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Re: Re: Mathematica scoping / contexts / variable

David Park wrote:
> I'm not certain why many people seem to have problems with localization of
> symbols. I write lots of Mathematica definitions and code, I never use
> CleanSlate or Remove or Clear all Global` symbols and I never get into
> trouble (well, hardly ever).
> There are a few simple Mathematica style principles that can avoid most such
> problems.
> 1) Never assign values to simple symbols that you might conceivably want to
> use as symbolic variables, for example in equation solving. To save
> intermediate results while working out some development use names that you
> would never use as theoretical symbols; names such as: step1, step2,
> testmat, temporary.
> 2) Always use ClearAll[functionname] before a function definition because in
> development one might easily change the lhs argument pattern, leaving old
> definitions around. Also clear function names before solving differential
> equations because afterwards you may want to define them from the solution.
> 3) Always have an Initialization Section and load all packages needed in the
> notebook there, usually with Initialization cells.
> The following is an example of the type of writing we often see in postings
> to MathGroup.
> a = .5;
> b = 3;
> f = Exp[-a x] Sin[b x];
> Plot[f, {x, 0, 6}]
> It works, but is an invitation to problems because one might later forget
> that these symbols have values, or where exactly they were set. So clean up
> the symbols and write a definition instead that localizes the arguments.
> Clear[a, b]
> ClearAll[f]
> f[a_, b_][x_] := Exp[-a x] Sin[b x]
> Plot[f[.5, 3][x], {x, 0, 6}]
> Or if one doesn't want to keep specifying the parameters in function calls
> because they aren't changed often, write:
> ClearAll[f]
> With[{a = .5, b = 3},
>  f[x_] := Exp[-a x] Sin[b x]]
> Plot[f[x], {x, 0, 6}]
> I apologize for a response that is more elementary than you were probably
> looking for but I hope it will be helpful to many new users. 
> As for having a construction that automatically localized all symbols within
> it, I think one would soon find that exceptions were desired, in which case
> it is not much more convenient than the present case. Perhaps you meant to
> localize all symbols that have a Global context? But then suppose you are
> not working in the Global context? One could end up with some complicated
> rules as to what is localized. It seems better in localization structures to
> specify explicitly what is being localized.
> David Park
> djmpark at
> From: Leo Alekseyev [mailto:dnquark at] 
> Dear Mathematica gurus,
> One of the things that initially made Mathematica difficult for me to
> use was scoping -- in particular, the fact that all symbols by default
> appear in the global namespace.  Even though this is a default
> behavior for interactive evaluation in many packages, e.g. 
> R, in Mathematica, it leads to a greater potential for errors because
> unlike those languages, in Mathematica
> (1). a symbol can have multiple DownValues, and
> (2). if one forgets to explicitly localize a symbol inside a scoping
> construct, it may silently be taken from the global namespace.
> After many years I finally figured out a (more or less) clean way to
> structure my code and workflow, through a combination of defining
> modules, contexts, packages, and careful use of Clear and Remove.
> I still wonder, however, why there isn't a construct similar to Module
> that would define a unique private context for _all_ symbols within
> the construct (i.e. without having to declare them in a list).  You
> can kind of simulate this behavior by using BeginContext["MyCont`"]
> together with redefining $ContextPath temporarily to only have
> "MyCont`" and "System`".  This is obviously too verbose to be of
> practical use, but I do wonder why there isn't a built-in construct.
> I suppose my question is -- is there a deep wisdom behind its absence,
> or perhaps I am an anomaly in thinking that such behavior (automatic
> lexical scoping for symbols in subroutines, present in R and
> many others) would be incredibly handy?..
> Thanks,
> --Leo
These are very useful to document David. I believe that many of us "old 
timers" have learned to use these style principles the hard way :-)

--V. Stokes

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