Is there a way to apply Module and LocalizedVariables -> False simultaneously?

Question

In my project, there are some variables that I want to define locally so that my defined function has no Manipulate dependency with each other when calling the function twice. By using Module, I am able to avoid this dependency by letting these variables be defined locally.

However, when evaluating the same function twice, it creates a new variable in the global setting due to Module. I have attempted to avoid this by defining the previous variable Globally after it is locally defined by implementing LocalizeVariables->False so that I can use this same variable every time I evaluate the same function.

Is there a happy medium where once a localized variable is defined, it can be used globally? Thank you!

EDIT: Here is a visually inaccurate (in terms of Manipulate visual placement) but working example to illustrate the issue that I am facing.

Testlistplot[{lis__}, {xmin_, xmax_, 
   sampint_, {xname_String, xunit_String}}] := ( 
  Module[{xInt, lists}, lists = {lis, {}};
   If[ValueQ[xInt] == False, xInt = {xmin, xmax};];
   Manipulate[Show[Table[ListLinePlot[lists[[k]], AxesLabel -> {xunit}, 
       DataRange -> {xmin, xmax}, PlotRange -> 
        If[ValueQ[xInt] == False, {{xmin, xmax}}, {xInt}]], {k, 1, 
       Length[lists]}]], {{xInt, {xmin, xmax}, Row[{xname}]}, xmin, 
     xmax, ControlType -> IntervalSlider, Appearance -> "Labeled", 
     Method -> "Stop", MinIntervalSize -> 0.001, 
     ImageSize -> {300, 25}}, ControlPlacement -> {Bottom}, 
    LocalizeVariables -> False]])
signal1 = Table[t^2, {t, 0, 3, 0.01}];
Testlistplot[{signal1}, {0, 3, 0.01, {"x-Axis", "seconds"}}]

Running the above code will store a Global variable defined as xInt$#### and lists$#### (#### indicates a randomly chosen number). This is perfectly fine. However, re-evaluating the above code will produce a new set of Global variables defined as xInt$&&&& and lists$&&&& (&&&& indicates another randomly chosen number different than ####). Is there some way to access xInt$#### and lists$#### after the first evaluation?

My inevitable goal is to try and distinguish "global variables" per cell. Therefore, every time when someone edits the cell, the "global variables" stored in that cell will be maintained. When someone inputs the same code in another cell, this will create a new set of "global variables" in that cell different than the ones previously defined. Thank you and sorry for the confusion!

Answer 1

I'm having a hard time understanding what you are looking for. Your example code demonstrates the problem with giving the option LocalizeVariables -> False to Manipulate, but doesn't really tell me what would you would accept as a replacement. The best idea I can come up with is to memo-ize the current value of {{xmin, xmax} in a Notebook level tagging rule.

Start by initializing the tag.

CurrentValue[EvaluationNotebook[], {TaggingRules, "testplot-x-span"}] = None;

To reestablish this initial value you will need to delete any running example of Testplot and re-evaluate the above code.

Now define the interactive tool.

Clear[Testplot]

Testplot[
    signals_: {__},
    {xmin_, xmax_, step_, {xname_String, xunit_String}}] :=
  DynamicModule[{initSpan},
    Manipulate[
      CurrentValue[EvaluationNotebook[], {TaggingRules, "testplot-x-span"}] = xSpan;
      ListLinePlot[signals,
        AxesLabel -> {xunit, None},
        DataRange -> {xmin, xmax},
        PlotRange -> {xSpan, All}],
        {{xSpan, initSpan, xname}, xmin, xmax, step,
          ControlType -> IntervalSlider,
          Appearance -> "Labeled",
          Method -> "Stop",
          MinIntervalSize -> step,
          ImageSize -> {300, 25}},
           ControlPlacement -> Bottom],
    Initialization :> (
      initSpan =
        CurrentValue[EvaluationNotebook[], {TaggingRules, "testplot-x-span"}];
       If[initSpan === None, initSpan = {xmin, xmax}])]

With this definition xmin and xmax will be remembered even over re-evaluation of calls to Testplot and even re-evaluations of Testplot that don't change the memoization part of the code.

Now call Testplot with data to see how it looks

signal1 = Table[t, {t, 0, 4, 0.1}];
signal2 = Table[t^(1/2), {t, 0, 4, 0.1}];
Testplot[{signal1, signal2}, {0, 4, 0.1, {"x-Axis", "seconds"}}]

Now reduce the domain span.

Now edit the control label (from "x-Axis" to "x-span") and re-evalute Testplot.

Testplot[{signal1, signal2}, {0, 4, 0.1, {"x-span", "seconds"}}]

The label to the left of the interval slider has changed, but the reduced domain is remembered.