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Re: RM and abstract syntax trees

From: David BL <davidbl_at_iinet.net.au>
Date: 31 Oct 2007 19:50:50 -0700

On Oct 31, 12:23 pm, paul c <toledobythe..._at_ooyah.ac> wrote:
> David BL wrote:
>
> ...
>
> > Yes RM references things uniquely with values, but pointers are "value
> > types"! ...
>
> Sure, but what good does it do to think of them that way, when plain old
> "values" suffices?

I guess I equate pointers with edges in a directed graph (where by directed graph I'm referring to the formalised notion of a set of nodes plus a set of directed edges between nodes), and naturally I regard an AST as an acyclic directed graph.

Using Prolog notation, consider the following relations

var(N,S) :- node N is a variable named S     number(N,I) :- node N is a number with value I     add(N,N1,N2) :- node N is the addition of nodes N1,N2     mult(N,N1,N2) :- node N is the product of nodes N1,N2

Suppose we define a view called nodes(N) which is a union of projections as follows

```    nodes(N) :- var(N,_).
nodes(N) :- number(N,_).
nodes(N) :- mult(N,_,_).

```

Note that I use underscores for attributes to be projected away.

There are numerous integrity constraints. Each of the following SPJ queries must be empty.

var(N,S1), var(N,S2), S1 <> S2?
number(N,I1), number(N,I2), I1 <> I2?     add(N,N1,_), add(N,N2,_), N1 <> N2?

```    add(N,_,N1), add(N,_,N2), N1 <> N2?
mult(N,N1,_), mult(N,N2,_), N1 <> N2?
mult(N,_,N1), mult(N,_,N2), N1 <> N2?
var(N,_),  number(N,_)?
var(N,_),  mult(N,_,_)?
```

number(N,_), mult(N,_,_)?
```    add(N,_,_), mult(N,_,_)?
```

mult(_,N,_), not nodes(N)?
mult(_,_,N), not nodes(N)?

>From these integrity constraints we can deduce that joins used to
traverse down through the AST give us back precisely one tuple in the result set.

Isn't it helpful to see the analogy with a pointer dereference?

I'll leave it up to you as to whether you dislike the analogy between node identifiers and pointer values, and the idea that a join can be compared to a pointer dereference. Perhaps you are right and the analogy creates confusion.

Anyway, what matters is whether RM is suited to representing ASTs. I find it significant that RM forces one to generate unique identifiers on all the nodes and exposes them for all to see, whereas LISP, Prolog and even C/C++ allow the user/programmer to work at a level of abstraction where node identifiers are hidden.

I find it particularly telling that Prolog provides the choice of

1. using the approach above (which is how RM would be used); or
2. using nested terms, (which is outside of RM's scope) and the clear winner is 2.
Received on Wed Oct 31 2007 - 21:50:50 CDT

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