Re: RM and abstract syntax trees

On Nov 9, 4:15 pm, David BL <davi..._at_iinet.net.au> wrote:
> On Nov 10, 7:29 am, "David Cressey" <cresse..._at_verizon.net> wrote:
>
> > One of the fundamental properties of a pointer is that you can "dereference"
> > it by using it as an address in an address space, in order to retrieve the
> > thing pointed to directly. There is no corresponding property in
> > sequentially generated arbitrary meaningless identifiers.
>
> The mathematician in me axiomatizes the concept of pointer in terms of
> its abstract properties, which (ignoring null pointers) are
>
> 1) the existence of an associated address space, which is just a
> set of objects
> 2) a bijection between objects in the address space and pointer
> values
> In one direction this bijection is "address of" and in the
> other
> it is "dereference"
> 3) the ability to compare pointer values
>
> This encompass physical address spaces, virtual address spaces, C++
> smart pointers, persistent OIDs and pointer swizzling etc.
>
> It also encompass node identifiers of an AST if we regard the DB as
> defining an address space of AST nodes, and an appropriate select
> query represents a dereference that logically binds to precisely one
> node of the AST.

One can make an abstraction in which pointers and keys are the same, simply by abstracting over their differences. But if one does that, that doesn't mean that the underlying unabstracted differences cease to exist.

> My perspective conflicts with your statement above.

Your perspective is relative to your "axiomatization," not to the relational model; it cannot speak to the attributes of the model that your axiomatization does not capture.

Marshall Received on Sat Nov 10 2007 - 04:33:42 CET