RE: Re: Dynamic: feature? No, in my opinion is UpValues feature

*To*: mathgroup at smc.vnet.net*Subject*: [mg88088] RE: [mg88068] Re: Dynamic: feature? No, in my opinion is UpValues feature*From*: "Jose Luis Gomez" <jose.luis.gomez at itesm.mx>*Date*: Thu, 24 Apr 2008 05:57:08 -0400 (EDT)*References*: <fukem6$s0m$1@smc.vnet.net> <200804230810.EAA29048@smc.vnet.net>

Dear Chris and Jean-Marc I believe the behavior that you report is Not a Dynamic feature, I think it is an UpValues feature, and I am Not surprised it happened, let me explain. (If there is in this forum any expert in DownValues, OwnValues and UpValues, please correct me if I make any mistake in the following:) First a simpler example: If I write the following two different rules for the same expression foo[a], which one will Mathematica obey? foo /: foo[a]=400; a /: foo[a]=12; The answer is that Mathematica will always say foo[a] is 12, it does Not matter which definition was evaluated before, because the rule a/:foo[a]=12 is an UpValue (definition assigned to an argument, similar to some aspects of object oriented programming) while foo /: foo[a]=400 is a DownValue (definition assigned to a Head, this are the "normal" definitions) And Mathematica will always try UpValues first, and if there is no UpValue that can be applied, then it will try DownValues. The reason for this behavior is that we can create specific rules with UpValues and general rules with DownValues that coexist. For example the following command will create a specific rule for the addition of "a" plus anything, without disturbing the behavior of addition in other situations: a /: a + x_ := myplus[a, x] This specific rule will always be used before the general rules of addition when the addition includes a. For example evaluate x+y+a+z and you will obtain myplus[a,x+y+z]. On the other hand, if you evaluate 3+4 you will obtain 7, no problem because you did not overwrite the general rules addition, you just added a specific rule for a special case, which coexist with the general rules. However, in the example above, the rule foo /: foo[a]=400 will never be used, because the rule a /: foo[a]=12 will always "win". Then the code above (definitions of foo) is in some sense bad programming, yet the output is predictable. Now the case that we are interested, What do you think it must happen if you have the following definitions for goo? What do you think Mathematica should do in this case? a /: goo[a,b]=400; b /: goo[a,b]=12; First, we can say that this definitions of goo are at least as bad programming as the example above with foo, because two different rules should apply to the same expression. Maybe you were expecting that the last rule evaluated will replace the first rule, but this does Not happen because the rules are assigned to different objects, a and b. You can verify that the two rules exist at the same time by evaluating ?a And evaluating ?b So, the second rule does not overwrite the first rule, the two conflicting rules coexist, BECAUSE they are assigned to different objects, "a" and "b". In order to have the second (last) rule to overwrite the first rule both rules must be assigned to the same object, for example "a". I think this bad programming (two different rules of the same hierarchy that should be applied to the same expression coexist), therefore we can expect the behavior of Mathematica to be unpredictable. If the two conflicting rules coexist, which one should Mathematica obey? I am Not surprise that Mathematica behavior is different if in different situations, for example, if one rule is evaluated first or second. Also it could happen that Mathematica 5.2 and Mathematica 6.0 could have (I do Not know if they do) different behavior in this bad programming example (goo). But those are my thoughts, Is there in the forum any expert in DownValues, OwnValues and UpValues that can tell us if my ideas are correct? Jose Mexico -----Mensaje original----- De: Jean-Marc Gulliet [mailto:jeanmarc.gulliet at gmail.com] Enviado el: Mi=E9rcoles, 23 de Abril de 2008 03:10 a.m. Para: mathgroup at smc.vnet.net Asunto: [mg88068] Re: Dynamic: feature? Chris Osborn wrote: > I have a cell containing this: > > Dynamic[f[a, b]] > > Then I do this: > > a /: f[a, b] = 12 > > and the dynamic cell updates to 12, as I would expect. > > When I do this: > > b /: f[a, b] = 45 > > The dynamic cell does *not* update for some reason. > It seems as though it does not realize an update has occurred when it > is associated with b. > > Does anyone know why this is? > > Thanks in advance, > Chris Weird. I witness the same behavior if the cells are evaluated in the given order. However, ff one change the order of the assignments (i.e. b first, then a) Dynamic[] works as expected. Evaluating the following expressions in that order, Dynamic[f[a, b]] (* The first output cell is: f[a, b] *) b /: f[a, b] = 45 (* The first output cell is now: 45 *) a /: f[a, b] = 12 (* The first output cell is now: 12 *) $Version => "6.0 for Mac OS X x86 (64-bit) (February 7, 2008)" I have also recorded the sessions in a PDF file. See http://homepages.nyu.edu/~jmg336/mathematica/weirddynamic.pdf Regards, -- Jean-Marc

**References**:**Re: Dynamic: feature?***From:*Jean-Marc Gulliet <jeanmarc.gulliet@gmail.com>

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