Trees and arrays and simple variables and databases may be represented by ordinal fractions, see http://www.statemaster.com/encyclopedia/Ordinal-fraction. That is my favorite representation of data.
Thanks. Bo. Den 18:28 lørdag den 6. september 2014 skrev 'Pascal Jasmin' via Programming <programm...@jsoftware.com>: > > >Hi Michal, > >maybe this is an interesting representation for what you want? > > ([:|. $ ;~ $ each) (i. 2 3) ; (,0) ; 0 1 >┌─┬─────────┐ >│3│┌───┬─┬─┐│ >│ ││2 3│1│2││ >│ │└───┴─┴─┘│ >└─┴─────────┘ > > > >----- Original Message ----- >From: Michal D. <michal.dobrog...@gmail.com> >To: programm...@jsoftware.com >Cc: >Sent: Saturday, September 6, 2014 12:06 PM >Subject: [Jprogramming] Ragged Array Shapes are Trees > >I just came to the realization that ragged array shapes, regardless of how >you want to represent them, are trees. I would be interested in any >references to prior exploration of this idea. > >Some example data (boxes are used to display ragged arrays, but otherwise >have no semantic meaning): > > ] A =. i. 2 3 >0 1 2 >3 4 5 > ] B =. (< @ i."0) 1+i.2 >+-+---+ >|0|0 1| >+-+---+ > ] C =. A ; B >+-----+-+---+ >|0 1 2|0|0 1| >|3 4 5| | | >+-----+-+---+ > ] D =. A ; < B >+-----+-------+ >|0 1 2|+-+---+| >|3 4 5||0|0 1|| >| |+-+---+| >+-----+-------+ > >The corresponding shape trees (monospace font required, root node is on the >left): > >A: 2 - 3 > > 1 > / >B: 2 > \ > 2 > > 2 - 3 > / >C: 3 - 1 > \ > 2 > > 2 - 3 > / >D: 2 1 > \ / > 2 > \ > 2 > >In some sense the shape tree for A is compressed, the verbose alternative >being: > > 3 > / >A: 2 > \ > 3 > >Compressing D in a similar manner leaves the full shape of the tree >ambiguous - there is no way to distinguish the duplicate structure of leaf >3 from the structure of leaves 1, 2. > > 3 > / >D: 2 - 2 - 1 > \ > 2 > >We could resolving this ambiguity by listing the shapes of all the items >explicitly. The problem here is that 'compression' could very easily lead >to an increase in representation size, although it is nice and uniform for >ragged arrays of uniform rank. > > 3 > / > | 3 > | / >D: 2 - 2 + > | \ > | 1 > \ > 2 > >Regardless of compression, I would be interested in prior work in >representing shapes of ragged arrays as trees. > >Cheers, > >Mike >---------------------------------------------------------------------- >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
