Refering to local module variables

Question

How can I do the following? I have code inside a Module such as Module[{a1,a2,a3,a4}, code...]. In this code I want to refer to these constants efficiently (for a large number of them) so I would construct them in ways such as Table[ToExpression["a" <> ToString[i]], {i, 4}]. The important point is that they are constructed as a1 (etc) after the module has done its renaming to a unique variable. So this does not work, see:

Module[{a1}, 
 MemberQ[Table[ToExpression["a" <> ToString[i]], {i, 3}], a1]]

Is it possible to do this correctly? (By the way, this is almost the opposite question of Refering to global variables inside modules.)

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As often, the time needed to formulating the question was enough to actually find a solution. While it isn't an answer to the question, the better way to avoid the whole problem is to assign multiple downvalues to one a , i.e. a[1],a[2],...

Answer 1

Using Block instead of Module:

Block[{a1}, MemberQ[Table[ToExpression["a" <> ToString[i]], {i, 3}], a1]]

True

From Block >> Properties and Relations:

• Block localizes values only; it does not create new symbols

• Module creates new symbols

Answer 2

It can be done using $ModuleNumber. However a[1], a[2],... is better

Module[{a1, a2, a3, mn = $ModuleNumber},
 MemberQ[Table[ToExpression[
    StringJoin["a", ToString[i], "$", ToString[mn]]], {i, 3}], a1]]

True

Note, if $ModuleNumber is called outside the local brackets it needs to be decremented.

Module[{a1, a2, a3, mn},
 mn = $ModuleNumber - 1;
 MemberQ[Table[ToExpression[
    StringJoin["a", ToString[i], "$", ToString[mn]]], {i, 3}], a1]]

True