Skip to main content

scoping - Is there any way to implement a "sequential" With[] in Mathematica?




I want the equivalent of Scheme's let*, or basically, a sequential With that works like this:


With[{a = 0,
a = a + 1,
a = a + 1},
a]

Is there any way to implement this? Everything I tried with Hold/Unevaluated/etc. led nowhere.



Answer



This is outside the scope of With. The documentation says:




With[{x=x₀, y=y₀, ...}, expr]


specifies that all occurrences of the symbols x, y, ... in expr should be replaced by x₀, y₀, ...



So even if there was a "sequential" With, it wouldn't be able to understand a = a+1 as updating the value of a. It would always just be a replace rule.


I think you'd be best off with a Module:


Module[{a},
a = 0;
a = a+1;
a = a+1;
a]


You can write your own command which rewrites the form of the command for you, for example:


letstar[init_List, expr_] :=
With[{vars = symbols[init]},
Module[vars, CompoundExpression @@ Join[init, {expr}]]]
symbols[init_List] := Union@Hold[init][[1, All, 1]]
SetAttributes[symbols, HoldFirst]
SetAttributes[letstar, HoldFirst]

This assumes that the first argument of letstar is a list of assignments (this is not checked) and holds its form so that they are not performed. Instead, they are passed to symbols which only extracts the left-hand sides and lists unique variables appearing in them. This is passed to a Module as the local variables, the init block is converted into a compound expression and finally expr is evaluated. So if you call



letstar[{a = 0, a = a + 1, a = a + 1}, a]

this gets internally transformed to


Module[{a}, a = 0; a = a+1; a = a+1; a]

and returns



2



Comments

Popular posts from this blog

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.