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The following Aldor code was given as an example by Ralf Hemmecke and added to the wiki by Martin Rubey. See the thread:

http://lists.gnu.org/archive/html/axiom-developer/2006-07/msg00046.html

fricas
)version
Value = "FriCAS 1.2.7 compiled at Tue Sep 29 13:45:04 UTC 2015"

aldor
#include "axiom"
define CatA: Category == with { }
define CatB: Category == with { }
define SomeCat: Category == with { CatA; CatB; }
Dom: SomeCat == Integer add;
A == Dom;
B: CatA == Dom;
H: CatA == Dom add;
main1():List Record(expression:String,result:Boolean) == [
  ["A has CatA",A has CatA],
  ["A has CatB",A has CatB],
  ["A has SomeCat",A has SomeCat],
  ["B has CatA",B has CatA],
  ["B has CatB",B has CatB],
  ["B has SomeCat",B has SomeCat],
  ["H has CatA",H has CatA],
  ["H has CatB",H has CatB],
  ["H has SomeCat",H has SomeCat]];
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3788028526442996283-25px002.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.
   The )library system command was not called after compilation.

You get...

fricas
main1()
There are no library operations named main1 Use HyperDoc Browse or issue )what op main1 to learn if there is any operation containing " main1 " in its name.
Cannot find a no-argument definition or library operation named main1 .

In particular, that "B has CatB?" is a bit surprising, isn't it?

Bill Page replied:

  I think you are dealing here with two separate but related issues:
  1) *static* typing, and 2) inheritance rules. All types in Aldor
  are static (or at least *nearly static*) meaning that they must be
  resolved during the compilation phase.

aldor
#include "axiom"
define CatA: Category == with; define CatB: Category == with; define CatX: Category == with {CatA; CatB;}
A: Join(CatX, CatA) == add; B: Join(CatX, CatB) == add; import from Integer; X: CatX == if odd? random(10) then A else B;
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/934600477956551444-25px004.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.
   The )library system command was not called after compilation.

Try a little harder to create dynamic types:

aldor
#include "axiom"
import from Integer;
define CatA: Category == with {n:Integer}; define CatB: Category == with {n:Integer}; define CatX: Category == with {n:Integer};
A: Join(CatX, CatA) == add { n:Integer==1 }; B: Join(CatX, CatB) == add { n:Integer==2 }; X1: CatX == if odd? random(10) then (A add) else (B add); X2: CatX == if even? random(10) then (A add) else (B add);
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/4046171615798297799-25px005.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.
   The )library system command was not called after compilation.

fricas
for i in 1..10 repeat output [n()$X1,n()$X2]
X1 is not a valid type.

Or this way:

aldor
#include "axiom"
import from Integer;
define CatA: Category == with {n:Integer}; define CatB: Category == with {n:Integer}; define CatX: Category == with {CatA; CatB; n:Integer};
A: Join(CatX, CatA) == add { n:Integer==1 }; B: Join(CatX, CatB) == add { n:Integer==2 }; Y1: CatX == if odd? random(10) then A else B; Y2: CatX == if even? random(10) then A else B;
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3471379723332304579-25px007.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.
   The )library system command was not called after compilation.

fricas
for i in 1..10 repeat output [n()$Y1,n()$Y2]
Y1 is not a valid type.

Or like this:

aldor
#include "axiom"
import from Integer;
define CatX: Category == with {foo: () -> Integer}
A: CatX == add {foo(): Integer == 0;}
B: CatX == add {foo(): Integer == 1;}
Z: CatX == if odd? random(10) then A else B;
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5702025508533234167-25px009.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.
   The )library system command was not called after compilation.

fricas
for i in 1..10 repeat output foo()$Z
Z is not a valid type.

Ralf Hemmecke asked: Why does the compiler reject the program without the "add" in line (*)?

aldor
#include "axiom"
define CatA: Category == with; define CatB: Category == with; define CatX: Category == with; A: CatX with { CatA } == add; B: CatX with { CatB } == add; X: CatX == if true then (A add) else (B add); -- (*)
main2():List Record(expression:String,result:Boolean) == [ ["X has CatA",X has CatA], ["X has CatB",X has CatB], ["X has CatX",X has CatX]];
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7712043450922662837-25px011.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.
   The )library system command was not called after compilation.

fricas
main2()
There are no library operations named main2 Use HyperDoc Browse or issue )what op main2 to learn if there is any operation containing " main2 " in its name.
Cannot find a no-argument definition or library operation named main2 .

Christian Aistleitner provided this answer:

I'd consider that a bug in comparison of exports. Replacing your (*) line by:

   X: CatX == if true then (A@CatX) else (B@CatX);

gives a working program.

aldor
#include "axiom"
define CatA: Category == with; define CatB: Category == with; define CatX: Category == with; A: CatX with { CatA } == add; B: CatX with { CatB } == add; X: CatX == if true then A@CatX else B@CatX; -- (*)
main3():List Record(expression:String,result:Boolean) == [ ["X has CatA",X has CatA], ["X has CatB",X has CatB], ["X has CatX",X has CatX]];
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1208324321343406004-25px013.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.
   The )library system command was not called after compilation.

fricas
main3()
There are no library operations named main3 Use HyperDoc Browse or issue )what op main3 to learn if there is any operation containing " main3 " in its name.
Cannot find a no-argument definition or library operation named main3 .

So the problem (wild guess) is that the compiler Has problems with seeing that the if statement gives CatX? in both branches of the if statement. Mainly because the types of A and B aro not equal. However, you can hint the compiler. My code is telling him "The if part gives CatX? and the else part gives CatX?". Then the compiler can infer, that the whole "if" statement gives CatX?. And it is at least the type of X (which is CatX?). So it matches.

aldor
#include "axiom"
import from Integer;
define CatA: Category == with;
define CatB: Category == with;
define CatX: Category == with;
A: Join(CatX, CatA) == add;
B: Join(CatX, CatB) == add;
MyPkg(X: CatX): with {isA?: () -> Boolean} == add { isA?(): Boolean == X has CatA; } main4(n:Integer): Boolean == { X: CatX == if zero? n then (A@CatX) else (B@CatX); isA?()$MyPkg(X); }
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/6804229532583544981-25px015.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.
   The )library system command was not called after compilation.

fricas
main4(0)
There are no library operations named main4 Use HyperDoc Browse or issue )what op main4 to learn if there is any operation containing " main4 " in its name.
Cannot find a definition or applicable library operation named main4 with argument type(s) NonNegativeInteger
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

In the following code we have the correspondence:

    A      <--> B
    String <--> with
    "x"    <--> String
    "y"    <--> Integer

aldor
#include "axiom"
define CatA(s: String): Category == with;
A(s: String): CatA(s) == add;
define CatB(s: with): Category == with; B(s: with): CatB(s) == add;
rhxmain(): List Record(s: String, b: Boolean) == [ ["A x has CatA x", (A("x") has CatA("x"))], ["A y has CatA x", (A("y") has CatA("x"))], ["B String has CatB String", (B(String) has CatB(String))], ["B Integer has CatB String",(B(Integer) has CatB(String))] ];
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7724360379013079758-25px017.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.
   The )library system command was not called after compilation.

The interesting part is that the truth value of the second and fourth list elements do not agree.

fricas
rhxmain()
There are no library operations named rhxmain Use HyperDoc Browse or issue )what op rhxmain to learn if there is any operation containing " rhxmain " in its name.
Cannot find a no-argument definition or library operation named rhxmain .

An example of a domain-valued variable

#include "axiom"
#pile
main5(n:Integer):List Boolean == local x:IntegralDomain local y:Category
if n=1 then y := Field else y := Ring
x := Integer test1:Boolean := x has y x := Fraction Integer test2:Boolean := x has y [test1,test2]
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1586618870818532942-25px019.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.
   The )library system command was not called after compilation.

fricas
main5(1)
There are no library operations named main5 Use HyperDoc Browse or issue )what op main5 to learn if there is any operation containing " main5 " in its name.
Cannot find a definition or applicable library operation named main5 with argument type(s) PositiveInteger
Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

The compiler checks static types.

aldor
#include "axiom"
#pile
main6():List Boolean == local x:IntegralDomain
x := Integer test1:Boolean := x has Field x := String test2:Boolean := x has Field [test1,test2]
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/395909315557564304-25px021.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.
   The )library system command was not called after compilation.

But note that we cannot define domain-valued variables in the Axiom interpreter.

fricas
x:IntegralDomain
IntegralDomain is a category, not a domain, and declarations require domains.

Try to write a self-describing domain --Bill Page, Wed, 26 Jul 2006 06:28:37 -0500 reply
aldor
#include "axiom"
#pile
MyDom: with sigs:List Category add2:(MyDom,MyDom) -> MyDom sub2:(MyDom,MyDom) -> MyDom neg: MyDom -> MyDom == add import from Integer Rep == Integer
sigs:List Category == [with {add2:(MyDom,MyDom)->MyDom}, with {sub2:(MyDom,MyDom)->MyDom}, with {neg:MyDom->MyDom}]
add2(x:%,y:%):% == per(rep(x) + rep(y)) sub2(x:%,y:%):% == per(rep(x) - rep(y)) neg(x:%):% == per(-rep(x))
main8():List Boolean == import from ListFunctions2(Category,Boolean)
map((i:Category):Boolean+->(MyDom has i), sigs$MyDom)
aldor
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7325620604487185069-25px023.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.
   The )library system command was not called after compilation.

fricas
)sh MyDom
The )show system command is used to display information about types or partial types. For example, )show Integer will show information about Integer .
MyDom is not the name of a known type constructor. If you want to see information about any operations named MyDom , issue )display operations MyDom main8()
There are no library operations named main8 Use HyperDoc Browse or issue )what op main8 to learn if there is any operation containing " main8 " in its name.
Cannot find a no-argument definition or library operation named main8 .




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