Re: RM and abstract syntax trees

From: David BL <>
Date: Wed, 31 Oct 2007 05:53:33 -0700
Message-ID: <>

On Oct 31, 12:23 pm, paul c <> 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?

A fair question.

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) :- add(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,_),  add(N,_,_)?
    var(N,_),  mult(N,_,_)?

    number(N,_), add(N,_,_)?
    number(N,_), mult(N,_,_)?
    add(N,_,_), mult(N,_,_)?
    add(_,N,_), not nodes(N)?
    add(_,_,N), not nodes(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 (which also gives us a single result)?

I find it interesting that LISP and Prolog have far simpler integrity constraints. RM is trying to *emulate* pointers, and the shoe doesn't fit too well.

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 but otherwise meaningless 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 - 13:53:33 CET

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