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SandBoxOverloading

Edit detail for SandBoxOverloading revision 7 of 8

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Editor: Bill Page Time: 2008/05/22 11:09:45 GMT-7
Note: anonymous functions with unnamed arguments

added:
    bar8: () -> ((Integer,Integer) -> Integer)

added:
    bar8 == (#1 * #1) + (#2 * #2)

changed:
-bar8() == x +-> x + x
-bar8()(3)
bar7x() == x +-> x + x
bar7x()(3)
bar8()(3,4)
bar8x() == (x,y) +-> x*x + y*y
bar8x()(3,4)

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/lib/zope2.10/instance/axiom-wiki/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 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)

fricas

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/lib/zope2.10/instance/axiom-wiki/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(constructor): Not documented!!!!
--->-->Aaa0((bar0 ((Integer) (Integer)))): Not documented!!!!
--->-->Aaa0((foo ((Integer) (Integer)))): Not documented!!!!
--->-->Aaa0((foo ((Integer) (Float)))): Not documented!!!!
--->-->Aaa0(): Missing Description
; compiling file "/var/aw/var/LatexWiki/AAA0.NRLIB/AAA0.lsp" (written 31 JUL 2013 04:47:33 PM):

; /var/aw/var/LatexWiki/AAA0.NRLIB/AAA0.fasl written
; compilation finished in 0:00:00.018
------------------------------------------------------------------------
   Aaa0 is now explicitly exposed in frame initial 
   Aaa0 will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/AAA0.NRLIB/AAA0

fricas

bar0(3)

$\label{eq1}3$

(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/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3603377070621137033-25px005.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.
#1 (Warning) Could not use archive file `libaxiom.al'.
#2 (Warning) Could not use archive file `libaxiom.al'.
"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 4: 
import from AxiomLib;
............^
[L4 C13] #3 (Error) No meaning for identifier `AxiomLib'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 15: 
import { true: %, false: % } from Boolean;
..................................^
[L15 C35] #4 (Error) No meaning for identifier `Boolean'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 17: 
        string:         Literal -> %;
........................^.......^
[L17 C25] #5 (Error) No meaning for identifier `Literal'.
[L17 C33] #6 (Error) There are no suitable meanings for the operator `->'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 18: 
} from String;
.......^
[L18 C8] #8 (Error) No meaning for identifier `String'.

"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3603377070621137033-25px005.as", line 5: 
    bar2: Integer -> Integer
..........^.......^..^
[L5 C11] #9 (Error) No meaning for identifier `Integer'.
[L5 C19] #10 (Error) There are no suitable meanings for the operator `->'.
[L5 C22] #11 (Error) No meaning for identifier `Integer'.

"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3603377070621137033-25px005.as", line 13: 
    bar2(z:Integer):Integer == foo(x)+foo(y)
...........^
[L13 C12] #12 (Error) No meaning for identifier `Integer'.
[L13 C12] #13 (Fatal Error) Too many errors (use `-M emax=n' or `-M no-emax' to change the limit).

   The )library system command was not called after compilation.

fricas

bar2(3)

   There are no library operations named bar2 
      Use HyperDoc Browse or issue
                                )what op bar2
      to learn if there is any operation containing " bar2 " in its 
      name.

   Cannot find a definition or applicable library operation named bar2 
      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"

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/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2796111966566536169-25px007.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.
#1 (Warning) Could not use archive file `libaxiom.al'.
#2 (Warning) Could not use archive file `libaxiom.al'.
"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 4: 
import from AxiomLib;
............^
[L4 C13] #3 (Error) No meaning for identifier `AxiomLib'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 15: 
import { true: %, false: % } from Boolean;
..................................^
[L15 C35] #4 (Error) No meaning for identifier `Boolean'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 17: 
        string:         Literal -> %;
........................^.......^
[L17 C25] #5 (Error) No meaning for identifier `Literal'.
[L17 C33] #6 (Error) There are no suitable meanings for the operator `->'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 18: 
} from String;
.......^
[L18 C8] #8 (Error) No meaning for identifier `String'.

"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2796111966566536169-25px007.as", line 5: 
    bar3: Integer -> Integer
..........^.......^..^
[L5 C11] #9 (Error) No meaning for identifier `Integer'.
[L5 C19] #10 (Error) There are no suitable meanings for the operator `->'.
[L5 C22] #11 (Error) No meaning for identifier `Integer'.

"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2796111966566536169-25px007.as", line 13: 
    bar3(z:Integer):Integer == foo(a)+foo(a)
...........^
[L13 C12] #12 (Error) No meaning for identifier `Integer'.
[L13 C12] #13 (Fatal Error) Too many errors (use `-M emax=n' or `-M no-emax' to change the limit).

   The )library system command was not called after compilation.

fricas

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/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8356965697444416280-25px009.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.
#1 (Warning) Could not use archive file `libaxiom.al'.
#2 (Warning) Could not use archive file `libaxiom.al'.
"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 4: 
import from AxiomLib;
............^
[L4 C13] #3 (Error) No meaning for identifier `AxiomLib'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 15: 
import { true: %, false: % } from Boolean;
..................................^
[L15 C35] #4 (Error) No meaning for identifier `Boolean'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 17: 
        string:         Literal -> %;
........................^.......^
[L17 C25] #5 (Error) No meaning for identifier `Literal'.
[L17 C33] #6 (Error) There are no suitable meanings for the operator `->'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 18: 
} from String;
.......^
[L18 C8] #8 (Error) No meaning for identifier `String'.

"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8356965697444416280-25px009.as", line 5: 
    bar4: Integer -> Integer
..........^.......^..^
[L5 C11] #9 (Error) No meaning for identifier `Integer'.
[L5 C19] #10 (Error) There are no suitable meanings for the operator `->'.
[L5 C22] #11 (Error) No meaning for identifier `Integer'.

"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8356965697444416280-25px009.as", line 13: 
    bar4(z:Integer):Integer == foo(a@Integer)+foo(a@Float)
...........^
[L13 C12] #12 (Error) No meaning for identifier `Integer'.
[L13 C12] #13 (Fatal Error) Too many errors (use `-M emax=n' or `-M no-emax' to change the limit).

   The )library system command was not called after compilation.

fricas

bar4(4)

   There are no library operations named bar4 
      Use HyperDoc Browse or issue
                                )what op bar4
      to learn if there is any operation containing " bar4 " in its 
      name.

   Cannot find a definition or applicable library operation named bar4 
      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.

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/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7154599798421986088-25px011.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.
#1 (Warning) Could not use archive file `libaxiom.al'.
#2 (Warning) Could not use archive file `libaxiom.al'.
"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 4: 
import from AxiomLib;
............^
[L4 C13] #3 (Error) No meaning for identifier `AxiomLib'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 15: 
import { true: %, false: % } from Boolean;
..................................^
[L15 C35] #4 (Error) No meaning for identifier `Boolean'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 17: 
        string:         Literal -> %;
........................^.......^
[L17 C25] #5 (Error) No meaning for identifier `Literal'.
[L17 C33] #6 (Error) There are no suitable meanings for the operator `->'.

"/usr/local/aldor/linux/1.1.0/include/axiom.as", line 18: 
} from String;
.......^
[L18 C8] #8 (Error) No meaning for identifier `String'.

"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7154599798421986088-25px011.as", line 5: 
    bar5: Integer -> Integer
..........^.......^..^
[L5 C11] #9 (Error) No meaning for identifier `Integer'.
[L5 C19] #10 (Error) There are no suitable meanings for the operator `->'.
[L5 C22] #11 (Error) No meaning for identifier `Integer'.

"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7154599798421986088-25px011.as", line 9: 
    bar5(z:Integer):Integer == foo(1)+foo(1,2)+foo(1,2,3)
...........^
[L9 C12] #12 (Error) No meaning for identifier `Integer'.
[L9 C12] #13 (Fatal Error) Too many errors (use `-M emax=n' or `-M no-emax' to change the limit).

   The )library system command was not called after compilation.

fricas

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/lib/zope2.10/instance/axiom-wiki/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 SEC.

   compiling exported bar8 : () -> (Integer,Integer) -> Integer
****** comp fails at level 3 with expression: ******
error in function bar8 

(+ (* |#1| |#1|) (* | << | (|#| 2) | >> | (|#| 2)))
****** level 3  ******
$x:= (# 2)
$m:= $EmptyMode
$f:=
((((|#2| #) (|#1| #) (|$Information| #) (|bar8| #) ...)))

   >> Apparent user error:
   cannot compile (# 2)

fricas

bar7()(3)

   There are no library operations named bar7 
      Use HyperDoc Browse or issue
                                )what op bar7
      to learn if there is any operation containing " bar7 " in its 
      name.

   Cannot find a no-argument definition or library operation named bar7
      .
bar7x() == x +-> x + x

Type: Void

fricas

bar7x()(3)

fricas

Compiling function bar7x with type () -> AnonymousFunction

$\label{eq2}6$

(2)

Type: PositiveInteger?

fricas

bar8()(3,4)

   There are no library operations named bar8 
      Use HyperDoc Browse or issue
                                )what op bar8
      to learn if there is any operation containing " bar8 " in its 
      name.

   Cannot find a no-argument definition or library operation named bar8
      .
bar8x() == (x,y) +-> x*x + y*y

Type: Void

fricas

bar8x()(3,4)

fricas

Compiling function bar8x with type () -> AnonymousFunction

$\label{eq3}25$

(3)

Type: PositiveInteger?