Typed keys

If an ID/IDREF replacement mechanism, is it sufficient to consider keys to
be strings or do we need to give them a datatype that controls when they are
considered equal?

For example,

<doc>
<foo>
   <bar>1</bar>
   ...
</foo>
<foo>
  <bar>01</bar>
  ...
</foo>
</doc>

Suppose within doc, foo elements are uniquely identified by their bar
children.  Do we need to be able to say that bar is of type xsd:int and so
that the above example is an error, because "1" and "01" are the same
integer even though they are different strings?

James