Your adverb (reduce) reminds me of an old one of mine (seq) [0]. Compare
also yours with the definition of right fold (foldr) [1], and the
corresponding adverb
(fr=. (((&.>)/)(@:([ , <@:])))(>@:)) shown in the Slide 115 of my J
conference 2012 talk [2]:
( X=. 'X' )
X
( Y=. 'Y' )
Y
u=. ('('"_ , [ , ' u '"_ , ] , ')'"_)
X u Y
(X u Y)
( XS=. <;._1 ' X0 X1 .. XN' )
┌──┬──┬──┬──┐
│X0│X1│..│XN│
└──┴──┴──┴──┘
XS u seq Y
(XN u (.. u (X1 u (X0 u Y))))
XS u fr Y
(X0 u (X1 u (.. u (XN u Y))))
XS u (&.> reduce) Y
┌─────────────────────────────┐
│(X0 u (X1 u (.. u (XN u Y))))│
└─────────────────────────────┘
(>XS) u reduce Y
(X0 u (X1 u (.. u (XN u Y))))
(>XS) u (fr ((<"1@:[)`) (`]) (`:6)) Y
(X0 u (X1 u (.. u (XN u Y))))
[0] Jforum: Can all verbs be tacit?
http://www.jsoftware.com/pipermail/general/2001-December/008429.html
[1] Fold (higher-order function)
http://en.wikipedia.org/wiki/Fold_%28higher-order_function%29
[2] Schedule J Conference 2012
http://www.jsoftware.com/jwiki/Community/Conference2012#Schedule
On Mon, Apr 27, 2015 at 10:23 PM, 'Pascal Jasmin' via Programming <
programm...@jsoftware.com> wrote:
> I figured you were generating these from higher level "language". The
> output is a bit hard to digest though.
>
> Do you have a solution for making this tacit? (or version close to it ...
> where items of y and x have different shapes)
>
> reducE =: 1 : (':'; 'o=. x for_i. y do. o =. o u i end.')
>
> I have this similar solution (inverted xy) with boxing:
>
> boxscan =: ((&.>)/)(>@:)
> reduce =: 1 : '<"_1@[ ([: u boxscan ,) <@:]'
>
>
> The list has brought this up before, but is a foreign to do this something
> easy and worthwhile?
>
>
>
> ----- Original Message -----
> From: Jose Mario Quintana <jose.mario.quint...@gmail.com>
> To: Programming forum <programm...@jsoftware.com>
> Cc:
> Sent: Monday, April 27, 2015 7:45 PM
> Subject: Re: [Jprogramming] Permutations with repeats (combinations?)
>
> Right, this is because "I did not make any effort to simplify or to try to
> optimize the tacit verbs" The tools I used to produce the tacit versions
> are meant for general cases (for instance, permitting boxed arguments);
> specific cases can allow for specific simplifications (and optimizations).
> I did not try for three reasons: I wanted to know what would be the penalty
> in performance for the row versions; I wanted to preserve Boss' melodies as
> much as possible; and I was not interested or motivated to make the effort
> to try. Your versions are, literally, very neat particularly when compared
> to those I presented; but, my current interest is in the opposite: how to
> produce effortlessly and generally tacit verbs versions of explicit verbs .
>
>
> Knocking it up another notch: with the aid of my wicked adverb mu and other
> tools, running in a Jx interpreter, it is becoming almost boring for me to
> convert a fairly large class of explicit verbs and I can see already that
> it could be done with even less effort. There is an overhead, which is
> expected, but typically it fades away when the verbs take large amount of
> data (which is key for verb, explicit or tacit, performance anyway). The
> following is an execution of tacit transcriptions that are even more
> closely related to the original explicit versions (the definitions of most
> of these tools are not shown here but I have done so before for many of
> them):
>
> oan=. o (an&>)
>
> set'X Y D K Z'
> 0 1 2 3 4
>
> combt2=. [tv d f.
> '. . .'ln
>
> (K h ([: dd 'i.>:dd' mu oan o (D ff))) o (D h ([: yy xx 'yy - xx' mu oan
> o ((Y,X)ff)))
> Z h ([: dd '(dd$<i.0 0),<i.1 0' mu oan o (D ff))
> Z h ([: kk zz 'kk ,.&.> ,&.>/\. >:&.> zz' mu oan o ((K,Z)ff)) t (X f)
> [: zz '; zz' mu oan o (Z ff)
> )
>
> 2 (combt2 -: comb) 5
> 1
> 100 st&> ' 2 combt2 5' ; ' 2 comb 5'
> ┌───────────┬─────┬──────────────┬───────────┐
> │ 2 combt2 5│16896│0.000263358188│4.44969995 │
> ├───────────┼─────┼──────────────┼───────────┤
> │ 2 comb 5 │12032│2.78562153e_5 │0.335165982│
> └───────────┴─────┴──────────────┴───────────┘
>
> 11 (combt2 -: comb) 17
> 1
> 100 st&> ' 11 combt2 17' ; ' 11 comb 17'
> ┌─────────────┬───────┬─────────────┬──────────┐
> │ 11 combt2 17│5036928│0.00520454777│26214.9324│
> ├─────────────┼───────┼─────────────┼──────────┤
> │ 11 comb 17 │5032064│0.00472455783│23774.2774│
> └─────────────┴───────┴─────────────┴──────────┘
>
>
> set'Y A B C'
> 0 1 2 3
>
> cmbcombt2=. [tv f.
> '. . .'ln o <
>
> A h ([: yy '|.#/.~ yy' mu oan o (Y ff))
> B h ([: aa '|.(] <@combt2"0 +/\) aa' mu oan o (A ff))
> C h ([: bb '; ([:,/ [,"1"1 _1 ]{"1"_ 1 [-.~"1 i.@(+&({:@$)))L:0/ bb' mu
> oan o (B ff))
> [: yy ccc 'yy {~ /:"1 ccc' mu oan o ((Y,C)ff)
> )
>
> (cmbcombt2 -:cmbcomb) 2#>:i.2
> 1
> 10 st&> 'cmbcombt2 2#>:i.2' ; 'cmbcomb 2#>:i.2'
> ┌─────────────────┬─────┬──────────────┬──────────┐
> │cmbcombt2 2#>:i.2│27136│0.000567683124│15.4046493│
> ├─────────────────┼─────┼──────────────┼──────────┤
> │cmbcomb 2#>:i.2 │17152│9.21696831e_5 │1.58089441│
> └─────────────────┴─────┴──────────────┴──────────┘
>
> (cmbcombt2 -:cmbcomb) 2#>:i.5
> 1
> 10 st&> 'cmbcombt2 2#>:i.5' ; 'cmbcomb 2#>:i.5'
> ┌─────────────────┬────────┬────────────┬──────────┐
> │cmbcombt2 2#>:i.5│50343808│0.0685517701│3451157.15│
> ├─────────────────┼────────┼────────────┼──────────┤
> │cmbcomb 2#>:i.5 │50340352│0.0678081433│3413485.8 │
> └─────────────────┴────────┴────────────┴──────────┘
>
> (cmbcombt2 -:cmbcomb) 2#>:i.6
> 1
> 1 st&> 'cmbcombt2 2#>:i.6' ; 'cmbcomb 2#>:i.6'
> ┌─────────────────┬──────────┬──────────┬─────────────┐
> │cmbcombt2 2#>:i.6│3221239680│6.6813202 │2.15221338e10│
> ├─────────────────┼──────────┼──────────┼─────────────┤
> │cmbcomb 2#>:i.6 │3221236224│6.83664885│2.20224609e10│
> └─────────────────┴──────────┴──────────┴─────────────┘
>
> Both, combt2 and cmbcombt2 are tacit; yet, combt2 is fixed but cmbcombt2
> is not completely fixed because combt2 appears in ([: aa '|.(] <@combt2"0
> +/\) aa' mu) and it is not resolved. Nevertheless, a complete fixed
> version can be produced with little additional effort. This verb
> (cmbcombt2f) exhibits even more overhead but, again, it fades away as the
> amounts of data increase:
>
>
> (cmbcombt2f -:cmbcomb) 2#>:i.2
> 1
> 10 st&> 'cmbcombt2f 2#>:i.2' ; 'cmbcomb 2#>:i.2'
> ┌──────────────────┬──────┬─────────────┬──────────┐
> │cmbcombt2f 2#>:i.2│399744│0.00108473525│433.616407│
> ├──────────────────┼──────┼─────────────┼──────────┤
> │cmbcomb 2#>:i.2 │17152 │8.74402125e_5│1.49977453│
> └──────────────────┴──────┴─────────────┴──────────┘
>
> (cmbcombt2f -:cmbcomb) 2#>:i.5
> 1
> 10 st&> 'cmbcombt2f 2#>:i.5' ; 'cmbcomb 2#>:i.5'
> ┌──────────────────┬────────┬────────────┬──────────┐
> │cmbcombt2f 2#>:i.5│50343808│0.0689236018│3469876.58│
> ├──────────────────┼────────┼────────────┼──────────┤
> │cmbcomb 2#>:i.5 │50340352│0.0676761215│3406839.78│
> └──────────────────┴────────┴────────────┴──────────┘
>
> (cmbcombt2f -:cmbcomb) 2#>:i.6
> 1
> 1 st&> 'cmbcombt2f 2#>:i.6' ; 'cmbcomb 2#>:i.6'
> ┌──────────────────┬──────────┬──────────┬─────────────┐
> │cmbcombt2f 2#>:i.6│3221239680│6.62842712│2.13517525e10│
> ├──────────────────┼──────────┼──────────┼─────────────┤
> │cmbcomb 2#>:i.6 │3221236224│6.71277742│2.16234418e10│
> └──────────────────┴──────────┴──────────┴─────────────┘
>
>
>
>
> On Mon, Apr 27, 2015 at 1:12 AM, 'Pascal Jasmin' via Programming <
> programm...@jsoftware.com> wrote:
>
> > Here is a more literal tacit translation of comb. I'm not doing
> > everything you are, but unsure why its needed. IIUC, your version puts
> > everything on the right hand side of ^:
> >
> > combT =: ([: ; ([ ; [: i.@>: -~) ((1 {:: [) ,.&.> [: ,&.>/\.
> > >:&.>@:])^:(0 {:: [) (<i.1 0),~ (< i.0 0) $~ -~)
> >
> > 100 timespacex&> ' 2 combT 5' ; ' 2 combt 5'
> > 1.91616e_5 5888
> > 3.6608e_5 9088
> >
> >
> > 100 timespacex&> ' 11 combT 17' ; ' 11 combt 17'
> > 0.00314064 4.13094e6
> > 0.00317854 4.13414e6
> >
> >
> >
> > Then there is a pretty direct mapping of RE Boss's version as it doesn't
> > repeat intermediate variable use.
> >
> >
> > cmbcombT =: ({~ [: /:"1 [: ; [: ([:,/ [,"1"1 _1 ]{"1"_ 1 [-.~"1 i.@
> (+&({:@$)))L:0/
> > [: |.@:(] <@combT f."0 +/\) [: |. #/.~)
> >
> > 10 timespacex&> 'cmbcomb 2#>:i.5' ; 'cmbcombT 2#>:i.5'
> > 0.0584915 5.03404e7
> > 0.0580249 3.38226e7
> >
> >
> > ----- Original Message -----
> > From: Jose Mario Quintana <jose.mario.quint...@gmail.com>
> > To: Programming forum <programm...@jsoftware.com>
> > Cc:
> > Sent: Sunday, April 26, 2015 9:55 PM
> >
> > Subject: Re: [Jprogramming] Permutations with repeats (combinations?)
> >
> > Tacit vs. explicit seems to be a never-ending controversy. May as it be,
> > the following is a brute force transcription of Boss' compositions for a
> > tacit interpretation:
> >
> > st=. (, */&.:>@:(1 2&{))@:(] ; 7!:2@:] ; 6!:2)
> >
> > ". noun define -. CRLF
> >
> > combt=.
> >
> > ;@:(4&({::))@:((<@:((3&({::) ([ ,.&.> ,&.>/\.@:(>:&.>@:])) 4&({::)
> > )@:]) 4} ])^:(0&({::)))@:(<@:((<i.1 0) ,~ (<i.0 0) $~ 2&({::)) 4}
> > ])@:(<@:(i.@:>:@:(2&({::))) 3} ])@:(<@:(1&({::) - 0&({::)) 2} ])@:
> > ('. . .'&(] , ;:@:[))@:(,&:>/@:(<^:(L. = 0:)&.>))@:(,&<)
> >
> > )
> >
> >
> > 2 (comb -: combt) 5
> > 1
> >
> > 100 st&> ' 2 comb 5' ; ' 2 combt 5'
> > ┌───────────┬─────┬──────────┬────────┐
> > │ 2 comb 5 │12032│6.24855e_5│0.751825│
> > ├───────────┼─────┼──────────┼────────┤
> > │ 2 combt 5│9088 │9.51077e_5│0.864338│
> > └───────────┴─────┴──────────┴────────┘
> >
> > 11 (comb -: combt) 17
> > 1
> > 100 st&> ' 11 comb 17' ; ' 11 combt 17'
> > ┌─────────────┬───────┬──────────┬───────┐
> > │ 11 comb 17 │5032064│0.0107722 │54206.5│
> > ├─────────────┼───────┼──────────┼───────┤
> > │ 11 combt 17│4134144│0.00735863│30421.6│
> > └─────────────┴───────┴──────────┴───────┘
> >
> >
> > ". noun define -. CRLF
> >
> > cmbcombt=.
> >
> > (0&({::) {~ /:"1@:(3&({::)))@:(<@:(;@:(,/@:([ ,"1"1 _1 ] {"1"_ 1 [
> > -.~"1 i.@(+&({:@$)))L:0/)@:(2&({::))) 3} ])@:(<@:(|.@:(] <@(;@:(4
> > &({::))@:((<@:((3&({::) ([ ,.&.> ,&.>/\.@:(>:&.>@:])) 4&({::))@:])
> > 4} ])^:(0&({::)))@:(<@:((<i.1 0) ,~ (<i.0 0) $~ 2&({::)) 4} ])@:(
> > <@:(i.@:>:@:(2&({::))) 3} ])@:(<@:(1&({::) - 0&({::)) 2} ])@:('. .
> > .'&(] , ;:@:[))@:(,&:>/@:(<^:(L. = 0:)&.>))@:(,&<))"0 +/\)@:(1&({
> > ::))) 2} ])@:(<@:(|.@:(#/.~)@:(0&({::))) 1} ])@:('. . .'&(] , ;:@:
> > [)@:<)
> >
> >
> > )
> >
> >
> >
> > (cmbcomb -:cmbcombt) 2#>:i.5
> > 1
> > 10 st&> 'cmbcomb 2#>:i.5' ; 'cmbcombt 2#>:i.5'
> > ┌────────────────┬────────┬────────┬─────────┐
> > │cmbcomb 2#>:i.5 │50340352│0.139288│7.0118e6 │
> > ├────────────────┼────────┼────────┼─────────┤
> > │cmbcombt 2#>:i.5│50339072│0.157125│7.90951e6│
> > └────────────────┴────────┴────────┴─────────┘
> >
> > (cmbcomb -:cmbcombt) 2#>:i.6
> > 1
> > 1 st&> 'cmbcomb 2#>:i.6' ; 'cmbcombt 2#>:i.6'
> > ┌────────────────┬──────────┬───────┬──────────┐
> > │cmbcomb 2#>:i.6 │3221236224│10.6752│3.43873e10│
> > ├────────────────┼──────────┼───────┼──────────┤
> > │cmbcombt 2#>:i.6│3221234944│11.2508│3.62415e10│
> > └────────────────┴──────────┴───────┴──────────┘
> >
> > The associated performances are similar. I did not make any effort to
> > simplify or to try to optimize the tacit verbs. Each assignment in the
> > original explicit constructions corresponds to a form (<@:v N} ]) in the
> > tacit versions with the following mappings,
> >
> > comb: x y d k z -> 0 1 2 3 4
> > cmbcomb: y a b c -> 0 1 2 3
> >
> > Needless to say, combt is embedded in cmbcombt.
> >
> >
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
>
> ----- Original Message -----
> From: Jose Mario Quintana <jose.mario.quint...@gmail.com>
> To: Programming forum <programm...@jsoftware.com>
> Cc:
> Sent: Monday, April 27, 2015 7:45 PM
> Subject: Re: [Jprogramming] Permutations with repeats (combinations?)
>
> Right, this is because "I did not make any effort to simplify or to try to
> optimize the tacit verbs" The tools I used to produce the tacit versions
> are meant for general cases (for instance, permitting boxed arguments);
> specific cases can allow for specific simplifications (and optimizations).
> I did not try for three reasons: I wanted to know what would be the penalty
> in performance for the row versions; I wanted to preserve Boss' melodies as
> much as possible; and I was not interested or motivated to make the effort
> to try. Your versions are, literally, very neat particularly when compared
> to those I presented; but, my current interest is in the opposite: how to
> produce effortlessly and generally tacit verbs versions of explicit verbs .
>
>
> Knocking it up another notch: with the aid of my wicked adverb mu and other
> tools, running in a Jx interpreter, it is becoming almost boring for me to
> convert a fairly large class of explicit verbs and I can see already that
> it could be done with even less effort. There is an overhead, which is
> expected, but typically it fades away when the verbs take large amount of
> data (which is key for verb, explicit or tacit, performance anyway). The
> following is an execution of tacit transcriptions that are even more
> closely related to the original explicit versions (the definitions of most
> of these tools are not shown here but I have done so before for many of
> them):
>
> oan=. o (an&>)
>
> set'X Y D K Z'
> 0 1 2 3 4
>
> combt2=. [tv d f.
> '. . .'ln
>
> (K h ([: dd 'i.>:dd' mu oan o (D ff))) o (D h ([: yy xx 'yy - xx' mu oan
> o ((Y,X)ff)))
> Z h ([: dd '(dd$<i.0 0),<i.1 0' mu oan o (D ff))
> Z h ([: kk zz 'kk ,.&.> ,&.>/\. >:&.> zz' mu oan o ((K,Z)ff)) t (X f)
> [: zz '; zz' mu oan o (Z ff)
> )
>
> 2 (combt2 -: comb) 5
> 1
> 100 st&> ' 2 combt2 5' ; ' 2 comb 5'
> ┌───────────┬─────┬──────────────┬───────────┐
> │ 2 combt2 5│16896│0.000263358188│4.44969995 │
> ├───────────┼─────┼──────────────┼───────────┤
> │ 2 comb 5 │12032│2.78562153e_5 │0.335165982│
> └───────────┴─────┴──────────────┴───────────┘
>
> 11 (combt2 -: comb) 17
> 1
> 100 st&> ' 11 combt2 17' ; ' 11 comb 17'
> ┌─────────────┬───────┬─────────────┬──────────┐
> │ 11 combt2 17│5036928│0.00520454777│26214.9324│
> ├─────────────┼───────┼─────────────┼──────────┤
> │ 11 comb 17 │5032064│0.00472455783│23774.2774│
> └─────────────┴───────┴─────────────┴──────────┘
>
>
> set'Y A B C'
> 0 1 2 3
>
> cmbcombt2=. [tv f.
> '. . .'ln o <
>
> A h ([: yy '|.#/.~ yy' mu oan o (Y ff))
> B h ([: aa '|.(] <@combt2"0 +/\) aa' mu oan o (A ff))
> C h ([: bb '; ([:,/ [,"1"1 _1 ]{"1"_ 1 [-.~"1 i.@(+&({:@$)))L:0/ bb' mu
> oan o (B ff))
> [: yy ccc 'yy {~ /:"1 ccc' mu oan o ((Y,C)ff)
> )
>
> (cmbcombt2 -:cmbcomb) 2#>:i.2
> 1
> 10 st&> 'cmbcombt2 2#>:i.2' ; 'cmbcomb 2#>:i.2'
> ┌─────────────────┬─────┬──────────────┬──────────┐
> │cmbcombt2 2#>:i.2│27136│0.000567683124│15.4046493│
> ├─────────────────┼─────┼──────────────┼──────────┤
> │cmbcomb 2#>:i.2 │17152│9.21696831e_5 │1.58089441│
> └─────────────────┴─────┴──────────────┴──────────┘
>
> (cmbcombt2 -:cmbcomb) 2#>:i.5
> 1
> 10 st&> 'cmbcombt2 2#>:i.5' ; 'cmbcomb 2#>:i.5'
> ┌─────────────────┬────────┬────────────┬──────────┐
> │cmbcombt2 2#>:i.5│50343808│0.0685517701│3451157.15│
> ├─────────────────┼────────┼────────────┼──────────┤
> │cmbcomb 2#>:i.5 │50340352│0.0678081433│3413485.8 │
> └─────────────────┴────────┴────────────┴──────────┘
>
> (cmbcombt2 -:cmbcomb) 2#>:i.6
> 1
> 1 st&> 'cmbcombt2 2#>:i.6' ; 'cmbcomb 2#>:i.6'
> ┌─────────────────┬──────────┬──────────┬─────────────┐
> │cmbcombt2 2#>:i.6│3221239680│6.6813202 │2.15221338e10│
> ├─────────────────┼──────────┼──────────┼─────────────┤
> │cmbcomb 2#>:i.6 │3221236224│6.83664885│2.20224609e10│
> └─────────────────┴──────────┴──────────┴─────────────┘
>
> Both, combt2 and cmbcombt2 are tacit; yet, combt2 is fixed but cmbcombt2
> is not completely fixed because combt2 appears in ([: aa '|.(] <@combt2"0
> +/\) aa' mu) and it is not resolved. Nevertheless, a complete fixed
> version can be produced with little additional effort. This verb
> (cmbcombt2f) exhibits even more overhead but, again, it fades away as the
> amounts of data increase:
>
>
> (cmbcombt2f -:cmbcomb) 2#>:i.2
> 1
> 10 st&> 'cmbcombt2f 2#>:i.2' ; 'cmbcomb 2#>:i.2'
> ┌──────────────────┬──────┬─────────────┬──────────┐
> │cmbcombt2f 2#>:i.2│399744│0.00108473525│433.616407│
> ├──────────────────┼──────┼─────────────┼──────────┤
> │cmbcomb 2#>:i.2 │17152 │8.74402125e_5│1.49977453│
> └──────────────────┴──────┴─────────────┴──────────┘
>
> (cmbcombt2f -:cmbcomb) 2#>:i.5
> 1
> 10 st&> 'cmbcombt2f 2#>:i.5' ; 'cmbcomb 2#>:i.5'
> ┌──────────────────┬────────┬────────────┬──────────┐
> │cmbcombt2f 2#>:i.5│50343808│0.0689236018│3469876.58│
> ├──────────────────┼────────┼────────────┼──────────┤
> │cmbcomb 2#>:i.5 │50340352│0.0676761215│3406839.78│
> └──────────────────┴────────┴────────────┴──────────┘
>
> (cmbcombt2f -:cmbcomb) 2#>:i.6
> 1
> 1 st&> 'cmbcombt2f 2#>:i.6' ; 'cmbcomb 2#>:i.6'
> ┌──────────────────┬──────────┬──────────┬─────────────┐
> │cmbcombt2f 2#>:i.6│3221239680│6.62842712│2.13517525e10│
> ├──────────────────┼──────────┼──────────┼─────────────┤
> │cmbcomb 2#>:i.6 │3221236224│6.71277742│2.16234418e10│
> └──────────────────┴──────────┴──────────┴─────────────┘
>
>
>
>
> On Mon, Apr 27, 2015 at 1:12 AM, 'Pascal Jasmin' via Programming <
> programm...@jsoftware.com> wrote:
>
> > Here is a more literal tacit translation of comb. I'm not doing
> > everything you are, but unsure why its needed. IIUC, your version puts
> > everything on the right hand side of ^:
> >
> > combT =: ([: ; ([ ; [: i.@>: -~) ((1 {:: [) ,.&.> [: ,&.>/\.
> > >:&.>@:])^:(0 {:: [) (<i.1 0),~ (< i.0 0) $~ -~)
> >
> > 100 timespacex&> ' 2 combT 5' ; ' 2 combt 5'
> > 1.91616e_5 5888
> > 3.6608e_5 9088
> >
> >
> > 100 timespacex&> ' 11 combT 17' ; ' 11 combt 17'
> > 0.00314064 4.13094e6
> > 0.00317854 4.13414e6
> >
> >
> >
> > Then there is a pretty direct mapping of RE Boss's version as it doesn't
> > repeat intermediate variable use.
> >
> >
> > cmbcombT =: ({~ [: /:"1 [: ; [: ([:,/ [,"1"1 _1 ]{"1"_ 1 [-.~"1 i.@
> (+&({:@$)))L:0/
> > [: |.@:(] <@combT f."0 +/\) [: |. #/.~)
> >
> > 10 timespacex&> 'cmbcomb 2#>:i.5' ; 'cmbcombT 2#>:i.5'
> > 0.0584915 5.03404e7
> > 0.0580249 3.38226e7
> >
> >
> > ----- Original Message -----
> > From: Jose Mario Quintana <jose.mario.quint...@gmail.com>
> > To: Programming forum <programm...@jsoftware.com>
> > Cc:
> > Sent: Sunday, April 26, 2015 9:55 PM
> >
> > Subject: Re: [Jprogramming] Permutations with repeats (combinations?)
> >
> > Tacit vs. explicit seems to be a never-ending controversy. May as it be,
> > the following is a brute force transcription of Boss' compositions for a
> > tacit interpretation:
> >
> > st=. (, */&.:>@:(1 2&{))@:(] ; 7!:2@:] ; 6!:2)
> >
> > ". noun define -. CRLF
> >
> > combt=.
> >
> > ;@:(4&({::))@:((<@:((3&({::) ([ ,.&.> ,&.>/\.@:(>:&.>@:])) 4&({::)
> > )@:]) 4} ])^:(0&({::)))@:(<@:((<i.1 0) ,~ (<i.0 0) $~ 2&({::)) 4}
> > ])@:(<@:(i.@:>:@:(2&({::))) 3} ])@:(<@:(1&({::) - 0&({::)) 2} ])@:
> > ('. . .'&(] , ;:@:[))@:(,&:>/@:(<^:(L. = 0:)&.>))@:(,&<)
> >
> > )
> >
> >
> > 2 (comb -: combt) 5
> > 1
> >
> > 100 st&> ' 2 comb 5' ; ' 2 combt 5'
> > ┌───────────┬─────┬──────────┬────────┐
> > │ 2 comb 5 │12032│6.24855e_5│0.751825│
> > ├───────────┼─────┼──────────┼────────┤
> > │ 2 combt 5│9088 │9.51077e_5│0.864338│
> > └───────────┴─────┴──────────┴────────┘
> >
> > 11 (comb -: combt) 17
> > 1
> > 100 st&> ' 11 comb 17' ; ' 11 combt 17'
> > ┌─────────────┬───────┬──────────┬───────┐
> > │ 11 comb 17 │5032064│0.0107722 │54206.5│
> > ├─────────────┼───────┼──────────┼───────┤
> > │ 11 combt 17│4134144│0.00735863│30421.6│
> > └─────────────┴───────┴──────────┴───────┘
> >
> >
> > ". noun define -. CRLF
> >
> > cmbcombt=.
> >
> > (0&({::) {~ /:"1@:(3&({::)))@:(<@:(;@:(,/@:([ ,"1"1 _1 ] {"1"_ 1 [
> > -.~"1 i.@(+&({:@$)))L:0/)@:(2&({::))) 3} ])@:(<@:(|.@:(] <@(;@:(4
> > &({::))@:((<@:((3&({::) ([ ,.&.> ,&.>/\.@:(>:&.>@:])) 4&({::))@:])
> > 4} ])^:(0&({::)))@:(<@:((<i.1 0) ,~ (<i.0 0) $~ 2&({::)) 4} ])@:(
> > <@:(i.@:>:@:(2&({::))) 3} ])@:(<@:(1&({::) - 0&({::)) 2} ])@:('. .
> > .'&(] , ;:@:[))@:(,&:>/@:(<^:(L. = 0:)&.>))@:(,&<))"0 +/\)@:(1&({
> > ::))) 2} ])@:(<@:(|.@:(#/.~)@:(0&({::))) 1} ])@:('. . .'&(] , ;:@:
> > [)@:<)
> >
> >
> > )
> >
> >
> >
> > (cmbcomb -:cmbcombt) 2#>:i.5
> > 1
> > 10 st&> 'cmbcomb 2#>:i.5' ; 'cmbcombt 2#>:i.5'
> > ┌────────────────┬────────┬────────┬─────────┐
> > │cmbcomb 2#>:i.5 │50340352│0.139288│7.0118e6 │
> > ├────────────────┼────────┼────────┼─────────┤
> > │cmbcombt 2#>:i.5│50339072│0.157125│7.90951e6│
> > └────────────────┴────────┴────────┴─────────┘
> >
> > (cmbcomb -:cmbcombt) 2#>:i.6
> > 1
> > 1 st&> 'cmbcomb 2#>:i.6' ; 'cmbcombt 2#>:i.6'
> > ┌────────────────┬──────────┬───────┬──────────┐
> > │cmbcomb 2#>:i.6 │3221236224│10.6752│3.43873e10│
> > ├────────────────┼──────────┼───────┼──────────┤
> > │cmbcombt 2#>:i.6│3221234944│11.2508│3.62415e10│
> > └────────────────┴──────────┴───────┴──────────┘
> >
> > The associated performances are similar. I did not make any effort to
> > simplify or to try to optimize the tacit verbs. Each assignment in the
> > original explicit constructions corresponds to a form (<@:v N} ]) in the
> > tacit versions with the following mappings,
> >
> > comb: x y d k z -> 0 1 2 3 4
> > cmbcomb: y a b c -> 0 1 2 3
> >
> > Needless to say, combt is embedded in cmbcombt.
> >
> >
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