> For example, what's the difference between
>
> 2 3 <@, 3 4 and 1 2 <@:, 3 4
>
> when the result is the same?
Well... the result is not the same here, because 2 3 is different from 1 2.
That said, <@, produces the same result as <@:, for the same
arguments. The difference between @ and @: would only matter if the
rank of an argument exceeded the rank of the right verb, and that
cannot happen when , is the right verb.
As for
(#~ 5=2#.@:|])z
3 4 5
It would probably be slightly easier to explain with this rephrasing:
(#~ 5=2#.2|])z
3 4 5
The first thing to note is:
2 | z
0 1 0
1 0 1
This sort of result is related to the result you get from z { 1 0 1 0 1 0
z { 1 0 1 0 1 0
1 0 1
0 1 0
1 - 2 | z
1 0 1
0 1 0
The next step, if we are evaluating things in the same order J
evaluates, we have:
2 #. 2 | z
2 5
In other words, each row from our result is now encoded as an integer
(we treat the individual values as bits).
5, in this case corresponds to 1 0 1 as the result of 2 | z which in
turn corresponds to 0 1 0 as the result of 1-2|z
This sort of rephrasing might get a more involved if we started to get
into variable width values for z, but it's not yet clear to me if that
becomes necessary, nor what the patterns would be like if we went
there.
Hopefully that makes sense?
Thanks,
--
Raul
On Sun, Jun 4, 2017 at 11:30 AM, Michael Rice <[email protected]> wrote:
> Two things come to mind: 1) *reductio ad absurdum* and 2) a Dustin Hoffman
> film, wherein he says to a man, "I going to explain something so you'll
> understand it!" and then shoots him.
>
> I already had a function that does what I needed (see below) but was musing
> about left/right parameter style, when one of the parameters remains
> constant and the other changes "functionally" in the program.
>
> Just looking at your first "simplification," I can see I have a lot of
> familiarization work to do. For example, what's the difference between
>
> 2 3 <@, 3 4 and 1 2 <@:, 3 4
>
> when the result is the same?
>
> Must be something subtle.
>
> =================
>
> Note: The moves marked with "<-" are moves to a known solution.
>
>
> NB. 15 position peg solitaire
> NB. The board (position 5 initially vacant)
>
> NB. 0
> NB. 1 2
> NB. 3 4 5
> NB. 6 7 8 9
> NB. 10 11 12 13 14
>
> move_table =: 36 3 $ 0 2 5 5 2 0 0 1 3 3 1 0 1 3 6 6 3 1 1 4 8 8 4 1 2 4
> 7 7 4 2 2 5 9 9 5 2 3 6 10 10 6 3 3 7 12 12 7 3 3 4 5 5 4 3 4 7 11 11 7 4 4
> 8 13 13 8 4 5 8 12 12 8 5 5 9 14 14 9 5 6 7 8 8 7 6 7 8 9 9 8 7 10 11 12 12
> 11 10 11 12 13 13 12 11 12 13 14 14 13 12
> id =: e. i. 15
> flip =: (~: 3 : 'if. ((< & 2) @: #) y do. ({ & id) y else. (+./ @: ({ &
> id)) y end. ')
> legal_moves =: (#~ ((-: & 1 1 0)"1 @: ({~ & move_table)))
> board =: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
> board
> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
> board =: board flip 5
> board
> 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1
> move_table legal_moves board
> 0 2 5 <-
> 3 4 5
> 12 8 5
> 14 9 5
> board =: board flip 0 2 5
> board
> 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1
> move_table legal_moves board
> 3 1 0 <-
> 7 4 2
> 9 5 2
> board =: board flip 3 1 0
> board
> 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1
> move_table legal_moves board
> 8 4 1
> 7 4 2
> 9 5 2
> 10 6 3
> 12 7 3
> 5 4 3 <-
> board =: board flip 5 4 3
> board
> 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1
> move_table legal_moves board
> 6 3 1 <-
> 11 7 4
> 13 8 4
> 12 8 5
> 14 9 5
> board =: board flip 6 3 1
> board
> 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1
> move_table legal_moves board
> 0 1 3 <-
> 12 7 3
> 11 7 4
> 13 8 4
> 12 8 5
> 14 9 5
> 8 7 6
> board =: board flip 0 1 3
> board
> 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1
> move_table legal_moves board
> 11 7 4 <-
> 13 8 4
> 12 8 5
> 14 9 5
> 8 7 6
> board =: board flip 11 7 4
> board
> 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1
> move_table legal_moves board
> 8 4 1
> 3 4 5 <-
> 12 8 5
> 14 9 5
> 9 8 7
> 13 12 11
> board =: board flip 3 4 5
> board
> 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1
> move_table legal_moves board
> 9 5 2 <-
> 13 8 4
> 9 8 7
> 13 12 11
> board =: board flip 9 5 2
> board
> 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1
> move_table legal_moves board
> 13 8 4
> 12 8 5
> 13 12 11 <-
> board =: board flip 13 12 11
> board
> 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1
> move_table legal_moves board
> 10 11 12 <-
> board =: board flip 10 11 12
> board
> 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1
> move_table legal_moves board
> 12 8 5 <-
> board =: board flip 12 8 5
> board
> 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1
> move_table legal_moves board
> 5 2 0
> 2 5 9 <-
> board =: board flip 2 5 9
> board
> 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1
> move_table legal_moves board
> 14 9 5 <-
> board =: board flip 14 9 5
> board
> 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
> move_table legal_moves board
>
>
>
>
> On Sun, Jun 4, 2017 at 10:03 AM, Raul Miller <[email protected]> wrote:
>
>> Like this?
>>
>> (#~ 5=2#.@:|])z
>> 3 4 5
>>
>> --
>> Raul
>>
>>
>> On Sun, Jun 4, 2017 at 9:43 AM, Michael Rice <[email protected]> wrote:
>> > How about
>> > 1 0 1 0 1 0 (#~ ((-: & 0 1 0)"1 @: ({~ & z)))~ z
>> > ?
>> >
>> > Odd, that's the KISS way, the way that always works, and the one way I
>> > hadn't considered.
>> >
>> > On to your "simplifications."
>> >
>> > On Sat, Jun 3, 2017 at 10:16 PM, Louis de Forcrand <[email protected]>
>> wrote:
>> >
>> >> How about
>> >> 1 0 1 0 1 0 (#~ ((-: & 0 1 0)"1 @: ({~ & z)))~ z
>> >> ?
>> >> You can then "simplify":
>> >>
>> >> First the hook (and {~&z)
>> >> ([ #~ -:&0 1 0"1@:(z&{)@])~
>> >> ([ #~ -:&0 1 0"1@:(z&{)@])~
>> >>
>> >> Then ~ can be "distributed" over the resulting fork:
>> >> [~ #~ -:&0 1 0"1@:(z&{)@(]~)
>> >> ] #~ -:&0 1 0"1@:(z&{)@[
>> >>
>> >> You can keep going;
>> >> From bonding to forks:
>> >> ] #~ (] -: 0 1 0"_)"1@:(z { ])@[
>> >> Composition and -: commutativity:
>> >> ] #~ (0 1 0 -: ])"1@:(z { ]@[)
>> >> Because 1=#$0 1 0:
>> >> ] #~ (0 1 0 -:"1 ])@:(z { [)
>> >> Trains:
>> >> ] #~ (0 1 0 -:"1 ]@:(z { [))
>> >> ] #~ 0 1 0 -:"1 ]@:(z { ])
>> >> ] #~ 0 1 0 -:"1 z { [
>> >>
>> >> Can't get it any simpler.
>> >>
>> >> Cheers,
>> >> Louis
>> >>
>> >> > On 4 Jun 2017, at 03:45, Michael Rice <[email protected]> wrote:
>> >> >
>> >> > z (#~ ((-: & 0 1 0)"1 @: ({~ & z))) 1 0 1 0 1 0
>> >>
>> >> ----------------------------------------------------------------------
>> >> 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
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