What is Expressiveness in a Computer Language

[Andreas Rossberg]

Chris Uppal wrote:
> 
>>>It's worth noting, too, that (in some sense) the type of an object can
>>>change over time[*].
>>
>>No. Since a type expresses invariants, this is precisely what may *not*
>>happen. If certain properties of an object may change then the type of
>>the object has to reflect that possibility. Otherwise you cannot
>>legitimately call it a type.
> 
> Well, it seems to me that you are /assuming/ a notion of what kinds of logic
> can be called type (theories), and I don't share your assumptions.  No offence
> intended.

OK, but can you point me to any literature on type theory that makes a 
different assumption?

> I see no reason,
> even in practise, why a static analysis should not be able to see that the set
> of acceptable operations (for some definition of acceptable) for some
> object/value/variable can be different at different times in the execution.

Neither do I. But what is wrong with a mutable reference-to-union type, 
as I suggested? It expresses this perfectly well.

- Andreas