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SandBox Aldor Join and Meet

Edit detail for SandBox Aldor Join and Meet revision 6 of 9

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Editor: 127.0.0.1 Time: 2007/11/20 01:59:04 GMT-8
Note:

added:

main4():Record(D1hasMeet:Boolean, D2hasMeet:Boolean, D1hasF:Boolean) ==
  [D1 has Meet(C1,C2), D2 has Meet(C1,C2), D1 has with {f:Integer}];

added:
\end{axiom}

Comment of Ralf Hemmecke 20-Nov-2007: I would expect (false,false) for main2(), because, DM12 is not explicitly declared to be of type C1 or C2 even if its "add" domain has all the exports (except for the names C1 and C2).
\begin{axiom}

added:
-- expect True, True, True
main4()

changed:
-
Comment of Ralf Hemmecke 20-Nov-2007: That main4() returns (false, false, true) should be considered a bug.

Aldor-Meet

On Date: Nov 19, 2007 10:58 AM Oleg Golubitsky wrote to aldor-l :

By analogy with Join, Meet(C1,C2) should return a category which has the intersection of exports of C1 and C2.

A simple test (see below) confirmed this semantics; I also could not find a description of Meet in the guide.

aldor#include "aldor"
define C1:Category == with {
       f: Integer;
       g: Integer;
}
define C2:Category == with {
       f: Integer;
       h: Integer;
}
D: Meet(C1,C2) == add {
       f: Integer == 1;  -- OK; if this line is commented out, error:
                               -- The domain is missing some exports.
                               -- Missing f: AldorInteger
}

aldor

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/2046275806961882305-25px001.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 
      ./2046275806961882305-25px001.lsp
   Issuing )library command for 2046275806961882305-25px001
   Reading /var/zope2/var/LatexWiki/2046275806961882305-25px001.asy
   C1 is now explicitly exposed in frame initial 
   C1 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/2046275806961882305-25px001
   C2 is now explicitly exposed in frame initial 
   C2 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/2046275806961882305-25px001
   D is now explicitly exposed in frame initial 
   D will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/2046275806961882305-25px001

The Axiom library apparently does not define Meet.

aldor#include "axiom"
Meet(T: Tuple Category): Category == with;
define C1:Category == with {
       f: Integer;
       g: Integer;
}
D1: C1 == add {
  f: Integer == 1;
  g: Integer == 2;
}
define C2:Category == with {
       f: Integer;
       h: Integer;
}
D2: C2 == add {
  f: Integer == 1;
  h: Integer == 3;
}
define M12:Category == Meet(C1,C2);
DM12: M12 == add {
  f: Integer == 1;  -- if this line is commented out, error:
                    -- The domain is missing some exports.
  g: Integer == 2;
  h: Integer == 3;
}
define J12:Category == Join(C1,C2);
DJ12: J12 == add {
  f: Integer == 1;
  g: Integer == 2;
  h: Integer == 3;
}
main1():Record(D1hasM12:Boolean,D2hasM12:Boolean) ==
  [D1 has M12, D2 has M12];
main2():Record(M12hasC1:Boolean,DM12hasC2:Boolean) ==
  [DM12 has C1, DM12 has C2];
main3():Record(DJ12hasC1:Boolean, DJ12hasC2:Boolean) ==
  [DJ12 has C1, DJ12 has C2];
main4():Record(D1hasMeet:Boolean, D2hasMeet:Boolean, D1hasF:Boolean) ==
  [D1 has Meet(C1,C2), D2 has Meet(C1,C2), D1 has with {f:Integer}];

aldor

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/7733253532576040717-25px002.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 
      ./7733253532576040717-25px002.lsp
   Issuing )library command for 7733253532576040717-25px002
   Reading /var/zope2/var/LatexWiki/7733253532576040717-25px002.asy
   C1 is already explicitly exposed in frame initial 
   C1 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/7733253532576040717-25px002
   C2 is already explicitly exposed in frame initial 
   C2 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/7733253532576040717-25px002
   J12 is now explicitly exposed in frame initial 
   J12 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/7733253532576040717-25px002
   M12 is now explicitly exposed in frame initial 
   M12 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/7733253532576040717-25px002
   DJ12 is now explicitly exposed in frame initial 
   DJ12 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/7733253532576040717-25px002
   DM12 is now explicitly exposed in frame initial 
   DM12 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/7733253532576040717-25px002
   D1 is now explicitly exposed in frame initial 
   D1 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/7733253532576040717-25px002
   Meet is now explicitly exposed in frame initial 
   Meet will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/7733253532576040717-25px002
   D2 is now explicitly exposed in frame initial 
   D2 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/7733253532576040717-25px002

axiom
f()$DM12

(1)

Type: Integer

axiom-- expect not defined
g()$DM12
   The function g is not implemented in DM12 .
-- expect not defined
h()$DM12
   The function h is not implemented in DM12 .
f()$DJ12

(2)

Type: Integer

axiom
g()$DJ12

(3)

Type: Integer

axiom
h()$DJ12

(4)

Type: Integer

axiom-- expect False, False
main1()

(5)

Type: Record(D1hasM12: Boolean,D2hasM12: Boolean)

Comment of Ralf Hemmecke 20-Nov-2007: I would expect (false,false) for main2(), because, DM12 is not explicitly declared to be of type C1 or C2 even if its "add" domain has all the exports (except for the names C1 and C2).

axiom-- expect True, True
main2()

(6)

Type: Record(M12hasC1: Boolean,DM12hasC2: Boolean)

axiom-- expect True, True
main3()

(7)

Type: Record(DJ12hasC1: Boolean,DJ12hasC2: Boolean)

axiom-- expect True, True, True
main4()

(8)

Type: Record(D1hasMeet: Boolean,D2hasMeet: Boolean,D1hasF: Boolean)

Comment of Ralf Hemmecke 20-Nov-2007: That main4() returns (false, false, true) should be considered a bug.