Re: relations aren't types?

From: Vadim Tropashko (vadimtro_at_yho.cm)
Date: 12/30/03 

Date: Tue, 30 Dec 2003 11:19:13 -0800

Mikito Harakiri wrote:

> Consider the "Group" type. Now, some groups are decomposable into direct
> products, like dihedral group D_3 (aka symmetric group S_3), while the
> others, like cyclic group Z_3, don't. I'm tempted to call Z_3 atomic, and
> S_3 composite value, then.

FYI there is a java library for groups. Dihedral group is there

http://jsci.sourceforge.net/api/JSci/maths/groups/DihedralGroup.html

but symmetric group apparently not. Alas, I was interested to
doublecheck if D_3 = S_3:

Group d3 = DihedralGroup(3);
Group s3 = SymmetricGroup(3);
System.out.println(d3.equals(s3));

That looks just like a special case, but OOP claims that they eliminate
special cases like this with subtyping, and I wonder how would they
organize groups into hierarchy of types such that D_3 = S_3.

Returning back to Marshall's argument about programming language
progress, note that int in java is atomic type, while java.lang.Integer
   is not. That's a solid foundation to advance relational implementation!