The __ trick is simply that J's 13 : has problems with variables inside conjunctions, so if you replace that part of an expression with an arbitrary constant it can work on the rest of the expression.
The rest of it probably deserves some time spent reading the dictionary page for ^: FYI, -- Raul On Fri, May 10, 2013 at 2:49 AM, Skip Cave <[email protected]> wrote: > Jose, > > That was a great description, showing the steps transforming my explicit > Josephus verb into a full tacit version.Thanks very much! > > I learned several tricks from your explanation, including the 13 : tacit > conversion, though it apparently doesn't always work. How you used infinity > to detect a cap error is still over my head, as is the use of the power > verb, but I will keep studying it. > > This would make a great wiki article entitled "Converting Explicit to Tacit" > > Skip > > On Thu, May 9, 2013 at 5:25 PM, Jose Mario Quintana < > [email protected]> wrote: > >> Skip, I finally was able to take a look at your version. The following >> should be a series of equivalent definitions of your version. I do not code >> explicitly thus the control words are alien to me but they probably are >> correct: >> >> jose1=: 4 : 0 >> k =. y - 1{x NB. k is the number of "kills" >> L =. i. y NB. L is the position list >> whilst. k =. k-1 do. >> L =. (<:0{x) |. L NB. Rotate by the skip number >> L =. }. L NB. Remove the dead index. >> end. >> ) >> >> Substituting L in the first line of the whilst block into the second line, >> >> jose10=: 4 : 0 >> k =. y - 1{x NB. k is the number of "kills" >> L =. i. y NB. L is the position list >> whilst. k =. k-1 do. >> L =. }. (<:0{x) |. L NB. Removing the dead index after rotating by the >> skip number >> end. >> ) >> >> Replacing the whilst by a for form, >> >> jose11=: 4 : 0 >> k =. y - 1{x NB. k is the number of "kills" >> L =. i. y NB. L is the position list >> for. i.k do. >> L =. }. (<:0{x) |. L NB. Removing the dead index after rotating by the >> skip number >> end. >> ) >> >> Eliminating L by reusing y, >> >> jose12=: 4 : 0 >> k =. y - 1{x NB. k is the number of "kills" >> y =. i. y NB. L is the position list >> for. i.k do. >> y =. }. (<:0{x) |. y NB. Removing the dead index after rotating by the >> skip number >> end. >> ) >> >> Finding a tacit form for the for block... >> >> '}. (<:0{x) |. y' (13 :) >> [: }. ] |.~ [: <: 0 { [ >> >> Replacing Caps by Ats because Caps are overused! ;) >> >> }.@:(] |.~ <:@:(0 { [)) >> }.@:(] |.~ <:@:(0 { [)) >> >> Replacing the for form by a power form, >> >> jose13=: 4 : 0 >> k =. y - 1{x >> y =. i. y >> x (}.@:(] |.~ <:@:(0 { [))) ^: k y >> ) >> >> Making a one-liner by substituting k and y in the first and second lines >> into the code of the last line, >> >> jose14=: 'x (}.@:(] |.~ <:@:(0 { [)))^:(y - 1{x) i. y' (4 :) >> >> Trying to find a tacit expression, >> >> 'x (}.@:(] |.~ <:@:(0 { [)))^:(y - 1{x) i. y' (13 :) >> 4 : 'x (}.@:(] |.~ <:@:(0 { [)))^:(y - 1{x) i. y' >> >> No, J is not smart enough; not yet anyway. Replacing (y - 1{x) by __ to >> find the form, >> >> 'x (}.@:(] |.~ <:@:(0 { [)))^:__ i. y' (13 :) >> [ }.@:(] |.~ <:@:(0 { [))^:__ [: i. ] >> >> Replacing the offending Cap, >> >> [ (}.@:(] |.~ <:@:(0 { [))^:__) i.@] >> [ }.@:(] |.~ <:@:(0 { [))^:__ i.@] >> >> Consulting the Dictionary for power... Yes, the gerund form fits the bill! >> >> jose15=. }.@:(] |.~ <:@:(0 { [))^:((] - 1 { [)`(i.@])) >> >> 3 7 (jose1 ; jose15) 10000 >> ┌────────────────────────────────┬────────────────────────────────┐ >> │8922 111 930 2691 3850 6154 6624│8922 111 930 2691 3850 6154 6624│ >> └────────────────────────────────┴────────────────────────────────┘ >> >> They compare as follows, >> >> st=. 7!:2@:] ; 6!:2 >> >> 10 st '3 7 jose1 10000' >> ┌──────┬────────┐ >> │133440│0.100217│ >> └──────┴────────┘ >> 10 st '3 7 jose15 10000' >> ┌──────┬────────┐ >> │263808│0.184226│ >> └──────┴────────┘ >> >> The explicit version is leaner and faster but my attitude is to wait for >> the implementation to catch up (I would not bet on it though). Wait! >> Apparently the issue is more complicated than just explicit versus tacit, >> >> ((<10) (((,@<@]) , st) &> ) (('3 7 ' , ] , ' 10000'"_)each @: ;:)) >> 'jose1 jose10 jose11 jose12 jose13 jose14 jose15' >> ┌────────────────┬──────┬────────┐ >> │3 7 jose1 10000 │133440│0.100398│ >> ├────────────────┼──────┼────────┤ >> │3 7 jose10 10000│199104│0.183993│ >> ├────────────────┼──────┼────────┤ >> │3 7 jose11 10000│265152│0.174459│ >> ├────────────────┼──────┼────────┤ >> │3 7 jose12 10000│265152│0.173494│ >> ├────────────────┼──────┼────────┤ >> │3 7 jose13 10000│265728│0.181894│ >> ├────────────────┼──────┼────────┤ >> │3 7 jose14 10000│265920│0.180529│ >> ├────────────────┼──────┼────────┤ >> │3 7 jose15 10000│263808│0.180721│ >> └────────────────┴──────┴────────┘ >> >> This is puzzling to me; then again, I do not know much (to say the least) >> about the performance of explicit code. >> >> >> -- > Skip Cave > Cave Consulting LLC > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
