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syntax - Treat all variables as local in a module




In most languages, any variable defined inside a function is considered local.


# a Python function
def toRomanNumerals(num):
    digits = # ...
    string = ''
    while num > 0:
        (value, letters) = # ...
        string = # ....
    return string


In a Mathematica Module, however, we must specify a list of all variables to treat as local.


toRomanNumerals[i_Integer?Positive] := 
 Module[{num = i, string = "", value, letters, digits}, 
  digits = (* ... *);
  While[num > 0, {value, letters} = 
    (* ... *);
   string = (* ... *).];
  string]

I sometimes find it tedious to manually type the list of all local variables. Do others feel the same way?



Is there a way to create a Module which treats all symbols defined inside as local?



Answer



This sort of programming is not my strength and I don't know Python. Reading the comments, perhaps this won't quite be perfect, but it might be good enough. It seems good enough for many purposes, at least in the way I interpret the question. It localizes all Symbols in the code that are in the "Global`" context and don't have Ownvalues or DownValues. If you want to exclude those with UpValues etc., then it should be easy how to modify it to do so.


ClearAll[localizeAll];
SetAttributes[localizeAll, HoldAll];
localizeAll[code_] := 
  With[{vars = Join @@ Union @
    Cases[Hold[code], 
          s_Symbol /; Context[s] == "Global`" &&
             Length@OwnValues[s] == 0 && Length@DownValues[s] == 0 :> Hold[s],

          Infinity,
          Heads -> True]},
   (* Module[{##}, code] & @@ vars *)  (* original *)
   vars /. Hold[v___] :> Module[{v}, code] (* Leonid Shifrin's suggestion *)
   ]

Example:


Clear[z];
z[a_] := a^2;
localizeAll[x = 2; y = x++; z[x] = y; q[r_] := s; z[2x]]

z[3]
z[x]
q[1]

(* 36 *)
(* 2 *)
(* x^2 *)
(* q[1] *)

Note that because z was defined, z[3] got redefined.



I think I might rather take a few seconds and type out the variables explicitly. It might save time in the long run.


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