Experiment with TagSetDelayed involving Part

Question

Reading Associating Definitions With Different Symbols, I was intrigued by this:

You can think of upvalues as a way to implement certain aspects of object-oriented programming. A symbol like quat represents a particular type of object. Then the various upvalues for quat specify "methods" that define how quat objects should behave under certain operations, or on receipt of certain "messages".

To play with this idea, I attempted to implement a variation on List called ContiguousOrderedIntegerMap: like List, but any attempts to get an index beyond its length return Null; and any attempts to set an index beyond its length automatically fill intermediate indices with Null. I started,

ClearAll[ContiguousOrderedIntegerMap, foo, bar];
SetAttributes[ContiguousOrderedIntegerMap, HoldAll];
ContiguousOrderedIntegerMap /: 
  Part[ContiguousOrderedIntegerMap[expr_], i_] := (
   If[Length@expr < i, expr = PadRight[expr, i, Null]];
   return = expr[[i]];
   expr = ContiguousOrderedIntegerMap@expr;
   return
   );
foo = {100, 200, 300};
bar = ContiguousOrderedIntegerMap@foo;
Print@bar;
Print@bar[[2]];
Print@bar[[5]];

(* ContiguousOrderedIntegerMap[foo] *)
(* 200 *)
(* Null *)

This is however, of course, wrong, because I'm mistakenly modifying foo instead of bar and creating nonsense recursion, i.e.

foo = ContiguousOrderedIntegerMap[foo];

So, the first thing I'm stuck on is, How can I access the symbol passed into Part? Scanning through all Mathematica's available operators, I came across Pattern (:), which seemed like exactly what I needed, and applied it like so:

ContiguousOrderedIntegerMap /: 
  Part[symbol : ContiguousOrderedIntegerMap[expr_], i_] := (
   Print@symbol;

(* ContiguousOrderedIntegerMap[foo] *)

But wait, instead of bar, I got back bar's OwnValue. Why? Ah, because Part evaluates its first argument:

Attributes[Part]

(* {NHoldRest, Protected, ReadProtected} *)

So, what's next? Do I find some way to set HoldFirst on Part only when applying to a ContiguousOrderedIntegerMap? (If that's even possible.) Instead, is there a more obvious, idiomatic way to go about this all?

^{I have other questions in mind, e.g. "How do I set a separate UpValue for Set given that attempting to TagSet Part[Set[...]] would push ContiguousOrderedIntegerMap a level too deep?". However, I end my question here for now, since it's where I'm stuck, and I'll probably need to edit this question a few times as I receive help and make progress.}

Answer 1

I don't understand why you need this functionality. If you really need Part to write to your object, then again, I suggest you use one of the ways of simulating OOP in MMA (see my linked question in comments). You ask if instead there is a simpler, more obvious approach.

I think that all you really need is the following:

ContiguousOrderedIntegerMap /: 
 Part[ContiguousOrderedIntegerMap[expr_], i_] /; 
  Length@expr < i := Null
ContiguousOrderedIntegerMap /: 
 Part[ContiguousOrderedIntegerMap[expr_], i_] := expr[[i]]
map = ContiguousOrderedIntegerMap@{1, 2, 3};
map[[1]]
(* 1 *)
map[[4]] // ToString
(* Null *)

There's no need to resize your list when you attempt to read out of range - the results will be the same either way.

When setting, however, I can see why one might want to pad your list. However, with setting this problem will not appear since when you set you are guaranteeing that the lhs is a symbol that a value can be bound to. As described here, you will have to use a custom set function in order to have part-setting like list[[4]]=4. However, you can set this custom function's attributes to be HoldFirst and avoid the previous issue.