scoping - Why modules with no variables?

I was reading some code, in particular, recipe 4.13 on unification pattern-matching in Sal Mangano's Mathematica Cookbook, and there were many instances of Modules with no variables in them, such as

Lookup[x_] := Module[{}, x /. $bindings]

i didn't understand the point. Why not just write

Lookup[x_] := x /. $bindings

? Sal uses such modules frequently, so I'm supposing there is some deep reason I'm missing, hence the question here.

Answer

For a single code statement, this is probably an overkill. If you have two or more of them, you have to group them in any case. CompoundExpression is one obvious choice, such as

f[x_]:=
  (
    Print[x];
    x^2

  )

Instead, you could also do

f[x_]:=
  Module[{},
    Print[x];
    x^2
  ]

which is what I personally often prefer. Apart from some stylistic preferences, this may make sense if you anticipate that your function will grow in the future, and some local variables will be introduced.

EDIT

There is a more important point, which was escaping me for a while but which I had on the back of my mind. I will quote Paul Graham here (ANSI Common Lisp, 1996, p.19):

When we are writing code without side effects, there is no point in defining functions with bodies of more than one expression. The value of the last expression is returned as the value of the function, but the values of any preceding expressions are thrown away.

So, what Module really signals (since it is better recognizable than CompundExpression) is a piece of code where side effects are present or expected. And, at least for me, having an easy way to locate such parts in code when I look at it is important, since I try to minimize their presence and, generally, they tend to produce more bugs and problems than side-effects-free code. But, even when they are really necessary, it is good to isolate and clearly mark them, so that you can see which parts of your code are and are not side-effects free.

Comments

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.

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