This fails

(1) -> (Integer,Float)

 LISP output:
(UNPRINTABLE UNPRINTABLE)

Tuple Type

 LISP output:
(UNPRINTABLE)

But this works

List Type

(1)

The following domain called Domain provides some of the missing functionality. It is based on AldorDomain by Peter Broadbery who writes:

  [One] can still do some useful things with them by disguising
  the fact that they are domains, so in aldor have a type and
  your aldor programs can return this to axiom.

For example:

#include "axiom.as"

AldorDomain(T:Type): with {
      make: () -> %;
      coerce: (%) -> OutputForm;
} == add {
      Rep ==> Type;

      make(): % == per T;

      coerce(t: %): OutputForm == {
              import from SExpression;
              devaluate(t pretend SExpression)::OutputForm
      };

      import {
              BOOT_:_:devaluate: SExpression -> SExpression;
      } from Foreign Lisp;

      local devaluate(s: SExpression): SExpression == {
              BOOT_:_:devaluate(s);
      }
}

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5624154441249846913-25px004.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/5624154441249846913-25px004.as", line 1: 
#include "axiom.as"
^
[L1 C1] #1 (Error) Could not open file `axiom.as'.

   The )library system command was not called after compilation.

aInteger:=make()$AldorDomain(Integer)

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

   Cannot find a definition or applicable library operation named 
      AldorDomain with argument type(s) 
                                    Type

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Ref:

http://lists.nongnu.org/archive/html/axiom-developer/2005-09/msg00250.html

http://lists.nongnu.org/archive/html/axiom-developer/2005-09/msg00248.html

#include "axiom.as"

Domain: SetCategory == add {

        (a: %) = (b: %): Boolean == {
                import from SExpression;
                a pretend SExpression = b pretend SExpression
        }

        coerce(t: %): OutputForm == {
                import from SExpression;
                devaluate(t pretend SExpression)::OutputForm
        };

        import {
                BOOT_:_:devaluate: SExpression -> SExpression;
        } from Foreign Lisp;

        local devaluate(s: SExpression): SExpression == {
                BOOT_:_:devaluate(s);
        }
}

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/domain.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/domain.as", line 1: 
#include "axiom.as"
^
[L1 C1] #1 (Error) Could not open file `axiom.as'.

   The )library system command was not called after compilation.

And it nearly solves the problem!

a:=(Integer,Float)

 LISP output:
(UNPRINTABLE UNPRINTABLE)

Except:

  \begin{axiom}
  select(a,1)
  \end{axiom}

causes Axiom to abort.