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Re: Unevaluated subtleties

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92726] Re: Unevaluated subtleties
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 11 Oct 2008 06:46:32 -0400 (EDT)
  • References: <gcn49r$75b$1@smc.vnet.net>

Hi,

have a look what Hold[] does.
Unevaluated[] is only for functions that
evaluate the argument but you don't want
that. Hold[] will prevent the evaluation
general.

Regards
   Jens

magma wrote:
> I was thinking at how to measure the Length of an expression in the
> form that is entered by the user.
> The way to do it is:
> 
> Length[Unevaluated[expr]]
> 
> For example
> 
> Length[Unevaluated[2+5]]
> 
> gives
> 
> 2
> 
> which is what I wanted since 2+5 is really Plus[2,5], a function with
> 2 arguments.
> So far so good.
> 
> Then I started to experiment a bit with Unevaluated and I soon
> discovered that it behaves curiously .
> 
> To peek at the inner workings of Mathematica I always like to switch
> 
> On[]
> 
> and then try remembering to switch
> 
> Off[]
> 
> again very quickly, before doing something silly.
> So look at this:
> 
> Type:
> 
> On[]
> Unevaluated[2+5]//Length
> Off[]
> 
> and you get (line numbering added for clarity)
> 
> On::trace: On[] --> Null. >>
> Length::trace: Length[Unevaluated[2+5]] --> Length[2+5]. >>        (*
> Line 1 *)
> Length::trace: Length[2+5] --> 2.
>>>                                           (* Line 2 *)
> 
> Out[269]= 2
> 
> Which is what we got before.
> Now let's see what happens if we split the oneliner expression
> 
> Unevaluated[2+5]//Length
> 
> in 2 parts. Normally this should have no consequences, but in this
> case...
> 
> On[]
> Unevaluated[2+5]
> %//Length
> Off[]
> 
> On::trace: On[] --> Null. >>
> 
> Out[280]= Unevaluated[2+5]
> 
> Out::trace: % --> Out[$Line-1]. >>
>  $Line::trace: $Line --> 281. >>
> Plus::trace: $Line-1 --> 281-1. >>
> Plus::trace: 281-1 --> 280. >>
> Out::trace: Out[$Line-1] --> %280. >>
> Out::trace: %280 --> Unevaluated[2+5]. >>
> Length::trace: Length[%] --> Length[Unevaluated[2+5]]. >>
> Length::trace: Length[Unevaluated[2+5]] --> 1.
>>>                       (* Line 3 *)
> 
> Out[281]= 1
> 
> It gives a  different result!
> This is vaguely hinted at in the Unevaluated info page under
> Properties & Relations
> 
> "Unevaluated works only where it appears; it is not propagated"
> This probably means that it is not wise to split things up when
> dealing with Unevaluated.
> Yet, how does Mathematica know?
> Compare line 1  with line 3 : both start with the same
> Length[Unevaluated[2+5]], yet the result is different!
> I find this a bit amazing. Obviously something is going on behind the
> scenes that is not revealed with a simple On[].
> Look now at Line 2.
> Isn't that amazing? A simple looking Length[2+5] is evaluated as 2.
> It should be either 0, because Length[7] is 0 or it should be 1, if we
> imagine some invisible wrapper (HoldForm?, Unevaluated?) protecting
> 2+5.
> Length has no special attributes, yet 2+5 is taken as Plus[2,5] and
> its length evaluates to 2.
> However all of this is totally invisible.
> 
> Just for comparison type
> 
> In[283]:= On[]
> Length[2+5]
> Off[]
> 
> On::trace: On[] --> Null. >>
> Plus::trace: 2+5 --> 7. >>
> Length::trace: Length[2+5] --> Length[7]. >>                       (*
> Line 4 *)
> Length::trace: Length[7] --> 0. >>
> 
> Out[284]= 0
> 
> Compare line 2 above with Line 4 here, they start the same, yet they
> end up very differently.
> 
> All this suggests to me that either Unevaluated has a very odd and
> unique non-standard evaluation or that it has some undocumented side
> effects at least at a local (ie. temporary) level.
> Any comments?
> 


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