I guess what you're looking for are sorted arrays:
  1) O(log n) lookup and insertion via binary search
  2) O(n) union and intersection are simple
  3) Equal sets are represented by structurally equivalent objects.

-Fred

> -----Original Message-----
> From: owner-caml-list@pauillac.inria.fr 
> [mailto:owner-caml-list@pauillac.inria.fr] On Behalf Of 
> Harrison, John R
> Sent: Friday, November 07, 2003 9:16 AM
> To: erayo@cs.bilkent.edu.tr; caml-list@inria.fr
> Cc: Harrison, John R
> Subject: RE: [Caml-list] Efficient and canonical set representation?
> 
> 
> | You basically want O(1) for set equality, I suppose.
> 
> Actually, no --- perhaps I should have made clearer what I 
> *really* want. The efficiency of comparison wasn't my 
> motivation, but rather elegance and aesthetics. And I meant 
> "canonical" with respect to ordinary structural equality, not 
> necessarily pointer equality, so the problem is potentially a 
> bit easier than you might have thought.
> 
> I want to be able to treat an abstract type in a truly 
> abstract way, and not worry about special-purpose equality 
> relations on certain types. Otherwise it's an ugly mess 
> dealing with complicated nestings like sets of pairs of lists of sets.
> 
> Now, I think the right solution, conceptually speaking, is to 
> allow user-defined equality on abstract types. But as far as 
> I know this cannot be done in OCaml, and I've never met much 
> enthusiasm for the idea among the CAML or SML experts.
> 
> So a poor second best is to define abstract types in a canonical way, 
> which was the starting-point of my question.
> 
> After your remarks and Brian's, I'm starting to wonder if it 
> is possible at all to do what I want. Maybe I should be 
> looking for an impossibility proof instead...
> 
> John.
> 
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