The "Array Thinking" page is at https://code.jsoftware.com/wiki/Array_Thinking but it still needs some work on formatting.
On Sun, Mar 15, 2020 at 12:12 PM Devon McCormick <[email protected]> wrote: > Yes - on the "Array Thinking" page I referred to a similar note you sent a > while back and I quote from the Perlis paper. The explicit reference to > the APL expression on the Ken Iverson page (at > https://en.wikipedia.org/wiki/Kenneth_E._Iverson#/media/File:APLparen.png) > is nice, especially in its similarity to the J version I'm using. > > On Sun, Mar 15, 2020 at 10:49 AM Roger Hui <[email protected]> > wrote: > >> Your one-liner on parentheses nesting has an ancient and honorable >> pedigree. See the Ken Iverson Wikipedia page >> <https://en.wikipedia.org/wiki/Kenneth_E._Iverson> (in the IBM >> (1960-1980) >> section) and the third paragraph of Alan Perlis's "*APL is more French >> than >> English*" <https://www.jsoftware.com/papers/perlis78.htm>. >> >> >> >> On Sun, Mar 15, 2020 at 12:38 AM Devon McCormick <[email protected]> >> wrote: >> >> > There's this (adapted from my new "Array Thinking" page on the J wiki): >> > NB. String from https://wiki.c2.com/?LispShowOffExamples >> > string=. '(flet ((inside-p (obj) (lambda (d) (inside-p obj (ray-point >> > ray d)))))' >> > string,:' '-.~":'()' ([:+/\1 _1 0{~i.) string NB. Example result >> > (flet ((inside-p (obj) (lambda (d) (inside-p obj (ray-point ray d))))) >> > 1111112333333333344443344444444554455555555555555666666666666666654321 >> > NB. Final "1" indicates we are missing a closing paren >> > The one-liner is " '()' ([:+/\1 _1 0{~i.) string"; the bit preceding >> this >> > simply squishes the parentheses' counts to single, text digits so they >> > align character-by-character with the string (won't work if the string >> > presents more than 9 levels of nesting). >> > Also, that "LISP Show-off" page referenced might be a good source of >> > succinct algos amenable to translation into J. >> > >> > Another one I resurrected recently is something I wrote a long time ago >> in >> > APL called "interval sum". Given two two-column tables - "iv0" and >> "iv1" - >> > of start, stop points defining intervals, this expression returns the >> > (#iv0) x #iv1 table of intersections between each interval. This is >> > positive for intervals that overlap, negative for disjunct intervals >> > (measuring the gap between them), and zero for intervals that share only >> > one endpoint. So, for example: >> > >> > (iv0=. 0 5,_1 4,2 3,6 3,5 8,:6 8);iv1=. _1 0,1 3,0 5,_1 8,:9 10 >> > +----+-----+ >> > | 0 5|_1 0| >> > |_1 4| 1 3| >> > | 2 3| 0 5| >> > | 6 3|_1 8| >> > | 5 8| 9 10| >> > | 6 8| | >> > +----+-----+ >> > >> > iv0 (([:|: [:/:~"1 [) (([:|:[ 0}~ [:- 0{[) +/ . <./ ]0}~ [:- 0{]) >> [:|: >> > [:/:~"1 ]) iv1 >> > 0 2 5 5 _4 >> > 1 2 4 5 _5 >> > _2 1 1 1 _6 >> > _3 0 2 3 _3 >> > _5 _2 0 3 _1 >> > _6 _3 _1 2 _1 >> > >> > The following attempts to illustrate how the inner product " +/ . <./ " >> > works. The trick is that we negate the 0th column of each set of >> intervals >> > (after sorting so that the starting point of the interval is less than >> or >> > equal to the ending point) so that the <./ gives us the negative of the >> > larger of the two starting points. I have a marvelous proof of why this >> > works but the margin is too small to contain it*. >> > >> > In any case, we see here the two sets of intervals as shown above but >> with >> > their initial columns negated and the result of the inner product >> > positioned in a way to try to make clear what is happening: >> > +----+-----------------+ >> > ||:iv1| 1 _1 0 1 _9 | >> > |iv0 | 0 3 5 8 10 | >> > +-----+----------------+ >> > | 0 5 | 0 2 5 5 _4 | (0<.1)+(5<.0)=0; (0<._1)+(5<.3)=2; >> > (0<.0)+(5<.5)=5... >> > | 1 4 | 1 2 4 5 _5 | (1<.1)+(4<.0)=1; (1<._1)+(4<.3)=2; >> > (1<.0)+(4<.5)=4... >> > |_2 3 |_2 1 1 1 _6 | >> > |_6 3 |_3 0 2 3 _3 | >> > |_5 8 |_5 _2 0 3 _1 | >> > |_6 8 |_6 _3 _1 2 _1 | >> > +-----+----------------+ >> > >> > *Come to NYCJUG on Tuesday, April 14th to see the proof. >> > >> > >> > >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > > > -- > > Devon McCormick, CFA > > Quantitative Consultant > > -- Devon McCormick, CFA Quantitative Consultant ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
