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This page deals with specification of isomorphic domains.

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

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/zope2/var/LatexWiki/5159550970087145340-25px001.as using 
      AXIOM-XL compiler and options 
-O -Fasy -Fao -Flsp -laxiom -Mno-ALDOR_W_WillObsolete -DAxiom -Y $AXIOM/algebra -I $AXIOM/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/zope2/var/LatexWiki/5159550970087145340-25px001.asy
   DomS is now explicitly exposed in frame initial 
   DomS will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/5159550970087145340-25px001
   Dom2 is now explicitly exposed in frame initial 
   Dom2 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/5159550970087145340-25px001
   Dom1 is now explicitly exposed in frame initial 
   Dom1 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/5159550970087145340-25px001
   IsIsomorphicTo is now explicitly exposed in frame initial 
   IsIsomorphicTo will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/5159550970087145340-25px001
   AbelianMonoid1 is now explicitly exposed in frame initial 
   AbelianMonoid1 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/5159550970087145340-25px001
>> System error: The bounding indices 163 and 162 are bad for a sequence of length 162. See also: The ANSI Standard, Glossary entry for "bounding index designator" The ANSI Standard, writeup for Issue SUBSEQ-OUT-OF-BOUNDS:IS-AN-ERROR

Some tasks:

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




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