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ambitious proposal: polymorphic arithmetics
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 Date: 2005-04-07 (00:13) From: William Lovas Subject: Re: [Caml-list] ambitious proposal: polymorphic arithmetics
```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

```