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 Date: -- (:) From: Pierre Weis Subject: Re: [Caml-list] Understanding why Ocaml doesn't support operator overloading.
> On Fri, Nov 29, 2002 at 07:00:21PM -0500, Mike Lin wrote:
> > If this is really a problem then what gets generated when you write any
> > polymorphic function at all?
>
> I think the whole idea behind polymorphic functions is that they don't
> *care* about the type that 'a is instantiated as -- generic code that works
> for all instantiations can be generated.  This is only really useful for
> parametrized types, like 'a list, which is why it's called parametric
> polymorphism.

Although, you are right in that parametric polymorphism shines when
used with parameterized types, this far from being the only use of it.

>  As an exercise, try to write a useful function that operates
> on just 'a's -- you'll find it a challenge :)  (in fact, i think there's a
> theorem in one of Philip Wadler's papers that says the *only* function of
> type 'a -> 'a in a purely functional language is the identity function).

This is a theorem that was stated about $\lambda$-calculus long time
ago, way before Phil Wadler's papers, back to Reynolds as I remember.

The challenge you proposed is not so difficult in Caml. You can easily
define functions that operates on justs'a's, or even just return plain
'a's!

Objective Caml version 3.06+18 (2002-11-07)

# raise;;
- : exn -> 'a = <fun>
# ignore;;
- : 'a -> unit = <fun>

Furthermore, this is even easier if you consider using true side effects
that we have in Caml.

> > The proposal is to allow constrained
> > polymorphism; the polymorphism that is already in OCaml seems to
> > supersede this with regard to the above objection.
>
> basically means "rule-based" -- you can't generate generic code, but you
> can generate all possibilites and pick the right one based on some set of
> rules.

This is untrue. You can generate fully generic code for ad-hoc
polymorphic functions without bothering to generate all
possibilities''. See Jun Furuse's thesis
(http://pauillac.inria.fr/~furuse/thesis/).

> Just because "constrained polymorphism" seems less powerful than fully
> parametric polymorphism doesn't mean it's just as tractable.  The analogy
> that immediately came to mind for me comes from theory of computation -- a
> subset of a regular language is not necessarily regular, even though it's
> smaller.

This is not right as well. Extensional polymorphism is MORE powerful
than fully parametric polymorphism, in that it can express all
parametric polymorphism types and functions, plus types and functions
that you have not even dreamed of!

Once more, have a look to http://pauillac.inria.fr/~furuse/thesis/ or
POPL'95 initial article
(ftp://ftp.inria.fr/INRIA/Projects/cristal/Pierre.Weis/generics.dvi.Z)

> > I wonder if the unification algorithm can be generalized to intersect
> > sets of allowable types instead of unifying "for all" type variables.
> > It doesn't seem too ludicrous in principle but I could easily have
> > missed some nasty corner case.
>
> The type inference algorithm simply assigns type variables to expressions,
> generates a set of constraints based on how those expressions are put
> together, and then unifies' those constraints to make sure that they don't
> lead to any contradictory equalities, like int = float'.  Trying to
> generalize this would mean changing the =' relation to something more
> interesting, like maybe subset containment or something.  Clearly, this
> would not be a trivial undertaking..

This is correct. That's why the extensional polymorphism theory is
based on the usual plain unification, for both efficiency and
conservativity with respect to the Caml langauge considerations.

> There has been research into "intersection types", but i don't know if they
> have anything to do with your proposal... maybe someone else can shed some
> light?
>
> cheers,
> William
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>

Pierre Weis

INRIA, Projet Cristal, Pierre.Weis@inria.fr, http://pauillac.inria.fr/~weis/

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