Re: [Axiom-developer] about Expression Integer

[Ralf Hemmecke]

> > UnivariateFreeRing2(
> >      R : Join(ArithmeticType, ExpressionType),
> >      RX: UnivariateFreeRing R,
> >      S : Join(ArithmeticType, ExpressionType),
> >      SX: UnivariateFreeRing S
> > ): with {
> >         map: (R -> S) -> RX -> SX;
> > } == add {
> >         map(f:R -> S)(p:RX):SX == {
> >                 q:SX := 0;
> >                 for term in p repeat {
> >                         (c, n) := term;
> >                         q := add!(q, f c, n);
> >                 }
> >                 q;
> >         }
> > }

> > Can you write that in JAVA or CLOS? I would be happy to see it.

> Ignoring for now the details of the Aldor library, why would you
> expect this to be difficult? Java supports functions that return
> functions ...

I'm not so fluent in JAVA, but take for example a semigroup.
Can you do such simple thing as giving an interface for it in JAVA.

define Monoid: Category == with {
  1: %
  *: (%, %) -> %
}

The problem is the "1: %" as a constant (not a nullary function).
An abstract class is no solution since, we might need multiple 
inheritance from various interfaces (imagine to build a Ring afterwards).

Maybe it works to translate UnivariateFreeRing2 to JAVA, but I guess the 
code will look terribly complicated if it incorporates the conditions on 
R and RX, S and SX. Yes, JAVA generics are allowed.
(Well, I shut up, that is not a mailing list about JAVA.)

Ralf