Question

I find it useful sometimes to be able to make a local module (inside a parent module) with its own local symbols, which does a small task to be used only by the parent module. This is useful when the module becomes large, and there is no good reason to make smaller helper functions OUTSIDE the module as those helper functions are really needed and used by only that one parent module.

Here is a silly example with one module, and a helper module inside it to something

foo[x_] := Module[{r},

  r = Module[{y, sol},
    sol = First@Solve[y^2 + 3 y + 2 == 0];
    y /. sol
    ];

  x^r

  ]

But the problem in the above, is that the local variables for the inner module, could conflict with local variables with the parent module, because M notebook makes the inner module local variables red when I do the following, which tells me I am doing something I am not supposed to do: (I do not want to worry all the time with checking if I am using a unique local symbol for the inner module which is different from one used as local symbols for the parent Module, after all, it is supposed to be local. And also having to come up with a different symbol name when this is the case)

foo[x_] := Module[{r, y=0},

  r = Module[{y, sol},
    sol = First@Solve[y^2 + 3 y + 2 == 0];
    y /. sol
    ];

  x^r

  ]

Notice the red coloring, which according to the help, it is local scope conflict or shadowing in multiple contexts.

(M needs to use better colors, hard to make a difference between many colors, all shades of red).

(I think it is a shadowing warniong) Either way, it tells me I am not supposed to do this, even though I did not see any problem with such construct when I used it.

Value of parent module local variable ‘y’ in this example did not get over-written by the call to the inner module ‘r’ which is good.

Again, I did not want to make a function outside foo, because this small task is only used by foo[] and no need to move it to the Global context.

Ofcourse, I could always just write:

foo[x_] := Module[{r, y, sol},

  sol = First@Solve[y^2 + 3 y + 2 == 0];
  r = y /. sol;

  x^r

  ]

But I am just giving an example, and this is for large module, where it helps to break the tasks inside the module itself into even few smaller tasks. Internal functions, inside functions is something I used before in other languages such as Ada/Pascal and such which has this construct and can be useful for large programs.

My question is: Just want to check with the experts here if it is safe for me to use the above, even though M gives me this red coloring warning? and if there is something I need to worry about doing this

thanks,

Answer 1

Yes, it is safe to use the same variable in nested Modules as long as you don’t lose track of them. Mathematica treats each variable defined in a Module as local to that module. Local variables are Temporary, and are numbered as variable$ModuleNumber. You can check this for yourself with the following example:

Module[{x = 1},
 Print[HoldForm@x, " = ", x]
  Module[{x = 2},
   Print[HoldForm@x, " = ", x]
    Module[{x = 3},
     Print[HoldForm@x, " = ", x]
    ];
   Print[HoldForm@x, " = ", x]
  ];
 Print[HoldForm@x, " = ", x]
]

(*Output
x$4576 = 1
x$4577 = 2
x$4578 = 3
x$4577 = 2
x$4576 = 1
*)