Re: can one make local symbol in a pure function?

• To: mathgroup at smc.vnet.net
• Subject: [mg127392] Re: can one make local symbol in a pure function?
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Fri, 20 Jul 2012 23:43:40 -0400 (EDT)
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On 7/20/12 at 3:51 AM, nma at 12000.org (Nasser M. Abbasi) wrote:

>I was learning a bit about pure functions. Suppose we have this toy
>example:

>Clear[f, x]
>f[x_] := Module[{a = 2}, x^a]
>lst = {1, 2, 3};
>Map[f[#] &, lst]

>{1, 4, 9}

>Now I'd like to define the pure function in-line, using the Function[]
>syntax, but at the same time be able to make a local symbol 'a' like I
>did when using Module. But the syntax does not allow one to do that.
>There is no place to define it:

>lst = {1, 2, 3};
>Map[Function[{x}, x^2], lst]

>{1, 4, 9}

I really don't understand your motivation here. What is the
problem with using Module itself as part of the inline function
definition? That is,

Map[Function[{x}, Module[{a = 2}, x^a]], Range@3]

seems to satisfy all of your requirements other than perhaps an
implied requirement not to use Module.

Or you could use Block instead of Module as in

Map[Function[{x}, Block[{a = 2}, x^a]], Range@3]

>So if someone wants to make a temporary symbol to use for temporary
>calculation inside the pure function, like 'a' in this example, and at
>the same time not have it be global symbol, then one must use a Module?

This makes it sound like you want to have a local variable in
your function that does not create a new global symbol. If this
is your goal, you should be aware Module does not do this. If
you start a fresh session and do

?Global`*
f[x_]:=Module[{a=2},x^a]
f[Range@3];
?Global`*

you will find that new symbols a, a\$ appear in the Global
context. They simply don't have values in the Global context

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