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Re: Re: Weird localization bug!
*To*: mathgroup at smc.vnet.net
*Subject*: [mg106098] Re: [mg106047] Re: Weird localization bug!
*From*: DrMajorBob <btreat1 at austin.rr.com>
*Date*: Fri, 1 Jan 2010 05:36:23 -0500 (EST)
*References*: <hhf5pa$h0e$1@smc.vnet.net> <200912310816.DAA24789@smc.vnet.net>
*Reply-to*: drmajorbob at yahoo.com
Bug.
Bobby
On Thu, 31 Dec 2009 02:16:00 -0600, Norbert P. <bertapozar at gmail.com>
wrote:
> On Dec 30, 1:16 am, Derek Yates <yat... at mac.com> wrote:
>> I can't figure this out, and think it is a bug. I'm using Mathematica
>> 7.0.0 and get the same behaviour on both Mac OS X (10.5.8) and on
>> Windows XP.
>>
>> I want a function which creates a rule. The rule is of the form
>> "manipulated input" -> "input". Here is my first attempt (I have
>> simplified from what I really want to do, in order to illustrate the
>> bug):
>>
>> (1) makerule[input_] :=(input /. a_Integer :> 2 a) -> input
>> In: makerule[5]
>> Out: 2a->5
>>
>> (I expect to get 10->5)
>>
>> (2) makerule2[input_] := (input /. a_Integer :> 2 a)~myrule~input
>> In: makerule2[5]
>> Out: myrule[10,5]
>>
>> as expected
>>
>> Forcing an extra layer of localization seems to squash the bug:
>>
>> (3) makerule3[input_] :=Block[{inputcopy = input},(input /.
>> a_Integer :> 2 a) -> inputcopy]
>> In: makerule[5]
>> Out: 10->5
>>
>> Is it a bug, or have I misunderstood how the localization is meant to
>> work?
>
> This is gonna be one of these weird Mathematica features that surprise
> me every day. I played around with your code (Mathematica 6.0.2) and
> this occurs for any of the lexical scoping constructs: function
> definition, rule and With. But only when the value is inserted in the
> right-hand side of a rule, as in:
>
> With[{x = 2}, (2 /. a_ :> 2 a) :> x]
>
> but not in
>
> With[{x = 2}, (x /. a_ :> 2 a) :> 2]
>
> One can see what is happening using Trace:
>
> In[1]:= Trace[With[{x=2},(2/.a_:>2a):> x]]//Column
> Out[1]=
> With[{x=2},(2/.a_:>2 a):>x]
> (2/.a$_:>2 a):>2
> {{a$_:>2 a,a$_:>2 a},2/.a$_:>2 a,2 a}
> 2 a:>2
> 2 a:>2
>
> You can see that the localization renames a to a$, but only on the
> left-hand side of the rule. And this is imho wrong.
>
> Even simpler:
> In[2]:= Trace[With[{x=2},(a_:>a):> x]]//Column
> Out[2]=
> With[{x=2},(a_:>a):>x]
> (a$_:>a):>2
> {a$_:>a,a$_:>a}
> (a$_:>a):>2
> (a$_:>a):>2
>
> but
>
> In[3]:= Trace[With[{x=2}, a_:>a x]]//Column
> Out[3]= With[{x=2},a_:>a x]
> a$_:>a$ 2
>
> which gives the correct result, even though the renaming is completely
> unnecessary. Compare with
>
> In[4]:= Trace[With[{x=2}, x a_:>a ]]//Column
> Out[4]= With[{x=2},x a_:>a]
> 2 a_:>a
>
> No renaming.
>
> Very interesting ;))
>
> Best,
> Norbert
>
--
DrMajorBob at yahoo.com
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