Re: [Axiom-developer] Axisp news

[Stephen Wilson]

Ralf Hemmecke <address@hidden> writes:

> On 06/26/2007 08:07 PM, Stephen Wilson wrote:
> > Martin Rubey <address@hidden> writes:
> >> Dear Stephen,
> >>
> >> many thanks for your detailed answer.  I must admit however, that I dislike
> >> your idea writing
> >>
> >>    D(P : Polynomial (R : Ring)) : ... == ...
> >>
> >> for
> >>
> >>    D(R : Ring, P : Polynomial R) : ... == ...
> >>
> >> Isn't this just syntactic sugar?  My feeling (!) is that this will pose 
> >> more
> >> questions than answers.  Enforcing case sensitivity on values, domains and
> >> categories also does not look very appealing to me, sorry.
> > It may be syntactic sugar for the sake of a function definition, but
> > it
> > implies a handling of types which diverges from how things are
> > currently done.
> 
> I must say, no matter whether it is syntactic sugar or not, a
> definition of the form
> 
> (*)     D(P : Polynomial (R : Ring)) : ... == ...
> 
> would confuse me. How am I supposed to used that? Should I write

Boy, my first email this morn had a few more typos than I would have
liked.  Ill try to ensure I have at least one cup of coffee before
sitting down to write an email :)

In the scheme I was (trying, badly) to suggest would have looked as
follows:

        D(p : Polynomial (R : Ring)) : ... == ..

Notice the p is lowercased, hense denoting a domain value.

Note that Martins email gave me some understanding into how the
advantages of such `patterns' can be expressed in target types using
only the notion of tuple.  So this really is just syntatic sugar.  Im
not married to it at all :)
 
> D(P) for some polynomial? (Note that Polynomial is a domain so P is an
> element.)
> You probably don't mean that. So let's assume that Polynom(R) is a category.
> 
> Now suppose I define
> 
> define MyPolyCat:Category == Polynom(Integer) with ...
> MyPoly: MyPolyCat == add ...
> 
> Now can I write
> 
>    D MyPoly
> 
> ??? (Note that it doesn't exactly match your pattern (*).)
> Or should I rather write
> 
>    D(Integer, MyPoly)
> 
> even with just the definition (*)?
> 
> I cannot see that I would like such sugar.

Ok, sorry for the confusion.  Using your example, I would have
written:  D(P : Polynom(R : Ring)) ...

Then yes, you would write `D MyPoly'.


As an involved example, consider the following from libalgebra.  We have:

  macro {
          DRX == DenseUnivariatePolynomial R;
          UPC == UnivariatePolynomialAlgebra;
          UTSC == UnivariateTaylorSeriesType;
  }

  UnivariateTaylorSeriesNewtonSolver(R:Join(ArithmeticType, ExpressionType),
                                     RXX:UTSC R, RXXY:UPC RXX): with {
                                     ...

One way you could write such a thing using the scheme I proposed is:

   macro { 
          DUP(R) == DenseUnivariatePolynomial R;
          UPC == UnivariatePolynomialAlgebra;
          UTSC == UnivariateTaylorSeriesType;
          UTSNS == UnivatiateTaylorSeriesNewtonSolver;
   }

   UTSNS(RXXY : UPC(RXX: UTSC(R : Join(ArithmeticType, ExpressionType))))

Thus, a user of the solver would only need to supply a single pice of
information, a domain implementing UnivariatePolynomialAlgebra.  The
arity is reduced from three to one.

But it is just syntatic sugar.

> 
> Ralf


Thanks again,
Steve