This fails in SPAD:

(1) -> <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)

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.

)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)

   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 13 FEB 2025 07:44:28 PM):

; wrote /var/aw/var/LatexWiki/AAA0.NRLIB/AAA0.fasl
; compilation finished in 0:00:00.008
------------------------------------------------------------------------
   Aaa0 is now explicitly exposed in frame initial 
   Aaa0 will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/AAA0.NRLIB/AAA0

bar0(3)

(1)

But it works in 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)

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3603377070621137033-25px005.as
      using Aldor compiler and options 
-O -Fasy -Fao -Flsp -lfricas -Mno-ALDOR_W_WillObsolete -DFriCAS -Y $FRICAS/algebra -I $FRICAS/algebra
      Use the system command )set compiler args to change these 
      options.
"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/3603377070621137033-25px005.as", line 2: 
#include "axiom"
^
[L2 C1] #1 (Error) Could not open file `axiom'.

   The )library system command was not called after compilation.

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.

#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)

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2796111966566536169-25px007.as
      using Aldor compiler and options 
-O -Fasy -Fao -Flsp -lfricas -Mno-ALDOR_W_WillObsolete -DFriCAS -Y $FRICAS/algebra -I $FRICAS/algebra
      Use the system command )set compiler args to change these 
      options.
"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/2796111966566536169-25px007.as", line 2: 
#include "axiom"
^
[L2 C1] #1 (Error) Could not open file `axiom'.

   The )library system command was not called after compilation.

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.

#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)

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8356965697444416280-25px009.as
      using Aldor compiler and options 
-O -Fasy -Fao -Flsp -lfricas -Mno-ALDOR_W_WillObsolete -DFriCAS -Y $FRICAS/algebra -I $FRICAS/algebra
      Use the system command )set compiler args to change these 
      options.
"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8356965697444416280-25px009.as", line 2: 
#include "axiom"
^
[L2 C1] #1 (Error) Could not open file `axiom'.

   The )library system command was not called after compilation.

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.

#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)

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7154599798421986088-25px011.as
      using Aldor compiler and options 
-O -Fasy -Fao -Flsp -lfricas -Mno-ALDOR_W_WillObsolete -DFriCAS -Y $FRICAS/algebra -I $FRICAS/algebra
      Use the system command )set compiler args to change these 
      options.
"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7154599798421986088-25px011.as", line 2: 
#include "axiom"
^
[L2 C1] #1 (Error) Could not open file `axiom'.

   The )library system command was not called after compilation.

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.