Re: Re: Warning from Piecewise

*To*: mathgroup at smc.vnet.net*Subject*: [mg61608] Re: [mg61569] Re: [mg61523] Warning from Piecewise*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sun, 23 Oct 2005 05:46:23 -0400 (EDT)*References*: <FF69AAF8-0118-46DB-B123-C2DC1A80204A@mimuw.edu.pl> <200510220724.DAA12416@smc.vnet.net> <acbec1a40510221104s9e9e07cn668a994a1b3189fb@mail.gmail.com>*Sender*: owner-wri-mathgroup at wolfram.com

On 23 Oct 2005, at 03:04, Chris Chiasson wrote: > I thought evaluation was the transformation of an expression using > rules? It seems to me that the Head has to be, in some sense, evaluated if a DownValue is going to be assigned to it. Otherwise how would Mathematica know which symbol to assign a DownValue to? You can see this happen here: SetDelayed[Print[x], p] SetDelayed::write: Tag Print in Print[x] is Protected $Failed Note that x was not printed but still I think we can say the head of the expression Print[x] was evaluated. This was why I sent my correction. Andrzej Kozlowski > > On 10/22/05, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > >> Having thought more about this, I think I should add a few comments >> about why I described below happens, that si why parts of the left >> hand side of a SetDelayed (and Set) function are evaluated. The >> reason has to do with pattern matching: pattern matching is done >> after parts of an expression have been evaluated. >> >> I also wrote somewhat vaguely: >> >> >>> SetDelayed does not evaluate the head of an expression on the LHS >>> >> >> what I mean was that the head is actually evaluated but any rules >> associated with the head are not applied. >> >> Andrzej Kozlowski >> >> >> >> On 21 Oct 2005, at 20:57, Andrzej Kozlowski wrote: >> >> >>> On 21 Oct 2005, at 13:38, Chris Rodgers wrote: >>> >>> >>> >>> >>>> Hi, >>>> >>>> When I try to set a delayed expression like this: >>>> >>>> Comm[Piecewise[A:{{_, _}..}], Piecewise[B:{{_, _}..}]] := >>>> Comm[Testy[A], Testy2[B]] >>>> >>>> I get a warning from Piecewise that says: >>>> >>>> Piecewise::pairs: The first argument A : {{_, _} ..} of Piecewise >>>> is not >>>> a list of pairs. >>>> >>>> I thought that the HoldAll attribute on SetDelayed should prevent >>>> evaluation of the LHS argument, so where is this warning coming >>>> from? >>>> >>>> Can I ignore a warning like this, or should I instead use a >>>> different >>>> sort of pattern? >>>> >>>> Many thanks, >>>> >>>> Chris Rodgers. >>>> >>>> >>>> >>>> >>>> >>> >>> Actually Set and SetDelayed are special functions and their >>> behaviour in this sort of situation is not determined by their >>> attributes. You can see the difference as follows. First, let us >>> create a function H, to which we give the Attribute HoldAll. >>> >>> SetAttributes[H, HoldAll] >>> >>> Let's also define a function f to be: >>> >>> f[x_] := Print[x] >>> >>> (There is a reason why I need another function that does the same >>> thing as Print). >>> Let's first try the following using a function G which evaluates >>> its arguments: >>> >>> >>> G[f[x=1+1],p] >>> >>> From In[3]:= >>> 2 >>> >>> Out[3]= >>> G(Null,p) >>> >>> we can check that x has the value 2: >>> >>> In[4]:= >>> x >>> >>> Out[4]= >>> 2 >>> >>> Now let's clear x and do the same thing with H: >>> >>> >>> In[5]:= >>> Clear[x] >>> >>> In[6]:= >>> H[f[x=1+1],p] >>> >>> Out[6]= >>> H(f(x=1+1),p) >>> >>> In[7]:= >>> x >>> >>> Out[7]= >>> x >>> >>> No evaluation at all, as expected. Now let's again clear x and set >>> H to be SetDelayed: >>> >>> In[8]:= >>> Clear[x] >>> >>> In[9]:= >>> H=SetDelayed; >>> >>> In[10]:= >>> H[f[x=1+1],p] >>> >>> We get no output, and nothing gets printed, which means f was not >>> evaluated. However: >>> >>> In[11]:= >>> x >>> >>> Out[11]= >>> 2 >>> >>> In other words, although SetDelayed does not evaluate the head of >>> an expression on the LHS it does evaluate its other parts. >>> Why does it behave in this way? I think the reason is related to >>> the way SetDelayed defines DownValues for symbols. Finally, you can >>> avoid your message by defining Comm as follows: >>> >>> Comm[Unevaluated[Piecewise[A : {{_, _} ..}]], Unevaluated[ >>> Piecewise[B : {{_, _} ..}]]] := >>> Comm[Testy[A], Testy2[B]] >>> >>> In fact however it does not really matter. If you evaluate the >>> definition with Unevaluated and one without and then check what >>> Mathematica knows about Comm with >>> >>> ?Comm >>> >>> you will see exactly the same Output. So I think you are safe using >>> your function, provided of course the rest of your code that you >>> did not include is O.K. >>> >>> Andrzej Kozlowski >>> Tokyo, Japan >>> >>> >>> >>> >>> >>> >> >> >> > > > -- > Chris Chiasson > http://chrischiasson.com/contact/chris_chiasson >

**References**:**Re: Warning from Piecewise***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>