Here's the mentioned excerpt from KEI's Concrete
Mathhematics Companion, Ch 0 "Notation":
"
.....
a=: 0 1 2 3 4
The copula =: assigns a name to any entity
.....
We conclude these samples of notation with the
tie conjunction (`) that applies to verbs
to produce a gerund (a noun that carries the
force of a verb), and the agenda (@.) that
selects for action one of the verbs that comprise a gerund:
+`* / a
14
0+1*2+3*4
14
Unparenthesized sentences are executed from right
to left; there is no hierarchy among functions
0+(1*(2+(3*4)))
14
.....
"
It's a bit hard to decide from this example what
happens as there are two verbs in the gerund,
which itself is repeated twice to fill the four
gaps (as the vector has five elements).
Given the thoroughness Iverson was/is reknowned
for it looks to me that, this being a "left join"
of two patterns didn't occur to him as much of a
problem (sort of natural, coming from a culture
where most people write left-to-right).
Taking the example one step further in defining
] a=. 1 2 3 4 5 6
1 2 3 4 5 6
we get
+`*/ a
95
1+2*3+4*5+6
95
but
1*2+3*4+5*6
104
which clearly indicates a pattern "left join".
Thanks
-M
At 2016-06-14 03:07, you wrote:
Perhaps easier to see with more
formal/expressive verbs: in =. 1 :'[,''
'',u,'' '',]' NB. String to infix
function ('f0'in)`('f1'in)`('f2'in)/ 'abcde'
a f0 b f1 c f2 d f0 e The verbs in the gerund
are arranged from left to right starting at the
beginning of the array, while application (as in
the non-gerund case) proceeds from right to
left. I would avoid calling either of these
things "unrolling" without further explanation
as it's not clear which that would mean. Dan's
example has typos, and his wording is vague
enough that I can't tell whether it is correct.
Marshall On Tue, Jun 14, 2016 at 02:21:37AM
+0000, 'Pascal Jasmin' via Programming wrote: >
+`-/ 1 2 3 > 0 > +`+`-/ 1 2 3 > 6 > > > I call
this as being inserted between items on a right
to left basis. > > 1 + 2 - 3 + 4 > > +`-/ 1 2 3
4 > _4 > +`-/ 1 2 > 3 > > > > ----- Original
Message ----- > From: Dan Bron <[email protected]> > To:
J Programming <[email protected]> >
Sent: Monday, June 13, 2016 9:04 PM > Subject:
Re: [Jprogramming] Am I understanding m/y ? > >
Louis wrote: > > > There was some talk a while
ago about the ambiguity of the dictionary about
the direction of gerund insertion. Reading
through the first pages of Iverson's Concrete
Math Companion, I stumbled on a snippet of J
that dates back to 2002 and was written by
Iverson at the bottom of page 6: > > > >
http://www.jsoftware.com/books/pdf/cmc.pdf
<http://www.jsoftware.com/books/pdf/cmc.pdf> > >
> > According to this source, gerunds do indeed
"unroll" from left to right correctly in the
current implementation. > > > Iâm also on
mobile, so forgive my terse answer and potential
misunderstanding of your question, but
yes: > > > v0`v1`v2`v3/ y > > is
indeed: > >
(_8{y) v2 (_7{y) v3
(_6{y) v0 (_5{y) v1 (_4{y) v2 (_3{y) v1 (_2{y)
v0 _1{y > > That is, the insertion of verbs
starts at the rightmost (last) elements of y,
but the leftmost (first) elements of the gerund
G, where G/y . > > The rationale for this is
left as an exercise for a less lazy respondent
(though the right-to-left nature of insertion in
y should be familiar to veteran Jâers). > >
-Dan > > > >
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