I want to do in Mathematica what the following does in C.

int array[7] = {0, 0, 0, 0, 0, 0, 0};

int& foo(size_t idx)
    return array[idx];

foo(4) = 43;

// array should now be {0, 0, 0, 0, 43, 0, 0}

In other words, I'd like to use = to assign to a reference (to some variable outside the scope of the function) returned by a function.

I did read a few threads about references, but it seemed I'd have to "overload" the = operator (if that's even possible) to make things work.


I wouldn't be surprised if such practice were discouraged in Mathematica, but would still appreciate the knowledge, as well as alternatives. My motivation for this is in trying to write a tool for non-programmers (or those with mostly C backgrounds but completely unfamiliar to Mathematica) for rapid testing of hypotheses, and the tool must be intuitive, familiar, and easy to pick up (else I'm afraid my pitch to use Mathematica wouldn't gain traction). To be more specific, the tool would analyze time-series data, the user specifying an expression to be run per time-step; and that expression would have "access" to a (pseudo-)array, say, price, such that price[0] refers to the current price, price[-1] refers to the previous price, etc.—so price[0] refers to a different price at each timestep. Of course C doesn't allow negative indexing; I just thought it'd be most intuitive that way—so my plan was to implement price as a function, and retrieve values from an array behind-the-scenes. You can probably see already where this is going: I'd also like for users to be able to assign to price[0], and that's where I'm stuck. I know I could (and perhaps should) just write a separate function like set_price[0, val], but this would take away from the aesthetic goal I'm trying to achieve to win everyone over.

I'm open to alternative ideas that may keep aesthetic though not in the same way.

  • $\begingroup$ possible duplicate of How to modify function argument? $\endgroup$ Commented Oct 26, 2013 at 20:59
  • $\begingroup$ @LeonidShifrin I don't think that is a duplicate, as this case is about modifying a known external symbol, not treating the argument as a symbol. That comment section linked to a ton of interesting questions though :) There are plenty of Set overloading questions that I can't seem to find. $\endgroup$
    – ssch
    Commented Oct 26, 2013 at 21:24
  • 1
    $\begingroup$ @ssch Yes, you are probably right. Then indeed, there were a number of attempts usually involving UpValues, like in your answer. One relevant post that comes to mind is this, but there were many more. $\endgroup$ Commented Oct 26, 2013 at 21:50
  • 1
    $\begingroup$ Some time ago I made an emulation of something like a pointer, in my answer to this question. May be, you may find it useful. $\endgroup$ Commented Oct 26, 2013 at 23:10
  • 2
    $\begingroup$ These two questions seem relevant: 1 and 2 $\endgroup$
    – m_goldberg
    Commented Oct 26, 2013 at 23:18

1 Answer 1


Have a look at UpValues:

l = ConstantArray[0, 10];
pos = 5;
price[i_] := l[[pos + i]]
price /: (price[i_] = val_) := (l[[pos + i]] = val)


(* {0, 0, 1, 2, -1, 3, 0, 0, 0, 0} *)

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