[cap-talk] "Composite", was "Same" key

[Norman Hardy]

On Feb 15, 2007, at 8:11 AM, David Hopwood wrote:

> Charles Landau wrote:
>> At 1:15 AM +0000 2/15/07, David Hopwood wrote:
>>
>>> I wrote:
>>>> Charles Landau wrote:
>>>>>              1                          >1                 >=1
>>>
>>>>> 1 (MarkM)   Object                   Composite           ?
>>>>
>>>> The "?" is "Composite".
>>
>> I couldn't find a formal definition of "composite" in MarkM's  
>> thesis, so
>> perhaps he can clarify. But it seems to defy common English to say a
>> single atomic object is also a "composite".
>
> In section 6.2:
>
> # For compactness of description, we often aggregate a set of  
> objects into
> # a composite.
>
> So a composite is a set of objects, which may be a singleton set.  
> Nothing
> else in section 6.2 contradicts a single object being a special  
> case of
> a composite. More to the point, it is useful to view it as such,  
> because
> clients of a composite cannot necessarily tell whether it is made  
> up of
> more than one object.

Thanks for quoting chapter and verse.
I also agree with your point.
I think that the purpose of such 'composites' can generally be  
explained only in a context where it is known that there is just one  
underlying entangled state of that composite.
But known to whom?
If I get a powerful key to an object and from that key generate  
several facets, then I know the relationship between these keys.
(It makes no difference here whether the facet technology is primitive.)
I typically disseminate these facets to others who I trust to some  
limited extent.
Now those others will each hold just one of the facets typically.
The correctness of my code demands reasoning about the distribution  
of facets and the relations between them.
The correctness of the code of the others does not.
My code knows and that is enough.
The reasoning about the correctness of the other programs does not  
require knowledge of the relations between the facets.

Conjecture, Those who need to know relations between keys, are in a  
position to know.

If I hold two keys to mutable objects, it is often (generally?)  
necessary for me to learn whether their state is entangled.
A formalism is needed here. Perhaps it is available.
It is a common source of bugs.