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Re: [Axiom-developer] RE: Types as values, and Re: Static versusDynamica

From: Martin Rubey
Subject: Re: [Axiom-developer] RE: Types as values, and Re: Static versusDynamicallytyped(was:Philosophy... )
Date: Tue, 27 Sep 2005 14:03:11 +0200

Ralf Hemmecke writes:
 > William Sit wrote:
 > > For example, if I have a constructor that requires an integral domain R as
 > > a parameter, and I constructed in the package the quotient field of R, as
 > > you may suggest as an explicit way to achieve efficiency, then the package
 > > will FAIL if R is actually a field (you can consider this as a bug if you
 > > like), even though a field IS an integral domain, mathematically.

Why would it fail? I don't think it does, in fact. However, if you are going to
apply FRAC you can simply ask whether the domain is a Field.

On the other hand, given a Field to ask whether it is a QuotientField is a
question that I consider quite important. 

However, the desirable query

  if R has QuotientField S

thus defining S is, I think, quite difficult to implement sensibly. Throughout
Axiom, this effect is obtained by adding another parameter to the
Package/Domain signature like:

MyPackage(F: Field, S: IntegralDomain): ...

  if F is Fraction S then


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