On Wed, Apr 06, 2005 at 03:33:56PM -0400, Eijiro Sumii wrote:
> From: "William Lovas" <wlovas@stwing.upenn.edu>
> > (This argument breaks down in
> > the face of code which relies on abstract types to enforce modularity -- in
> > such cases, incomparability can become "the rule" rather than the
> > exception, putting =, <, etc. on the same footing as +, -, etc.)
> 
> Yes, polymorphic comparison already breaks type abstraction.

I did not realize this!  Can somebody explain the following interactions?

    # let r = Ratio.ratio_of_int 5;;
    val r : Ratio.ratio = <abstr>
    # r = r;;
    Exception: Invalid_argument "equal: abstract value".

    # module M : sig type t;; val of_int : int -> t end =
        struct type t = int;; let of_int x = x end;;
        module M : sig type t val of_int : int -> t end
    # let t = M.of_int 5;;
    val t : M.t = <abstr>
    # t = t;;
    - : bool = true

I thought that perhaps all comparisons of abstract values resulted in a
runtime error, but evidently i was mistaken :/  What's the secret to making
a type "really" abstract?

William