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RE: Re: Defining a function in module problem?

• To: mathgroup at smc.vnet.net
• Subject: [mg46019] RE: [mg46007] Re: Defining a function in module problem?
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Tue, 3 Feb 2004 03:20:49 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

>-----Original Message-----
>From: phbrf at t-online.de [mailto:phbrf at t-online.de]
To: mathgroup at smc.vnet.net
>Sent: Monday, February 02, 2004 11:21 AM
>To: mathgroup at smc.vnet.net
>Subject: [mg46019] [mg46007] Re: Defining a function in module problem?
>
>
>jose flanigan <jflanigan at netzero.net> wrote:
>
>> a[x_] := Module[{f, g}, g = z/3; f = Function[z, Evaluate[g]]; f[x]]
>
>you could use
>
>a[x_] := Module[{f, g}, g[z_] = z/3; f = Function[z, 
>Evaluate[g]]; f[x]]
>
>or even more simple:
>
>a[x_] := Module[{f}, f = Function[z, Evaluate[z/3]]; f[x]]
>
>-- 
>Gruß Peter
>-- 
>==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==-==
>Peter Breitfeld, Bad Saulgau, Germany  -- <http://www.pBreitfeld.de>
>

Peter,

your first example doesn't work, as g has no DownValue.

Perhaps you meant:

 Clear[z]

 a[x_] := Module[{f, g}, g[z_] = z/3; f = Function[z, Evaluate[g[z]]];
    Scan[Information, Hold[f, g]];
    f[x] // Trace]

 a[1]


effectively this is the same as your second proposal:

 a[x_] := Module[{f}, f = Function[z, Evaluate[z/3]]; Information[f];
    f[x] // Trace]

 a[1]

Both break, if z has a global value. 


The second case should be replaced by 

 a[x_] := Module[{f}, f = Function[z, z/3]; f[x]]


but is completely trivial then. The first case by

 a[x_] := Module[{f, g}, g[z_] := z/3; f = Function[z, Evaluate[g[z]]];
    f[x]]


This method now opens the body to the renaming mechanism for z (see my reply
to this post). Now, when renaming z -> z$ occurs for the definition of f,
then z is visible to the renaming mechanism:

  Function[z, Evaluate[g[z]]]    -->
  Function[z$, Evaluate[g[z$]]   -->
  Function[z$, z$/3]


In fact this might be considered as a nice trick to succeed not knowing
whteher renaming will occur or not. 

My recomendation however was different (use Block).


--
Hartmut