Edit detail for SandBoxHiddenOverloading revision 2 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/6603601906039884450-25px001.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 
      ./6603601906039884450-25px001.lsp
   Issuing )library command for 6603601906039884450-25px001
   Reading /var/zope2/var/LatexWiki/6603601906039884450-25px001.asy
   MyWeirdPoly is now explicitly exposed in frame initial 
   MyWeirdPoly will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/6603601906039884450-25px001

)show MyWeirdPoly

 MyWeirdPoly R: Ring  is a domain constructor
 Abbreviation for MyWeirdPoly is MYWEIRD
 This constructor is exposed in this frame.
 Issue )edit 6603601906039884450-25px001.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)

Now lets try the same thing in SPAD

)abbrev package MWP2 MyWeirdPoly2
MyWeirdPoly2(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/4436499139492326087-25px004.spad using 
      old system compiler.
   MWP2 abbreviates package MyWeirdPoly2 
------------------------------------------------------------------------
   initializing NRLIB MWP2 for MyWeirdPoly2 
   compiling into NRLIB MWP2 
   compiling exported coerce : R -> $
      MWP2;coerce;R$;1 is replaced by r 
Time: 0.01 SEC.

   compiling exported * : (Integer,$) -> $
Time: 0 SEC.

   compiling exported * : (R,$) -> $
Time: 0 SEC.

(time taken in buildFunctor:  1)

;;;     ***       |MyWeirdPoly2| REDEFINED

;;;     ***       |MyWeirdPoly2| REDEFINED
Time: 0.01 SEC.

   Cumulative Statistics for Constructor MyWeirdPoly2
      Time: 0.02 seconds

--------------non extending category----------------------
.. MyWeirdPoly2 #1 of cat 
(|Join| (|Ring|)
        (CATEGORY |domain| (SIGNATURE * ($ (|Integer|) $))
            (SIGNATURE * ($ |#1| $)) (SIGNATURE |coerce| ($ |#1|))))   has no 
(|IntegerNumberSystem|)    finalizing NRLIB MWP2 
   Processing MyWeirdPoly2 for Browser database:
--->-->MyWeirdPoly2((* (% (Integer) %))): Not documented!!!!
--->-->MyWeirdPoly2((* (% R %))): Not documented!!!!
--->-->MyWeirdPoly2((coerce (% R))): Not documented!!!!
--->-->MyWeirdPoly2(constructor): Not documented!!!!
--->-->MyWeirdPoly2(): Missing Description
------------------------------------------------------------------------
   MyWeirdPoly2 is now explicitly exposed in frame initial 
   MyWeirdPoly2 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/MWP2.NRLIB/code

)show MyWeirdPoly2

 MyWeirdPoly2 R: Ring  is a domain constructor
 Abbreviation for MyWeirdPoly2 is MWP2
 This constructor is exposed in this frame.
 Issue )edit /var/zope2/var/LatexWiki/4436499139492326087-25px004.spad to see algebra source
code for MWP2 

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

q:=1$MyWeirdPoly2(Integer)

(3)

3*q

(4)

Surprise!

SPAD produces the opposite result from Aldor.