On Fri, 23 May 2003, hermanns wrote:
> I don't understand this, because comparison funtions ('<', '>', ...) 
> are polymorph.
> So, where is the problem with arithmetic functions?

There are several reasons.

First, short of considering arithmetic types to be objects, there is no
way to write types such as: forall ('a : arithmetic type), 'a -> 'a -> 'a.
You may only write types of the form: forall 'a, 'a -> 'a -> 'a.

This is not a problem since the polymorphic comparison function has the
type: forall 'a, 'a -> 'a -> int. Polymorphic comparisons is a priori
defined on all types; if used on functional objects, it may throw an
exception.

Second, it would be inefficient. Polymorphic comparison is implemented by
traversing the memory data structures, using the run-time type information
meant for the garbage collector.

Note that if the compiler can figure at compile time that the type of the
operands of <, <= etc..., it may generate some specialized version more
efficient than calling the polymorphic comparison routine.

In short, using a similar solution for +, -, *, / would be a bad idea:
- polymorphic comparisons are inefficient compared to comparisons on
  integers and IEEE floating-point numbers;
- short of a significant change in the type system, +, -, *, / would not
  refuse non-arithmetic operands, but would throw exceptions at runtime if
  applied to non-arithmetic arguments.

SML has a kind of operator overloading, but I don't know the details.

David Monniaux            http://www.di.ens.fr/~monniaux
Laboratoire d'informatique de l'École Normale Supérieure,
Paris, France

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