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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.




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