Re: Weird localization bug!
- To: mathgroup at smc.vnet.net
- Subject: [mg106047] Re: Weird localization bug!
- From: "Norbert P." <bertapozar at gmail.com>
- Date: Thu, 31 Dec 2009 03:16:00 -0500 (EST)
- References: <hhf5pa$h0e$1@smc.vnet.net>
On Dec 30, 1:16 am, Derek Yates <yat... at mac.com> wrote:
> I can't figure this out, and think it is a bug. I'm using Mathematica
> 7.0.0 and get the same behaviour on both Mac OS X (10.5.8) and on
> Windows XP.
>
> I want a function which creates a rule. The rule is of the form
> "manipulated input" -> "input". Here is my first attempt (I have
> simplified from what I really want to do, in order to illustrate the
> bug):
>
> (1) makerule[input_] :=(input /. a_Integer :> 2 a) -> input
> In: makerule[5]
> Out: 2a->5
>
> (I expect to get 10->5)
>
> (2) makerule2[input_] := (input /. a_Integer :> 2 a)~myrule~input
> In: makerule2[5]
> Out: myrule[10,5]
>
> as expected
>
> Forcing an extra layer of localization seems to squash the bug:
>
> (3) makerule3[input_] :=Block[{inputcopy = input},(input /.
> a_Integer :> 2 a) -> inputcopy]
> In: makerule[5]
> Out: 10->5
>
> Is it a bug, or have I misunderstood how the localization is meant to
> work?
This is gonna be one of these weird Mathematica features that surprise
me every day. I played around with your code (Mathematica 6.0.2) and
this occurs for any of the lexical scoping constructs: function
definition, rule and With. But only when the value is inserted in the
right-hand side of a rule, as in:
With[{x = 2}, (2 /. a_ :> 2 a) :> x]
but not in
With[{x = 2}, (x /. a_ :> 2 a) :> 2]
One can see what is happening using Trace:
In[1]:= Trace[With[{x=2},(2/.a_:>2a):> x]]//Column
Out[1]=
With[{x=2},(2/.a_:>2 a):>x]
(2/.a$_:>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