I have not yet learned Haskell well enough to answer your "something beautiful" question, but I am learning it for work, so I may be able to answer it in the not-too-distant future.
On Fri, May 9, 2014 at 1:35 PM, Roger Hui <[email protected]> wrote: > Yes. You can look at p: as an infinite sequence (series). Also t. and t: > > p: i.10 > 2 3 5 7 11 13 17 19 23 29 > p: 1e6 2e6 3e6 > 15485867 32452867 49979693 > > ^ t. i.10 > 1 1 0.5 0.166667 0.0416667 0.00833333 0.00138889 0.000198413 2.48016e_5 > 2.75573e_6 > ^ t. i.10x > 1 1 1r2 1r6 1r24 1r120 1r720 1r5040 1r40320 1r362880 > > 1&o. t: i.10 > 0 1 0 _1 0 1 0 _1 0 1 > > Can Haskell say this? +/(1+⍳∞)*-s ←→ ×/÷1-(⍭⍳∞)*-s , equivalent to > +/(1+i._)^-s and */%1-(p:i._)^-s, from Bring Something > Beautiful<http://archive.vector.org.uk/art10500390> > . > > > > > On Fri, May 9, 2014 at 10:19 AM, Devon McCormick <[email protected]> > wrote: > > > The Haskell language uses it to allow practical use of infinite series: > > only the necessary values are calculated when items are selected from > such > > a series and this is only done at the time of selection. > > > > This has obvious utility with the potentially very large datasets > generated > > by "catalog" even if they are not infinite. > > > > > > On Fri, May 9, 2014 at 1:06 PM, Roger Hui <[email protected]> > > wrote: > > > > > "Lazy evaluation" ←→ composition with algebraic simplification. > > > > > > > > > On Fri, May 9, 2014 at 10:01 AM, Devon McCormick <[email protected]> > > > wrote: > > > > > > > If there was ever a a candidate for "lazy evaluation", "catalog" > would > > be > > > > it. > > > > > > > > > > > > > > > > On Fri, May 9, 2014 at 1:00 PM, Devon McCormick <[email protected]> > > > > wrote: > > > > > > > > > I've used "catalog" in real-world apps but, as Dan indicates, it > was > > > with > > > > > arguments that gave fairly small results. > > > > > > > > > > > > > > > > > > > > On Thu, May 8, 2014 at 8:30 PM, 'Pascal Jasmin' via Programming < > > > > > [email protected]> wrote: > > > > > > > > > >> > one reason for its rarity is, at least, that in any real-world > > > > context, > > > > >> a complete MxN catalog would be prohibitively expensive > > > > >> > > > > >> its very cheap compared to A. and filtering permutations after > > you've > > > > >> generated them. In the resource matching application I linked to, > > > > where 1 > > > > >> user ends up with 1 resource, its also possible to prefilter the > > > > arguments > > > > >> to catalogue removing options where forced choices exist, and thus > > > > >> significantly reducing an exponential algorithm to allow solutions > > to > > > > >> moderately large problem spaces. > > > > >> > > > > >> Its fast compared to backtracking loop solutions in other > languages > > > even > > > > >> when they abort after finding first valid set of matches. It > seems > > > > like a > > > > >> very clean J way of approaching fairly hard problems. Polynomial > > and > > > > >> higher problems benefit from strategies that reduce search space. > > > > >> > > > > >> Using catalogue to analyze n moves with an average x possibilities > > per > > > > >> move has an expensive x ^ n search space. But reducing any move > > > > >> possibility to 1 reduces both average x, and reduces n by 1 > > > > >> > > > > >> > > > > >> ----- Original Message ----- > > > > >> From: Dan Bron <[email protected]> > > > > >> To: "[email protected]" <[email protected]> > > > > >> Cc: > > > > >> Sent: Thursday, May 8, 2014 6:39:14 PM > > > > >> Subject: Re: [Jprogramming] a cool permutation verb > > > > >> > > > > >> I don't see catalog used frequently in natural J code. It does > come > > up > > > > on > > > > >> these Forums from time to time, mostly in contrived situations. In > > my > > > > own > > > > >> code, I sometimes use it to generate J sentences in order to > compare > > > > >> performance statistics for semantically-equivalent phrases. But > > > outside > > > > of > > > > >> that, I don't see it too often. I suspect one reason for its > rarity > > > is, > > > > at > > > > >> least, that in any real-world context, a complete MxN catalog > would > > be > > > > >> prohibitively expensive. > > > > >> > > > > >> So it's unsurprising that APL didn't have a primitive catalog > > > function. > > > > >> Of course, you could express it as {jot} {dot} {comma}, dot as > being > > > > outer > > > > >> product (and jot in this context a placeholder, not unlike [:) > with > > > the > > > > >> usual caveats about the differences between J's rank and APL's > > > > >> multidimensionality (ie you could expect catalog to work for 1D > > > vectors > > > > in > > > > >> APL and generalized lists in J). > > > > >> > > > > >> So, when he got his chance to "rationalize" APL and rebuild it > from > > > > >> the ground up as J, did Ken have a change of heart about catalog's > > > > >> centrality to the discipline of computer science? Is that why he > > > > assigned > > > > >> to it that scarce and desirable resource, a primitive spelling? A > > > > >> one-character primitive, no less? > > > > >> > > > > >> I suspect not. Recall the other valence of {, to wit: from. You > > might > > > > >> think having this kind of partner is an even greater endorsement > of > > > > >> catalog's virtues ... until you realize: > > > > >> > > > > >> row_2n3n6_col_7n13 =: 2 3 6 ; 7 13 > > > > >> table =: i. 10 20 > > > > >> > > > > >> (< row_2n3n6_col_7n13) { table NB. "from" > > > > >> 47 53 > > > > >> 67 73 > > > > >> 127 133 > > > > >> > > > > >> ({ row_2n3n6_col_7n13) NB. "catalog" > > > > >> +---+----+ > > > > >> |2 7|2 13| > > > > >> +---+----+ > > > > >> |3 7|3 13| > > > > >> +---+----+ > > > > >> |6 7|6 13| > > > > >> +---+----+ > > > > >> > > > > >> ({ row_2n3n6_col_7n13) { table NB. "catalog from" > > > > >> 47 53 > > > > >> 67 73 > > > > >> 127 133 > > > > >> > > > > >> Ah, "from" *is* "catalog". Catalog is a primitive because from > > needed > > > a > > > > >> thematically related definition for monad { (and from, of course, > > > got a > > > > >> precious one-character primitive because it *is* central to array > > > > >> programming). And, incidentally, this is why the results of > catalog > > > are > > > > >> boxed, even though they don't need to be, and we end up writing > >@:{ > > > > >> instead of plain { every time we use it. > > > > >> > > > > >> That is, by definition, the results of { will be homogenous in > both > > > type > > > > >> and shape, and so we know for certain boxes aren't required ... > > except > > > > that > > > > >> dyad { has a scalar left rank, and so to completely address an > atom > > > (or > > > > >> anything more granular than an item, ie a Cartesian point in the > > frame > > > > >> specified as a vector of indices, one per axis), each selection > must > > > be > > > > >> boxed. > > > > >> > > > > >> True story. > > > > >> > > > > >> -Dan > > > > >> > > > > >> > > > > >> > > > > >> Sent from my iPhone > > > > >> > > > > >> > > > > >> > On May 8, 2014, at 5:34 PM, "'Pascal Jasmin' via Programming" < > > > > >> [email protected]> wrote: > > > > >> > > > > > >> > Its the same. Just more descriptive name than catalogue > perhaps. > > > > >> Google seems to only find J references to query "catalogue > function > > > > >> permutations". I feel as though catalogue and my use of it is a > > > > >> generalizable pattern, and the J designers agreed, but I don't > know > > if > > > > >> other languages did something similar, and just used a different > > name? > > > > >> > > > > > >> > Was catalogue in APL? > > > > >> > > > > > >> > > > > > >> > ----- Original Message ----- > > > > >> > From: David Lambert <[email protected]> > > > > >> > To: programming <[email protected]> > > > > >> > Cc: > > > > >> > Sent: Thursday, May 8, 2014 4:50:40 PM > > > > >> > Subject: Re: [Jprogramming] a cool permutation verb > > > > >> > > > > > >> > Indeed cool, does it differ from ,@{ :[: > > > > >> >> Date: Thu, 8 May 2014 10:53:53 -0700 (PDT) > > > > >> >> From: "'Pascal Jasmin' via Programming"< > > [email protected]> > > > > >> >> To: Programming forum<[email protected]> > > > > >> >> Subject: [Jprogramming] a cool permutation verb > > > > >> >> Message-ID: > > > > >> >> < > [email protected]> > > > > >> >> Content-Type: text/plain; charset=utf-8 > > > > >> >> > > > > >> >> cperm =: [: , [: < "1 [: > [: ,"0 1/ each/ (_2&}. , [: ,"0 0/ > > each/ > > > > >> _2&{.) > > > > >> >> > > > > >> >> this creates constrained permutations where each position in > the > > > list > > > > >> can only be drawn from its own set: > > > > >> >> > > > > >> >> ? ?cperm 3 4 ; 1 2 > > > > >> >> ????????????????? > > > > >> >> ?3 1?3 2?4 1?4 2? > > > > >> >> ????????????????? > > > > >> >> > > > > >> >> ? ?cperm 0 ; 3 4 ; 1 2; 5 > > > > >> >> ????????????????????????????????? > > > > >> >> ?0 3 1 5?0 3 2 5?0 4 1 5?0 4 2 5? > > > > >> > > ---------------------------------------------------------------------- > > > > >> For information about J forums see > > > http://www.jsoftware.com/forums.htm > > > > >> > > > > >> > > ---------------------------------------------------------------------- > > > > >> For information about J forums see > > > http://www.jsoftware.com/forums.htm > > > > >> > > > > > > > > > > > > > > > > > > > > -- > > > > > Devon McCormick, CFA > > > > > > > > > > > > > > > > > > > > > > -- > > > > Devon McCormick, CFA > > > > > ---------------------------------------------------------------------- > > > > For information about J forums see > http://www.jsoftware.com/forums.htm > > > > > > > ---------------------------------------------------------------------- > > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > > > > > > > -- > > Devon McCormick, CFA > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > -- Devon McCormick, CFA ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
