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Re: Mathematica daily WTF

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114900] Re: Mathematica daily WTF
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Wed, 22 Dec 2010 02:34:57 -0500 (EST)
  • References: <201012200539.AAA22695@smc.vnet.net>

Actually, there is nothing puzzling about this at all.

First of all, you are confusing the issue by your assignments =
Context=Context etc to local variables. This gives exactly the same =
answers:

Block[{Attributes, Context}, {Attributes[Context],
  Attributes[Attributes], Context[Context], Context[Attributes]}]

{{HoldFirst,Protected},{HoldAll,Listable,Protected},System`,System`}

 Block[{Context}, {Attributes[Context],
  Attributes[Attributes], Context[Context], Context[Attributes]}]

{{},{HoldAll,Listable,Protected},System`,System`}


In the first case both Context and Attributes have no value inside =
Block, hence they are not evaluated. Block returns 

{Attributes[Context],
  Attributes[Attributes], Context[Context], Context[Attributes]}
 but then these are evaluated outside Block giving the expected results.

In the second case,  Context has no value inside Block but Attributes =
has. This means that inside Block, Attributes[Context] evaluates to {}, =
but the rest are unevaluated. All the unevaluated expressions are then =
evaluated outside Block, returning the expected values, but {} remains =
unchanged.

Nothing could be more logical.

Andrzej Kozlowski

On 20 Dec 2010, at 06:39, kj wrote:

> I've often stated that Mathematica is unique in my experience in
> that despite my having used it for over two decades, still it
> happens that, on average once per session, I am deeply mystified
> by something it does.
>
> So, with apologies to Alex Papadimoulis for plagiarizing the title
> of his great website (http://thedailywtf.com), I thought I'd post
> an example of one of these "daily" (as in, "each day I use
> Mathematica") mystifications.
>
> First, by way of background, consider this slightly silly, but
> perfectly valid, Mathematica expression:
>
> In[1]:= {Attributes[Context], Attributes[Attributes],
> Context[Context], Context[Attributes]}
>
> Out[1]= {{HoldFirst, Protected}, {HoldAll, Listable,
>  Protected}, "System`", "System`"}
>
> No surprises here.  Neither should there be any surprises from the
> next one, if one groks Block scope:
>
> In[2]:= Block[{Attributes = Attributes, Context = Context},
> {Attributes[Context], Attributes[Attributes], Context[Context],
>  Context[Attributes]}
> ]
>
> Out[2]= {{HoldFirst, Protected}, {HoldAll, Listable,
>  Protected}, "System`", "System`"}
>
>
> OK, so much for background.
>
> What about this one?
>
> Block[{Context = Context},
> {Attributes[Context], Attributes[Attributes], Context[Context],
>  Context[Attributes]}
> ]
>
> (The input expression is identical to the previous one, except that
> only Context, not Attributes, is localized within the Block scope.
>
> I wont' write what this last one evaluates to, for those who may
> want to work it out.  In any case, it's easy enough to paste the
> expression into Mathematica to see what it evaluates to.
>
> The following questions are for those who got it right (I usually
> don't find after-the-fact rationalizations too illuminating).
>
> If you correctly deduced the output from the last evaluation, would
> you *please* explain your reasoning to me?  And how did you arrive
> at the knowledge that supports this reasoning?  Is it in the
> documentation?
>
> Mystifiedly,
>
> ~kj
>
> P.S. Caveat: the outputs shown or alluded to above all come from
> v. 7, unfortunately.  It is possible that the results of the
> experiments above will be different (and less worthy of a WTF) with
> v. 8.  If so, my apologies.
>



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