It certainly looks very interesting, at least to me, and I am sure I will enjoy tacitizing the whole thing (cheating if necessary ;) ). Thanks a lot; I really appreciate it.
Incidentally, I wrote: "How about TREE(3)? I have no idea, maybe it is really huge and would require an enormous large amount of J bytes to describe it (assuming that its mathematical definition is constructive and does not imply accomplishing supertasks; otherwise, it is game over for J and not just for J); SCG(13) seems pretty tough as is apparently tied somewhat to very large Turing machines." Apparently, there is nothing to fear. The final (theoretical) output of a C program of merely 512 bytes, loader.c, "is much larger than TREE(3), SCG(13), or (say) BH(9)." (See, http://googology.wikia.com/wiki/Loader.c.) Surely a shorter J program can produce at least D^:5 (99), right? Perhaps, one of the C literate members of the forum can transcribe it to J :) On Thu, Nov 26, 2015 at 10:47 AM, Arie Groeneveld <[email protected]> wrote: > > I was able to reproduce, not without some difficulties, the first couple of >> tables in that page following a pedestrian approach; but apparently there >> is a (theoretical based?) shortcut to define the gs function (see >> https://tromp.github.io/pearls.html ). Maybe, one of the Haskell >> literate >> members of the forum can transcribe it to J. >> > > If still of interest. Here's a J version: > > S=: 1 :0 > : > if. 0= y do. 0 > else. 'q r'=. (0,m) #: y > ( r *(1+m) ^ (0 (m S) x)) + (1+x) m S q > end. > ) > > G=: (>:@[ $: _1+ 4 : '0 (x S)y')`[@.(0=]) > > e.g. > > 2 G"0 i.4 > 2 3 5 7 > 3 G"0 i.13 > 3 4 5 7 9 11 15 19 23 63 159 383 2047 > > As an aside: in general n G i.k > > can be replaced for the first n^2 terms with > > Gdiff=:+/\@(,}.@($~#2^i.)) > > e.g. > > Gdiff 3 > 3 4 5 7 9 11 15 19 23 > > > -Arie > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
