You didn’t say that explicitly, but the only “statefulness” which I saw required changing the definitions associated with names. And the only way to avoid that kind of change is with tacit code.
Or did I overlook something important? Thanks, — Raul On Wednesday, November 28, 2018, <[email protected]> wrote: > I do not recall saying that tacitness was a requirement. > > Sent from my iPhone > > > On Nov 28, 2018, at 6:23 PM, Raul Miller <[email protected]> wrote: > > > > Hmm.. > > > > When I look at explanations of the Y combinator, I don't see any > > requirement that the implementations must be tacit. For example: > > https://en.wikipedia.org/wiki/Fixed-point_combinator#Fixed_ > point_combinators_in_lambda_calculus > > > > Instead, I see an entirely symbolic representations (where, granted, > > the symbols are eventually intended to refer to implementations). > > > > Put different: the use of references to memory which is not intended > > to be changed is not usually thought of as "state" even though that > > memory could be changed. > > > > That said, I will agree that it's possible to think of all memory as > > "state". I think this would mean that only logic implemented purely in > > hardware is "not state". > > > > That said, I will also agree that within a J environment, you aren't > > going to be able to changed unnamed function implementations while > > they're running without cheating (or, perhaps, being cheated). So, ... > > there's that. > > > > Thanks, > > > > -- > > Raul > > > > On Wed, Nov 28, 2018 at 5:38 PM Jose Mario Quintana > > <[email protected]> wrote: > >> > >>> [Aside: if I remember right, you wrote the tacit version there at > rosetta > >> code?] > >> > >> That is right. > >> > >>> After sleeping on this thread for a few days, I've finally realized > >>> that I don't have any idea what you mean by "ad hoc encodings". > >>> > >>> If you have time for some questions: What does "ad hoc encodings" > >>> mean? Is that a good thing or a bad thing? Why? > >> > >> As far as I can see, when the argument of Y, the higher-order function, > for > >> which the product of Y is a fixed-point, is represented by means of > >> standard code associated with recursions in J then one can produce > >> relatively simple versions of Y which are, as much as possible (given > the > >> lack of direct support of higher-order functions as arguments by the > >> current official interpreters), in compliance with the specifications of > >> the Rosetta Code (RC) task. > >> > >> (Beware of line-wrapping) > >> > >> As an illustration, this is a comparison between the slightly revised > >> version of my non-tacit version of the Y combinator for monadic > recursions, > >> > >> X=. 1 :'<(<,'':''),<(<1;~":0),<(":0);,(''u > u`:6('',(5!:5<''u''),'')`:6 > >> y'')'(1 :'u u`:6') > >> > >> renamed as X to be able to distinguish it from the explicit version of > Y in > >> the RC entry, > >> > >> Explicit alternate implementation > >> > >> https://rosettacode.org/wiki/Y_combinator#Explicit_ > alternate_implementation > >> > >> (which I suppose you wrote). > >> > >> Using recursive computations of factorials as an example, > >> > >> M=. 1 :'1:`(* u@:<:)@.*' > >> M=. (5!:1)<'M' > >> > >> Due to J`s aforementioned limitation, it is unavoidable the use of a > >> representation of the adverb (i.e., the higher-order function), the AR > of > >> the adverb (M) is chosen as the argument for X, > >> > >> M X ("0) i.11 > >> 1 1 2 6 24 120 720 5040 40320 362880 3628800 > >> > >> This argument is closely related to usual ways to define recursive > verbs, > >> > >> ( $:M`:6) ("0) i.11 > >> 1 1 2 6 24 120 720 5040 40320 362880 3628800 > >> (f=. f M`:6) ("0) i.11 > >> 1 1 2 6 24 120 720 5040 40320 362880 3628800 > >> > >> or, more generaly, > >> > >> (f=. 3 :'f M`:6 y')("0) i.11 > >> 1 1 2 6 24 120 720 5040 40320 362880 3628800 > >> > >> M=. 1 :'if. * y do. y * u <: y else. 1 end.' > >> M=. (5!:1)<'M' > >> > >> (f=. 3 :'f M`:6 y')("0) i.11 > >> 1 1 2 6 24 120 720 5040 40320 362880 3628800 > >> > >> In contrast, Y (as per the explicit RC J entry) is a noun (and a gerund) > >> and by itself does not produce anything, > >> > >> wrap=. _66 [\ (5!:5)@:< > >> > >> wrap'Y' > >> ,<(<,':'),<(<(,'0');3),<(,'0');3 21$'g=.y recur= > >> . sivelY`:6 g recur`:6 recur ' > >> > >> Not surprisingly, the argument for Y Ev (Ev is a name referring to `:6) > is > >> also a noun (and a gerund) and by itself does not produce anything > either, > >> > >> wrap'almost_factorial' > >> ,<(<(<,':'),<(<(,'0');2),<(,'0');5 26$' if. (_1 {:: m) <: #m do. > >> v |. y;_1 }. m else. (y;m) Defer > >> v`'''' end. '),<(<(<,'0'),<,<2),<(<,':' > >> ),<(<(,'0');3),<(,'0');3 25$'''f n''=.y if. 0 >: > >> n do. 1 else. n * f`:6 n-1 end.' > >> > >> and, it seems, its particular purpose is to be used as an argument for > (Y > >> Ev). > >> > >> On the one hand, regarding the recursive verbs produced by each of the > >> combinators, > >> > >> v=. (Y Ev almost_factorial)Ev > >> > >> is a verb, > >> > >> wrap'v' > >> ((<,<(<(<,':'),<(<(,'0');2),<(,'0');5 26$' if. (_1 {:: m) <: #m d > >> o. v |. y;_1 }. m else. (y;m) De > >> fer v`'''' end. '),<(<(<,'0'),<(<,<(<(<, > >> ':'),<(<(,'0');2),<(,'0');5 26$' if. (_1 {:: m) <: #m do. v |. > >> y;_1 }. m else. (y;m) Defer v`'''' > >> end. '),<(<(<,'0'),<,<2),<(<,':'),<(<(, > >> '0');3),<(,'0');3 25$'''f n''=.y if. 0 >: n do. > >> 1 else. n * f`:6 n-1 end.'),<2),<(<,':'),<(<(,'0');3),<(,' > >> 0');2 29$'''g recur''=.y (recursivelY`:6 g)`:6 r > >> ecur'),(<,<(<(<,':'),<(<(,'0');2),<(,'0');5 26$' if. (_1 {:: m) < > >> : #m do. v |. y;_1 }. m else. (y > >> ;m) Defer v`'''' end. '),<(<(<,'0'),<,<2 > >> ),<(<,':'),<(<(,'0');3),<(,'0');3 25$'''f n''=.y > >> if. 0 >: n do. 1 else. n * f`:6 n-1 end.'),<3) (2 : 0) (3 > >> : 0) > >> 'g recur x'=.y > >> (g`:6 recur`:6 recur)`:6 x > >> ) > >> > >> if. (_1 {:: m) <: #m do. > >> v |. y;_1 }. m > >> else. > >> > >> (y;m) Defer v`'' > >> end. > >> > >> ) > >> > >> and this linear representation of (Y Ev almost_factorial)Ev is > incomplete; > >> in other words, the verb produced is not stateless and consequently it > is > >> vulnerable to reassignments, > >> > >> (Y Ev almost_fibonacci)Ev ("0) i. 11 > >> 0 1 1 2 3 5 8 13 21 34 55 > >> > >> Defer=. 1 > >> > >> (Y Ev almost_fibonacci)Ev ("0) i. 11 > >> |syntax error > >> | (y;m)Defer v`'' > >> > >> Thus, the explicit entry in RC is not an implementation of the Y > combinator > >> complying with the specifications. > >> > >> On the other hand, the verb produced by M X is stateless and relatively > >> very simple, > >> > >> u=. M X > >> wrap'u' > >> <(<,':'),<(<(,'0');1),<<;._1 '|0|u u`:6(<(<,'':''),<(<(,''0'');1), > >> <(,''0'');,:''if. * y do. y * u <: y else. 1 end.'')`:6 y' (1 : 'u > >> u`:6(<(<,'':''),<(<(,''0'');1),<(,''0'');,:''if. * y do. y * u <: > >> y else. 1 end.'')`:6 y') > >> > >> Furthermore, according to the interpreter (Y Ev almost_factorial)Ev > seems > >> to be doing a lot of unnecessary stuff vs M X for the task at hand, > >> > >> stp=. ] (([ ((<;._1 '|Sentence|Space|Time|Space * Time') , (, > */&.:>@:(1 > >> 2&{))@:(] ; 7!:2@:] ; 6!:2)&>) (10{a.) -.&a:@:(<;._2@,~) ]) [ (0 0 $ > >> 13!:8^:((0 e. ])`(12"_)))@:(2 -:/\ ])@:(".&.>)@:((10{a.) -.&a:@:(<;._2@ > ,~) > >> ]) ::(0 0&$@(1!:2&2)@:('Mismatch!'"_))) ".@:('0( : 0)'"_) > >> > >> stp 11 > >> (Y Ev almost_factorial)Ev("0) i.11 > >> M X ("0) i.11 > >> ) > >> ┌──────────────────────────────────┬───────┬──────────┬────────────┐ > >> │Sentence │Space │Time │Space * Time│ > >> ├──────────────────────────────────┼───────┼──────────┼────────────┤ > >> │(Y Ev almost_factorial)Ev("0) i.11│1242368│0.0142416 │17693.3 │ > >> ├──────────────────────────────────┼───────┼──────────┼────────────┤ > >> │M X ("0) i.11│250304 │0.00179289│448.768 │ > >> └──────────────────────────────────┴───────┴──────────┴────────────┘ > >> > >> I hope it helps > >> > >> > >> On Mon, Nov 19, 2018 at 7:11 PM Jose Mario Quintana < > >> [email protected]> wrote: > >> > >>> I am on vacation this week. I will have more time (and access to a PC) > >>> when I get back. > >>> > >>>> On Monday, November 19, 2018, Raul Miller <[email protected]> > wrote: > >>>> > >>>> [Aside: if I remember right, you wrote the tacit version there at > rosetta > >>>> code?] > >>>> > >>>> After sleeping on this thread for a few days, I've finally realized > >>>> that I don't have any idea what you mean by "ad hoc encodings". > >>>> > >>>> If you have time for some questions: What does "ad hoc encodings" > >>>> mean? Is that a good thing or a bad thing? Why? > >>>> > >>>> Thanks, > >>>> > >>>> -- > >>>> Raul > >>>> > >>>> > >>>> > >> ---------------------------------------------------------------------- > >> 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
