Skip to main content

programming - Name rewriting for Function fails in closure



At its heart, Mathematica is a dynamically scoped language. While the choice of dynamic scope for Mathematica is very much a defensible one, lexical scope is too useful to do without, and Mathematica tries to fake it. Unfortunately, the abstraction is leaky.


One of the leaks comes is visible in constructs like With and Function, where symbols naming formal parameters sometimes must be changed to avoid the possibility of clashes. An example of this is:


In[1]:= With[{fun = Function[x, Take[x, 2]]},
gun[x_] := fun[x];

gun[{1, 2, 3}]]
Out[1]= {1, 2}

This is exactly what we wanted to have happen, and we can see how Mathematica pulled it off:


In[2]:= DownValues[gun];

Out[2]= {HoldPattern[gun[x$_]] :> Function[x, Take[x, 2]][x$]}

The formal parameter x for gun was changed to x$, so it does not clash with the formal parameter of the anonymous function bound to fun by the With statement.


Now, say we do this sort of thing often enough that we abstract out the construction of that anonymous function:


In[3]:= makeFun[len_] :=
Function[x,
Take[x, len]];

We can see signs of potential danger already:


In[3]:= makeFun[2] 

Out[3]= Function[x$, Take[x$, 2]]

The x is already being renamed, and the renaming could clash with other renamings. We can test this:


In[4]:= With[{fun = makeFun[10]},
hun[x_] := fun[x];

hun[1]]
Function::flpar: Parameter specification 1 in Function[1,Take[1,10]] should be a symbol or a list of symbols. >>
Function::flpar: Parameter specification 1 in Function[1,Take[1,10]] should be a symbol or a list of symbols. >>
Out[4]= Function[1, Take[1, 10]][1]


Ouch. Checking DownValues indicates that the predicted name clash did indeed come to pass:


In[5]:= DownValues[hun]
Out[5]= {HoldPattern[hun[x$_]] :> Function[x$, Take[x$, 10]][x$]}

Is there any way (perhaps with the right suite of init.m tweaks) to keep this from happening? It really compromises the ability to treat functions as first class objects in a modular way.


FWIW, this is something I saw for the first time in Mathematica 10.2. I have vague memories of doing this sort of thing is the past without particular difficulty, but I could well be mistaken on that count.




Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

list manipulation - Selecting multiple columns from a matrix?

Sample data: data = { {{2013, 1, 1}, 24.13, 167.67, 231.82}, {{2013, 1, 2}, 32.15, 170.92, 225.99}, {{2013, 1, 3}, 35.43, 172.68, 221.67}, {{2013, 1, 4}, 36.73, 173.05, 218.32}, {{2013, 1, 5}, 58.19, 165.96, 197.05}, {{2013, 1, 6}, 69.99, 163.50, 187.52}, {{2013, 1, 7}, 71.37, 154.21, 175.58}, {{2013, 1, 8}, 72.51, 149.66, 163.25}}; I want a DateListPlot with three graphs, so for a matrix formed by columns 1 and 2, one for columns 1 and 3, and 1 for columns 1 and 4. At the moment I'm using this code: data2 = Transpose[{data[[All, 1]], data[[All, 2]]}]; data3 = Transpose[{data[[All, 1]], data[[All, 3]]}]; data4 = Transpose[{data[[All, 1]], data[[All, 4]]}]; DateListPlot[{data2, data3, data4}, Joined -> True, Filling -> {3 -> {1}}] but I have a hunch that this can be done more efficiently. I don't like the Transpose s in particular. Any ideas? edit (for extra credit) What if I need to multiply the second column by 2, which in my solution is simp...