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Unevaluated subtleties
*To*: mathgroup at smc.vnet.net
*Subject*: [mg92683] Unevaluated subtleties
*From*: magma <maderri2 at gmail.com>
*Date*: Fri, 10 Oct 2008 04:35:56 -0400 (EDT)
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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