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 /var/aw/var/LatexWiki/5159550970087145340-25px001.asy
   DomS is now explicitly exposed in frame initial 
   DomS will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/5159550970087145340-25px001
   Dom2 is now explicitly exposed in frame initial 
   Dom2 will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/5159550970087145340-25px001
   Dom1 is now explicitly exposed in frame initial 
   Dom1 will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/5159550970087145340-25px001
   IsIsomorphicTo is now explicitly exposed in frame initial 
   IsIsomorphicTo will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/5159550970087145340-25px001
   AbelianMonoid1 is now explicitly exposed in frame initial 
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      /var/aw/var/LatexWiki/5159550970087145340-25px001

Some tasks:

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