 21, 2013 10:19 PM
> To: programm...@jsoftware.como
> Subject: Re: [Jprogramming] [Jprogrammingou Hermitian from triangular
>
> What would be most helpful
>
> -----Original Message-----
> From: programming-boun...@forums.jsoftware.com
> [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Dan
> Bron
> Sent: Monday, January 21, 2013 2:08 PM
> To: programm...@jsoftware.com
> Subject: Re: [Jprogramming] [Jprogrammingou Hermitian from triangular
>
> 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.htm
> l
>
>
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