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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

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