This page deals with specification of isomorphic domains.

See thread http://groups.google.com/group/fricas-devel/browse_thread/thread/ed7004a07ae07461

(1) -> <aldor>
#include "aldor"
#include "aldorio"

define IsIsomorphicTo(C: Category, T: C): Category == with {
        coerce: % -> T
}

-- abelian monoid with a distinguished element.
AbelianMonoid1: Category == with {
        0: %;
        1: %; -- a distinguished element (generator)
        +: (%, %) -> %;
}

-- Integers
Dom1: AbelianMonoid1 == add {
        Rep == Integer;
        import from Rep;
        0: % == per 0;
        1: % == per 1;
        (x: %) + (y: %): % == per(rep x + rep y);
}

-- Even integers
Dom2: AbelianMonoid1 == add {
        Rep == Integer;
        import from Rep;
        0: % == per 0;
        1: % == per 2;
        (x: %) + (y: %): % == per(rep x + rep y);
}

-- Integers represented as sticks.
DomS: AbelianMonoid1 == add {
        Rep == String;
        import from Rep;
        0: % == per "";
        1: % == per "|";
        (x: %) + (y: %): % == per(rep x + rep y);
}

extend Dom1: IsIsomorphicTo(AbelianMonoid1, Dom2) == add {
        coerce(x: %): Dom2 == never;
}
extend Dom2: IsIsomorphicTo(AbelianMonoid1, DomS) == add {
        coerce(x: %): DomS == never;
}
extend DomS: IsIsomorphicTo(AbelianMonoid1, Dom1) == add {
        coerce(x: %): Dom1 == never;
}</aldor>

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5159550970087145340-25px001.as
      using Aldor compiler and options 
-O -Fasy -Fao -Flsp -lfricas -Mno-ALDOR_W_WillObsolete -DFriCAS -Y $FRICAS/algebra -I $FRICAS/algebra
      Use the system command )set compiler args to change these 
      options.

Compiling Lisp source code from file 
      ./5159550970087145340-25px001.lsp
   Issuing )library command for 5159550970087145340-25px001

Reading #P"/var/aw/var/LatexWiki/5159550970087145340-25px001.asy"
   DomS is now explicitly exposed in frame initial 

   Dom2 is now explicitly exposed in frame initial 

   Dom1 is now explicitly exposed in frame initial 

   IsIsomorphicTo is now explicitly exposed in frame initial 

   >> System error:
   The function BOOT::ASHARPMKAUTOLOADFUNCTOR is undefined.

Some tasks:

1. Give implementations instead of never.
2. Give a uniform implementation instead of never that works for any Domain DomX.