Also you can remove ~ and if you use the same A and B but reverse them you get:
A=:<"1 ":":"0>:i.12 B=:;:'am pm' i=: 13 :'x(,~&.>)/y' j=: 13 :'x(,&.>)/y' A j B ┌────┬────┐ │1 am│1 pm│ ├────┼────┤ │2 am│2 pm│ ├────┼────┤ │3 am│3 pm│ ├────┼────┤ │4 am│4 pm│ ├────┼────┤ │5 am│5 pm│ ├────┼────┤ │6 am│6 pm│ ├────┼────┤ │7 am│7 pm│ ├────┼────┤ │8 am│8 pm│ ├────┼────┤ │9 am│9 pm│ ├────┼────┤ │10am│10pm│ ├────┼────┤ │11am│11pm│ ├────┼────┤ │12am│12pm│ └────┴────┘ Linda -----Original Message----- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Linda Alvord Sent: Saturday, April 05, 2014 12:22 PM To: programm...@jsoftware.com Subject: Re: [Jprogramming] I want to understand under Thanks Dan, You got me exactly what I needed. I'm not opposed to i=: ,~&.>/ I just want to explain it. ]A=:<"1 ":":"0>:i.12 ┌──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┐ │1 │2 │3 │4 │5 │6 │7 │8 │9 │10│11│12│ └──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┘ >A 1 2 3 4 5 6 7 8 9 10 11 12 ]B=:;:'am pm' ┌──┬──┐ │am│pm│ └──┴──┘ >B am pm (>B),~>A 1 2 3 4 5 6 7 8 9 10 11 12 am pm <(>B),~>A ┌──┐ │1 │ │2 │ │3 │ │4 │ │5 │ │6 │ │7 │ │8 │ │9 │ │10│ │11│ │12│ │am│ │pm│ └──┘ f =: 13 : '< (>x) ,~ >y' B f A ┌──┐ │1 │ │2 │ │3 │ │4 │ │5 │ │6 │ │7 │ │8 │ │9 │ │10│ │11│ │12│ │am│ │pm│ └──┘ f [: < ([: > [) ,~ [: > ] g=: 13 :'x(f"0)/y' B g A ┌────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┐ │1 am│2 am│3 am│4 am│5 am│6 am│7 am│8 am│9 am│10am│11am│12am│ ├────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤ │1 pm│2 pm│3 pm│4 pm│5 pm│6 pm│7 pm│8 pm│9 pm│10pm│11pm│12pm│ └────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┘ h=: 13 :'x(([: < ([: > [) ,~ [: > ])"0)/y' B h A ┌────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┐ │1 am│2 am│3 am│4 am│5 am│6 am│7 am│8 am│9 am│10am│11am│12am│ ├────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤ │1 pm│2 pm│3 pm│4 pm│5 pm│6 pm│7 pm│8 pm│9 pm│10pm│11pm│12pm│ └────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┘ h ([: < ([: > [) ,~ [: > ])"0/ NB. Here's the definition of Under: NB. As in APL, the right side implies the left side. NB. x u&.v y ↔ vi (v x) u (v y) i=: 13 :'x(,~&.>)/y' B i A ┌────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┬────┐ │1 am│2 am│3 am│4 am│5 am│6 am│7 am│8 am│9 am│10am│11am│12am│ ├────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼────┼────┤ │1 pm│2 pm│3 pm│4 pm│5 pm│6 pm│7 pm│8 pm│9 pm│10pm│11pm│12pm│ └────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┴────┘ (B i A)-:B h A 1 Linda -----Original Message----- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Dan Bron Sent: Friday, April 04, 2014 9:22 AM To: programm...@jsoftware.com Subject: Re: [Jprogramming] I want to understand under Linda, every time you try to use x u&.v y ↔ vi (v x) u (v y) to make a substitution, you must remember to respect rank (I know that one sentence in the definition of &. doesn't say so explicitly, so you must remember for yourself). Open (>) is rank 0, i.e. operates on individual atoms, so somewhere in your replacement you must do likewise. The most straightforward way to say this is just to say it: sh =: 13 : '< (>x) ,~ (>y)' NB. vi (v x) u (v y) h =: 13 : 'x sh"0/ y' NB. g with sh"0 substituted for ,~&.> (B h A) -: (B g A) 1 sh [: < ([: > [) ,~ [: > ] h f. ([: < ([: > [) ,~ [: > ])"0/ Here, it's the isolation of vi (v x) u (v y) and the explicit application of it at "0 (rank zero) that makes the substitution work. Try removing the "0 or embedding sh into h directly (in its x and y form, as opposed to its tacit from) and see what happens. Finally I'll recommend, as I do every time we discuss this, that you step back, try to shelve any preconceptions, and with new eyes, sincerely compare ([: < ([: > [) ,~ [: > ])"0/ with ,~ each/ and perhaps reconsider your position on eliminating conjunctions. If your goal is simplicity, to make J easier to learn for kids, I just can't see how anyone would look at those two expressions and say "whoa, the first one is simpler". -Dan PS: And not to pick nits, but the first sentence contains a conjunction as well (") and not only is it necessary, it's fundamental to the solution. So if we're going to accept ", why not also accept &. and stop worrying? > On Apr 4, 2014, at 2:25 AM, "Linda Alvord" <lindaalv...@verizon.net> wrote: > > Here’s the problem. Hopefully this looks better and fully defines the > problem. > > f=: 13 :' (B=:;:''am pm''),~&.>/A=:<"1 ":":"0>:i.y' > f 12 > ┌────┬────┬────┬────┬────┬────┬────┬── > ──┬────┬────┬────┬────┐ > │1 am│2 am│3 am│4 am│5 am│6 am│7 am│8 am│9 am│10am│11am│12am│ > ├────┼────┼────┼────┼────┼────┼────┼── > ──┼────┼────┼────┼────┤ > │1 pm│2 pm│3 pm│4 pm│5 pm│6 pm│7 pm│8 pm│9 pm│10pm│11pm│12pm│ > └────┴────┴────┴────┴────┴────┴────┴── > ──┴────┴────┴────┴────┘ > A > ┌──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┬──┐ > │1 │2 │3 │4 │5 │6 │7 │8 │9 │10│11│12│ > └──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┴──┘ > B > ┌──┬──┐ > │am│pm│ > └──┴──┘ > g=: 13 :'x(,~&.>)/y' > B g A > ┌────┬────┬────┬────┬────┬────┬────┬── > ──┬────┬────┬────┬────┐ > │1 am│2 am│3 am│4 am│5 am│6 am│7 am│8 am│9 am│10am│11am│12am│ > ├────┼────┼────┼────┼────┼────┼────┼── > ──┼────┼────┼────┼────┤ > │1 pm│2 pm│3 pm│4 pm│5 pm│6 pm│7 pm│8 pm│9 pm│10pm│11pm│12pm│ > └────┴────┴────┴────┴────┴────┴────┴── > ──┴────┴────┴────┴────┘ > g > ,~&.>/ > > NB. x u&.v y ↔ vi (v x) u (v y) Definition of Under > > > I can’t seem to write a simple definition h=: but use the second > definition of under. > > It should have the same result as B g A when you enter B h A > > Linda > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
