How do I use a passed-in symbol as a tag to define UpValues?

Question

ClearAll@foo;
foo[tag_] := (
   tag /: tag[i_] := tag[[i]]
   );
a = {7, 8, 9};
foo[a];
a[2]

I wanted the above to output 8, but encountered an error:

TagSetDelayed::sym: "Argument {7,8,9} at position 1 is expected to be a symbol. "

I think I understand that. It's currently a List, not a Symbol. So, I tried adding

SetAttributes[foo, HoldFirst];

after which I encountered another error:

TagSetDelayed::tagnf: "Tag a not found in {7,8,9}[i$_]."

Okay, so tag evaluated, I believe because it was in the form _[___]. So next, I added Unevaluated:

foo[tag_] := (
   tag /: Unevaluated[tag][i_] := tag[[i]]
   );

But this resulted in

TagSetDelayed::tagpos: "Tag a in Unevaluated[a][i$_] is too deep for an assigned rule to be found."

This, I don't understand...

Answer 1

Your problem has nothing to do with the function foo, but rather with the definition itself. Observe:

a = {7, 8, 9};

a /: a[i_] := a[[i]]

TagSetDelayed::tagnf: Tag a not found in {7,8,9}[i_]. >>

Because heads evaluate first you cannot even use the attempted definition for a while a has a direct (OwnValue) assignment:

ClearAll[a]
a /: a[i_] := z[i]

a = {7, 8, 9};

a[2]

{7, 8, 9}[2]

Further, TagSet serves no purpose here as you are actually defining a DownValue rule rather than an UpValue rule:

DownValues[a]

{HoldPattern[a[i_]] :> z[i]}

Answer 2

Mr.Wizard told you what you did wrong but he didn't answer the implied question of how to accomplish what you want to do. Here is one way to do it.

ClearAll[foo, a];
SetAttributes[foo, HoldFirst];
foo[var_Symbol, data_List] := (Set[var[#], data[[#]]] & /@ Range[Length[data]])

foo[a, {7, 8, 9}];
a[2]

8

DownValues @ a

{HoldPattern[a[1]]:>7, HoldPattern[a[2]]:>8, HoldPattern[a[3]]:>9}