MathAction SandBoxOverloading

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This fails in SPAD:

spad

)abbrev domain AAA Aaa
Aaa: with
    bar: Integer -> Integer
  == add
    foo(x:Float):Integer == 1
    foo(x:Integer):Integer == 2
    a:Integer == 1
    a:Float == 1.0
    x:Integer := 1
    y:Float := 1.0
    bar(z:Integer):Integer == foo(x)+foo(y)

spad

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/162293060307836856-25px001.spad using 
      old system compiler.
   AAA abbreviates domain Aaa 
------------------------------------------------------------------------
   initializing NRLIB AAA for Aaa 
   compiling into NRLIB AAA 
   compiling local foo : Float -> Integer
      AAA;foo is replaced by 1 
Time: 0.06 SEC.

   compiling local foo : Integer -> Integer
      AAA;foo is replaced by 2 
Time: 0 SEC.

   compiling local a : () -> Integer
      AAA;a is replaced by 1 
Time: 0 SEC.

   compiling local a : () -> Float
Time: 0 SEC.

   compiling exported bar : Integer -> Integer
****** comp fails at level 3 with expression: ******
error in function bar 

(+ (|foo| |x|) (|foo| | << y >> |))
****** level 3  ******
$x:= y
$m:= (Integer)
$f:=
((((|z| # #) (|y| # #) (* # # #) (** # # #) ...) ((|foo| #))
  ((|foo| #) (* # # #) (** # # #) (+ # #) ...)))

   >> Apparent user error:
   Cannot coerce y 
      of mode (Float) 
      to mode (Integer)

axiom

bar(3)

   There are no library operations named bar
      Use HyperDoc Browse or issue
                                )what op bar
      to learn if there is any operation containing " bar " in its
      name.

   Cannot find a definition or applicable library operation named bar
      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.

spad

)abbrev domain AAA0 Aaa0
Aaa0: with
    bar0: Integer -> Integer
    foo: Integer -> Integer
    foo: Float -> Integer
  == add
    foo(x:Float):Integer == 1
    foo(x:Integer):Integer == 2
    x:Integer := 1
    y:Float := 1.0
    bar0(z:Integer):Integer == foo(x)+foo(y)

spad

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/6395014362195898863-25px003.spad using 
      old system compiler.
   AAA0 abbreviates domain Aaa0 
------------------------------------------------------------------------
   initializing NRLIB AAA0 for Aaa0 
   compiling into NRLIB AAA0 
   compiling exported foo : Float -> Integer
      AAA0;foo;FI;1 is replaced by 1 
Time: 0 SEC.

   compiling exported foo : Integer -> Integer
      AAA0;foo;2I;2 is replaced by 2 
Time: 0 SEC.

   compiling exported bar0 : Integer -> Integer
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |Aaa0| REDEFINED

;;;     ***       |Aaa0| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor Aaa0
      Time: 0 seconds

   finalizing NRLIB AAA0 
   Processing Aaa0 for Browser database:
--->-->Aaa0((bar0 ((Integer) (Integer)))): Not documented!!!!
--->-->Aaa0((foo ((Integer) (Integer)))): Not documented!!!!
--->-->Aaa0((foo ((Integer) (Float)))): Not documented!!!!
--->-->Aaa0(constructor): Not documented!!!!
--->-->Aaa0(): Missing Description
------------------------------------------------------------------------
   Aaa0 is now explicitly exposed in frame initial 
   Aaa0 will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/AAA0.NRLIB/code

axiom

bar0(3)

(1)

Type: PositiveInteger

But it works in Aldor:

aldor

#pile
#include "axiom"

Bbb: with
    bar2: Integer -> Integer
  == add
    foo(x:Float):Integer == 1
    foo(x:Integer):Integer == 2
    a:Integer == 1
    a:Float == 1.0
    x:Integer := 1
    y:Float := 1.0
    bar2(z:Integer):Integer == foo(x)+foo(y)

aldor

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/3603377070621137033-25px005.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 
      ./3603377070621137033-25px005.lsp
   Issuing )library command for 3603377070621137033-25px005
   Reading /var/zope2/var/LatexWiki/3603377070621137033-25px005.asy
   Bbb is now explicitly exposed in frame initial 
   Bbb will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/3603377070621137033-25px005

axiom

bar2(3)

(2)

Type: PositiveInteger

aldor

#pile
#include "axiom"

Ccc: with
    bar3: Integer -> Integer
  == add
    foo(x:Float):Integer == 1
    foo(x:Integer):Integer == 2
    a:Integer == 1
    a:Float == 1.0
    x:Integer := 1
    y:Float := 1.0
    bar3(z:Integer):Integer == foo(a)+foo(a)

aldor

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/2796111966566536169-25px007.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'
"/var/zope2/var/LatexWiki/2796111966566536169-25px007.as", line 13: 
    bar3(z:Integer):Integer == foo(a)+foo(a)
...............................^......^
[L13 C32] #2 (Error) There are 2 meanings for the operator `foo'.
        Meaning 1: (x: Float) -> Integer
        Meaning 2: (x: Integer) -> Integer

   The )library system command was not called after compilation.

axiom

bar3(3)

   There are no library operations named bar3
      Use HyperDoc Browse or issue
                                )what op bar3
      to learn if there is any operation containing " bar3 " in its
      name.

   Cannot find a definition or applicable library operation named bar3
      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.

aldor

#pile
#include "axiom"

Ddd: with
    bar4: Integer -> Integer
  == add
    foo(x:Float):Integer == 1
    foo(x:Integer):Integer == 2
    a:Integer == 1
    a:Float == 1.0
    x:Integer := 1
    y:Float := 1.0
    bar4(z:Integer):Integer == foo(a@Integer)+foo(a@Float)

aldor

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/8356965697444416280-25px009.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 
      ./8356965697444416280-25px009.lsp
   Issuing )library command for 8356965697444416280-25px009
   Reading /var/zope2/var/LatexWiki/8356965697444416280-25px009.asy
   Ddd is now explicitly exposed in frame initial 
   Ddd will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/8356965697444416280-25px009

axiom

bar4(4)

(3)

Type: PositiveInteger

calling functions with tuple --Bill Page, Thu, 22 May 2008 08:24:21 -0700 reply

aldor

#pile
#include "axiom"

Eee: with
    bar5: Integer -> Integer
  == add
    foo(x:Tuple Integer):Integer == 1
    foo(x:Integer,y:Integer):Integer == 2
    bar5(z:Integer):Integer == foo(1)+foo(1,2)+foo(1,2,3)

aldor

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/7154599798421986088-25px011.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'
"/var/zope2/var/LatexWiki/7154599798421986088-25px011.as", line 9: 
    bar5(z:Integer):Integer == foo(1)+foo(1,2)+foo(1,2,3)
......................................^
[L9 C39] #2 (Error) There are 2 meanings for the operator `foo'.
        Meaning 1: (x: Tuple(Integer)) -> Integer
        Meaning 2: (x: Integer, y: Integer) -> Integer

   The )library system command was not called after compilation.

axiom

bar5(1)

   There are no library operations named bar5
      Use HyperDoc Browse or issue
                                )what op bar5
      to learn if there is any operation containing " bar5 " in its
      name.

   Cannot find a definition or applicable library operation named bar5
      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.

unnamed function arguments --Bill Page, Thu, 22 May 2008 10:26:36 -0700 reply

In SPAD a reference to #1, #2, in an expression denotes an anonymous function. E.g. #1 + #1 is the same as writing:

x +-> x + x

spad

)abbrev domain FFF Fff
Fff: with
    bar7: () -> (Integer -> Integer)
    bar8: () -> ((Integer,Integer) -> Integer)
  == add
    bar7 == #1 + #1
    bar8 == (#1 * #1) + (#2 * #2)

spad

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/712240775020227376-25px013.spad using 
      old system compiler.
   FFF abbreviates domain Fff 
------------------------------------------------------------------------
   initializing NRLIB FFF for Fff 
   compiling into NRLIB FFF 
   compiling exported bar7 : () -> Integer -> Integer
Time: 0.01 SEC.

   compiling exported bar8 : () -> (Integer,Integer) -> Integer
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |Fff| REDEFINED

;;;     ***       |Fff| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor Fff
      Time: 0.01 seconds

   finalizing NRLIB FFF 
   Processing Fff for Browser database:
--->-->Fff((bar7 ((Mapping (Integer) (Integer))))): Not documented!!!!
--->-->Fff((bar8 ((Mapping (Integer) (Integer) (Integer))))): Not documented!!!!
--->-->Fff(constructor): Not documented!!!!
--->-->Fff(): Missing Description
------------------------------------------------------------------------
   Fff is now explicitly exposed in frame initial 
   Fff will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/FFF.NRLIB/code

axiom

bar7()(3)

(4)

Type: PositiveInteger

axiom

bar7x() == x +-> x + x

Type: Void

axiom

bar7x()(3)

axiom

Compiling function bar7x with type () -> AnonymousFunction

(5)

Type: PositiveInteger

axiom

bar8()(3,4)

(6)

Type: PositiveInteger

axiom

bar8x() == (x,y) +-> x*x + y*y

Type: Void

axiom

bar8x()(3,4)

axiom

Compiling function bar8x with type () -> AnonymousFunction

(7)

Type: PositiveInteger

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