Your x is not rank 0, specifically rank of your x (which is a noun) is #$x but x is empty since 0 e. $x
I think it works like this, for sentence like (1 0 1$0) $ 1 2 3 since the left argument of ... $ 1 2 3 is shape 1 0 1 so that the shape of frame is 1 0 thus the shape of result is 1 0 , ($ (1$0) $ 1 2 3) which is 1 0 0 for (1 0 0$0) $ 1 2 3 the shape of result is 1 0 , ($ (0$0) $ 1 2 3) which is 1 0 for (1 0$0) $ 1 2 3 the shape of result is 1 , ($ (0$0) $ 1 2 3) which is 1 since this shape contains no 0 so the array must be non-empty Perhaps interpreting this way result of '' $ 1 2 3 is 1 but in case (2), the shape of frame is (1 0) so the the result 1 cannot be put into the frame so that the assembled result is empty. When the rank of argument is less than the rank of the verb, it is up to the verb how to handle it. OTOH, when the rank of argument is larger, then the verb will never see the original argument because J interpreter has sliced it into k-cells which are what to be received by the verb. (actual implementation is more efficient, eg atomic verbs such as +) Пт, 05 фев 2016, Matthew Baulch написал(а): > The 'x $ y' dyad, like you say, has rank 1 for x and _ for y. Examples > (1)-(3) have rank 0 arguments for x. The x arguments are arrays with > non-empty shape but no atoms in these cases. Your x arguments all have > atoms so, I'm sorry, I can't see their significance. My x arguments have > shapes containing only non-negative integers (as you mentioned), although > some are zero. I'm not sure what you mean by: > > "So your first example is not even going to get to the reshape part of the > operation. Your frame, which will hold your results, is empty." > > I understand and agree that the frame of the left argument is empty. That > doesn't surprise or concern me. What I don't understand are the reasons for > the result shapes in (1)-(3), and why the result for (3) has an atom. > > All verbs (that I can think of) with an argument of rank >= 1 are defined > also for arguments of rank 0. For instance, 'i. y', 'x # y' (x has rank > 1), and so on. Of course, there are very many verbs having arguments of > infinite rank too. Therefore, I don't see it as remarkable to apply a rank > 0 array as an argument to a verb with rank > 0. > > Your comment > > "the dictionary definitions for verbs mostly only deal with arguments which > fit within the dictionary defined rank for the verb" > > was enlightening and made me think. Is it simply that the case that most > verb definitions don't cover the case of rank 0 arguments with no atoms? > Perhaps my question relates to an undefined part of J? > > On Fri, Feb 5, 2016 at 7:27 PM, Raul Miller <[email protected]> wrote: > > > I'm going to go with the original vocab definition, because that's how > > I understand reshape. > > > > But also keep in mind that the left rank of reshape is 1. A shape is a > > (usually quite short) list of non-negative integers. This is something > > that we all have to go through - remembering that the dictionary > > definitions for verbs mostly only deal with arguments which fit within > > the dictionary defined rank for the verb. That's good enough for most > > purposes, when you need to concern yourself with rank it's the same > > rules for all verbs (except for the actual numeric values being > > different on some verbs). > > > > Perhaps http://www.jsoftware.com/help/dictionary/dictb.htm would be > > worth reviewing? > > > > Anyways, to see what that means for your reshape examples, consider this: > > > > <"1 x=: 1 0 1 $ 0 > > > > (that's an empty result - no boxes.) > > > > $<"1 x=: 1 0 1 $ 0 > > 1 0 > > > > (that's what your frame looks like, for this example.) > > > > So your first example is not even going to get to the reshape part of > > the operation. Your frame, which will hold your results, is empty. > > > > In your first example, x is empty, so you'll be using an array of > > fills (which are zeros) for the test run of reshape. So you actually > > do get a final dimension here - the last dimension is 1, and although > > x is empty, the interpreter uses that 1 to decide how many zeros it's > > going to use. > > > > Your second and third examples have the same issue - you're not doing > > a single reshape but a collection of reshapes. But in those examples > > your last dimension of x is zero. So when the interpreter does its > > test run on the verb to see what kinds of results it's getting instead > > of doing: > > > > (,0) $ 1 2 3 > > > > like it was in the first example, it is instead doing > > > > '' $ 1 2 3 > > 1 > > > > In other words there trial result doesn't have a shape, so you get one > > less dimension in your result than you had in x. > > > > As for your last example: > > > > <"1 x=: 1 $ 0 > > +-+ > > |0| > > +-+ > > $ <"1 x=: 1 $ 0 > > > > ...so your final example does do the reshaping, but you are reshaping > > with an empty shape, so you still get an empty result. > > > > Does this make sense? > > > > Thanks, > > > > -- > > Raul > > > > On Fri, Feb 5, 2016 at 3:06 AM, Matthew Baulch <[email protected]> > > wrote: > > > Original vocab says: > > > "The shape of x$y is x,siy where siy is the shape of an item of y." > > > > > > NuVoc says (for x $ y): > > > "If y is an atom or a list, the shape of the result is x", and "the shape > > > of [the result of x$y] is always x,}.$y". > > > > > > Let y =: 1 2 3 for all that follows. > > > > > > (1) > > > x =: 1 0 1 $ 0 > > > x$y has no atoms, shape 1 0 0 > > > (2) > > > x =: 1 0 0 $ 0 > > > x$y has no atoms, shape 1 0 > > > (3) > > > x =: 1 0 $ 0 > > > x$y has a single atom: 1, and shape 1 > > > (4) > > > x =: 1 $ 0 > > > x$y has no atoms, shape 0 > > > > > > Examples (1)-(3) appear to violate the definitions. Only example (4) > > > agrees. Can anyone shed some light on this? (3) strikes me as > > particularly > > > strange. I'm sure I must have missed something. > > > > > > My head is spinning! > > > ---------------------------------------------------------------------- > > > 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 -- regards, ==================================================== GPG key 1024D/4434BAB3 2008-08-24 gpg --keyserver subkeys.pgp.net --recv-keys 4434BAB3 gpg --keyserver subkeys.pgp.net --armor --export 4434BAB3 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
