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Re: Mathematica language issues
*To*: mathgroup at smc.vnet.net
*Subject*: [mg53032] Re: Mathematica language issues
*From*: David Bailey <dave at Remove_Thisdbailey.co.uk>
*Date*: Mon, 20 Dec 2004 06:35:13 -0500 (EST)
*References*: <200412171020.FAA16185@smc.vnet.net> <cq0tm1$2m2$1@smc.vnet.net> <cq3p4m$hs8$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Maxim wrote:
> On Sat, 18 Dec 2004 09:36:01 +0000 (UTC), Andrzej Kozlowski
> <akoz at mimuw.edu.pl> wrote:
>
>
>>On 17 Dec 2004, at 19:20, Maxim wrote:
>>
>>
>>>In[5]:=
>>>Unevaluated[1 + 1]*2
>>>2*Unevaluated[1 + 1]
>>>
>>>Out[5]=
>>>4
>>>
>>>Out[6]=
>>>2*Unevaluated[1 + 1]
>>>
>>
>>This is not a glitch but works exactly as one woudl expect. You can
>>see the difference and the reason by looking at Trace in both cases
>>(although there is no need for that, if you understand Unevaluated you
>>can see it right away).
>>
>>First:
>>2*Unevaluated[1+1]//Trace
>>
>>
>>{2 (1+1),2 Unevaluated[1+1]}
>>
>>
>>First Unevaluated is stipped away and Mathematica attempts ot evaluate
>>2*(1+1). Since it knows no rule to apply and the expression has not
>>changed Unevaluated is restored and evaluation is completed with the
>>output you see.
>>
>>
>>
>>Unevaluated[1+1]*2//Trace
>>
>>{(1+1) 2,2 (1+1),{1+1,2},2 2,4}
>>
>>As before, first Unevaluated is stripped away and Mathematica tires to
>>evaluate 2*(1+1). It now knows a rule to apply, which is given by the
>>Orderless attribute and the canonical ordering, so it converts the
>>expression into the form 2 (1+1). But now Unevaluated is not restored
>>because the expression has changed so evaluation continues with 1+1
>>evaluationg to 2 and finally you obtain 4.
>>
>>Now, I have honstly considered this case only because I could see at
>>once what what was going on. I do not knwo if any of the others are
>>glitches but jusdging by my experience with the past "language
>>glitches" you have reported (unlike the more serious problems desribed
>>in your last posting) I rather doubt it. However I have no time to
>>spend on this just to prove a point (again).
>>
>>
>>
>>Andrzej Kozlowski
>>Chiba, Japan
>>http://www.akikoz.net/~andrzej/
>>http://www.mimuw.edu.pl/~akoz/
>>
>
>
> I do not agree. Suppose we evaluate z*Unevaluated[1 + 1]; according to
> your explanation, after the reordering of the factors Unevaluated should
> disappear from the final result. However, the expression evaluates to
> Unevaluated[1 + 1]*z. Further, suppose we take Unevaluated[1
> + 1]*Sin[Pi/4]: Sin[Pi/4] evaluates to 1/Sqrt[2], so in this case an
> evaluation step definitely takes place; however, the output is
> Unevaluated[1 + 1]/Sqrt[2]. Your theory simply doesn't work. But even if
> it did, there is another problem: suppose I use Sin[Pi/8] instead of
> Sin[Pi/4] -- then first you would need to know whether Mathematica has a
> built-in rule for Sin[Pi/8] to arrive at any conclusion as to how it might
> work with Unevaluated (that is, what will count as an evaluation step?).
> So to apply your explanation we would have to search through all the
> built-in rules of Mathematica.
>
> Maxim Rytin
> m.r at inbox.ru
>
Hi,
Unevaluated does indeed seem inconsistent. Consider the following tests:
SetAttributes[foo,Orderless]
foo[Unevaluated[1+1],2]
foo[2,Unevaluated[1+1]]
foo[2,Unevaluated[1+1]]
foo[2,Unevaluated[1+1]]
I suppose my only objection to your original post is the implication
that the glitches that you report are a really big deal - I mean people
DO use Mathematica successfully in all sorts of research!
The other thing to remember here is that it can be very dangerous to
change things like this - because you can break existing code that
relies on such quirks - probably by mistake.
David Bailey
dbaileyconsultancy.co.uk
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