[cap-talk] Objects and Facets

[Norman Hardy]

On Aug 7, 2006, at 5:19 AM, David Hopwood wrote:

> Charles Landau wrote:
........
>
>> From a higher perspective, the object is the socket service, and an
>> invocation of the key sends a message on the socket. From a yet
>> higher perspective, the object is something on the other end of the
>> socket, and an invocation of the key sends a message and receives a
>> response from that thing.
>
> In this situation there are two capability systems, a local one and
> a distributed one. In the local system, there is a socket object; in
> the distributed system, there is a remote object. The socket object
> is part of the implementation of the remote object in the distributed
> system.
>

I think this may be a good way of speaking.
Useful precise statements must be made at an agreed abstraction  
level, or as David says in some particular capability system.
In our most careful writing on Keykos we often (usually?) forget to  
specify the level.
We are never confused when speaking among ourselves, but newcomers  
may justifiably be confused.
Mark Miller points out that many of our statements are true  
simultaneously at all levels.
But when we describe buying a page from a space bank it is useful to  
say that just after buying a page, the buyer holds the only key to  
the page.
This true at the level that abstracts the internal state of the bank,  
where in fact the bank still holds the page key it just created.

This jargon consonant with the application of models to real systems.
A model may fit a real system in more than one way.
A theorem proven within the model can yield different knowledge about  
the real system by fitting the model to the system in different ways.

Edmund Landau wrote the very short book "Foundations of Analysis" in  
1929 and there introduced the natural numbers, integers, rationals,  
reals, and complex numbers, each sort built upon the previous. (ISBN  
= 082182693X)
Abstraction played a similar role there.
With capabilities there are more theorems that work at all levels.
For Laudau x+y = y+x at all levels but division arose only with the  
rationals.
I think that Landau’s book may have kicked off the modern style of  
defining new mathematical constructs and has contributed to  
abstraction ideas in computer science.
I think that Landau’s book may introduced this style defining new  
mathematical constructs to the wide math community, and has from  
there contributed to abstraction ideas in computer science.
There is another difference in these two worlds:
   In Landau's layering, each construct was built exclusively on the  
previous.
   In Keykos a program is a machine language program that interfaces  
directly with both the CPU and the kernel.
      Commonly a Keykos program deals with several levels at once.