Re: functions inside Module
- To: mathgroup at smc.vnet.net
- Subject: [mg38343] Re: [mg38234] functions inside Module
- From: Gianluca Gorni <gorni at dimi.uniud.it>
- Date: Thu, 12 Dec 2002 01:36:55 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Thank you for your reply. I am sorry that my understanding
of scoping is so poor.
My rule-of-thumb for making Module[] was to start off without
local variables, for example:
Module[{},
num = x^2;
den = 1 + x^2;
h[x_] = num/den;
h'[1]]
so that I can debug easily. When I finally get it to work
I add the list of the local variables:
Module[{num, x, den, h},
num = x^2;
den = 1 + x^2;
h[x_] = num/den;
h'[1]]
But now it is broken!
I wish to be enlightened on this issue: How can I safely
write a function definition inside a Module?
Gianluca Gorni
> From: David Withoff <withoff at wolfram.com>
To: mathgroup at smc.vnet.net
> Date: Tue, 10 Dec 2002 15:02:17 -0600
> To: gorni at dimi.uniud.it
> Subject: [mg38343] Re: [mg38234] functions inside Module
>
>> I am confused by this result:
>>
>> In: Module[{a}, a = x; g[x_] = a]; g[y]
>>
>> Out: x
>>
>> Somehow I would expect the same output as
>>
>> In: Module[{}, a = x; g[x_] = a]; g[y]
>>
>> Out: y
>>
>> In the first case ?g gives g[x$_] = x,
>> while in the second it gives g[x_] = x.
>> The difference is a dollar sign.
>>
>> Can anyone explain why the dollar is inserted in one case
>> but not in the other? The x was not a local variable
>> in either case.
>
> Since the names of named patterns in rules and definitions
> are treated as local variables, the x in the definition of
> g[x_] is a local variable in these examples (section 2.6.4
> in The Mathematica Book). Module[{a}, a = x; g[x_] = a]
> therefore contains nested scoping constructs, so the local
> symbol x in g[x_] = a is renamed to prevent a potential
> conflict with the variable a from the enclosing Module.
>
> In Module[{}, a = x; g[x_] = a], where there are no conflicting
> variables from the nested scoping constructs, the definition of
> g is evaluated as if the Module was not present. Since this
> definition is an immediate assignment, the right side of the
> assignment is not held unevaluated, and will be affected by
> definitions (such as the now global definition of a) that are
> present when the assignment is evaluated.
>
> If you use a delayed assignment for the definition of g
> then both inputs will show the same result:
>
> In[1]:= Module[{a},a=x;g[x_]:=a];g[y]
>
> Out[1]= x
>
> In[2]:= Module[{},a=x;g[x_]:=a];g[y]
>
> Out[2]= x
>
> The only fundamentally troublesome issue here is that immediate
> assignments are treated as scoping constructs even though they
> do not hold their arguments unevaluated.