Edit detail for SandBoxHiddenOverloading revision 1 of 3

On Tue, Mar 24, 2009 at 4:24 AM, Ralf Hemmecke wrote:

Aldor's libalgebra has some bugs in it that seem to be really hard to track down. I faintly remember one such bug that I could nearly assign to the coexistence of:

  *: (Integer, %) -> % and *: (R, %) -> %

where R is instantiated with Integer. The problem here is a hidden overloading of implementations. Suppose you implement something like

#include "axiom"

MyWeirdPoly(R: Ring): Ring with {
  *: (Integer, %) -> %;
  *: (R, %) -> %;
  coerce: R -> %;
  -- ...
} == Integer add {
  coerce(r:R):% == r pretend %;
  (i: Integer) * (x: %): % == ((i+i)::%)*x;
  (r: R) * (x: %): % == (r::%) * x
  -- ...
}

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/3800008026135362624-25px001.as using 
      AXIOM-XL compiler and options 
-O -Fasy -Fao -Flsp -laxiom -Mno-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra
      Use the system command )set compiler args to change these 
      options.
#1 (Warning) Deprecated message prefix: use `ALDOR_' instead of `_AXL'
   Compiling Lisp source code from file 
      ./3800008026135362624-25px001.lsp
   Issuing )library command for 3800008026135362624-25px001
   Reading /var/zope2/var/LatexWiki/3800008026135362624-25px001.asy
   MyWeirdPoly is now explicitly exposed in frame initial 
   MyWeirdPoly will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/3800008026135362624-25px001

)show MyWeirdPoly

 MyWeirdPoly R: Ring  is a domain constructor
 Abbreviation for MyWeirdPoly is MYWEIRD
 This constructor is exposed in this frame.
 Issue )edit 3800008026135362624-25px001.as to see algebra source code for MYWEIRD 

------------------------------- Operations --------------------------------
 ?*? : (PositiveInteger,%) -> %        ?*? : (Integer,%) -> %
 ?*? : (%,%) -> %                      ?*? : (R,%) -> %
 ?**? : (%,PositiveInteger) -> %       ?+? : (%,%) -> %
 -? : % -> %                           ?-? : (%,%) -> %
 0 : () -> %                           1 : () -> %
 ?=? : (%,%) -> Boolean                ?^? : (%,PositiveInteger) -> %
 coerce : % -> OutputForm              coerce : Integer -> %
 coerce : R -> %                       hash : % -> SingleInteger
 latex : % -> String                   one? : % -> Boolean
 sample : () -> %                      zero? : % -> Boolean
 ?~=? : (%,%) -> Boolean
 ?*? : (NonNegativeInteger,%) -> %
 ?**? : (%,NonNegativeInteger) -> %
 ?^? : (%,NonNegativeInteger) -> %
 characteristic : () -> NonNegativeInteger
 recip : % -> Union(value1: %,failed: Enumeration failed)
 subtractIfCan : (%,%) -> Union(value1: %,failed: Enumeration failed)

p:=1$MyWeirdPoly(Integer)

(1)

3*p

(2)