Re: Warning from Piecewise

*To*: mathgroup at smc.vnet.net*Subject*: [mg61569] Re: [mg61523] Warning from Piecewise*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sat, 22 Oct 2005 03:24:08 -0400 (EDT)*References*: <FF69AAF8-0118-46DB-B123-C2DC1A80204A@mimuw.edu.pl>*Sender*: owner-wri-mathgroup at wolfram.com

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 > > > > >

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