I wrote:
> I found 34 foreigns whose nameclass wasn't verb.
Roger responded:
> All I can say is that you are chasing ghosts.
Everyone needs a hobby.
Anyway, as I said:
> I am intrigued.
An hour of investigation was entertaining and instructive, and cleared up a lot
of the mystery.
First I discovered that most of the extra foreigns were repeats. It turns out
foreigns are cyclical. That is, if there is a
foreign m!:n , then there are an infinite number of such foreigns, with the
relation:
m!:n <==> N!:(n + m -&:(120&*) N)
where N is any scalar integer (except 11 because 11!: is a callback to the
frontend, i.e. in Eric's purview).
For example, the following is a different kind of "foreign family" * :
(,. (5*120) - 120 * ]) i: 5
_5 1200
_4 1080
_3 960
_2 840
_1 720
0 600
1 480
2 360
3 240
4 120
5 0
If used as arguments to !: these foreigns are all identical to 5!:0 . Try
'+'_3!:960 (I should really keep a list of these
things for the inevitable Obfuscated J Competition).
So, 5!:0 accounted for a number of my "illegals" (undocumented foreign[er]s).
Scrubbing those from the list, and armed with the
knowledge of the 120-cycle, I concluded that the rest were also aliases, and
they led me to discover the true culprits, 13!:33
and 13!:34 .
Thanks again to RE Boss' generous donations of old J versions (early xmas!), I
was able to discover that these two foreigns were
introduced in J 601 beta i ** (well, actually, 13!:34 is much older than that,
but it was changed in the ibeta ***).
A directory diff of the two versions and some fiddling led me discover:
(A) 13!:33 is an adverb that produces the function call depth
of its verb argument. Its definition is something like
1 : '1 + L. >^:(1=#) 5!:2 {.;:''u'' ' . Example:
toJ f. 1 : '1 + L. >^:(1=#) 5!:2 {.;:''u'' '
7
toJ f. 13!:33
7
I'd guess this is related to the "recursion limit"
and/or "stack depth" changes introduced in the ibeta.
(B) 13!:34 is an adverb that takes a boolean function
as an argument and derives a dyad which compares
integers. The boolean functions are (almost)
the same as the ones on the b. Voc page:
0 1 *. *: +. +: -. < <: = > >: ~: NB. No 0: 1: x y [ ]
Example:
= 13!:34~ 4
1
~: 13!:34~ 4
0
These results aren't normal booleans in the sense
that their internal data type is 256 . That is,
256=3!:0=13!:34~4 .I didn't investigate these much
further, as 3!:1=13!:34~4 and things like it crash
J. I peeked around a little with 15!:6 and 15!:1
but other than the odd data type, they don't seem
exceptional.
That's my report. Like all ghost hunts, it was a success and a failure. The
ghosts were but smoke and mirrors.
http://dan.bron.us/case-closed.jpg
-Dan
* I had a bug in my !:-seeker that prevented many of these from
showing up in the original list.
** This beta was a big step. It was announced here:
http://www.jsoftware.com/pipermail/beta/2006-February/000565.html
This is the beta that removed the inflection from explicit
arguments, introduced FSM, changed the recursion limit,
decommitted dde, introduced the msg pump, changed box
drawing characters to unicode, and more.
*** Prior to J601 beta i, 13!:34 was a verb . I didn't investigate
too deeply but I discovered:
a) It's been around at least since J4.05a,
the earliest J version I have running.
b) Its ranks were _ 0 0 .
c) The monad always seems to return 0.
But I'm sure there's to it than that
d) The dyad always seems to return its
right argument, the domain of which
is, AFAICT, unrestricted. But the
left argument appears to be some
kind of function code. The only
Non-identity "function" I could discover,
however, was a crash with _1 (13!:34) a:
I have exhausted my curiosity for the day, however. Discovering the purposes
of 13!:34 (both old and new) and divining the
reason foreigns are mod 120 are left as exercises for the (dedicated) reader.
If you're really zealous you could take the
foreign-seeking code I posted, run it under J4, and start discriminating
between between valence and domain errors....
There are always more ghosts.
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