This fails

axiom
(Integer,Float)

 LISP output:
(UNPRINTABLE UNPRINTABLE)

axiom
Tuple Type

 LISP output:
(UNPRINTABLE)

But this works

axiom
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:

aldor
#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/zope2/var/LatexWiki/5624154441249846913-25px004.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 
      ./5624154441249846913-25px004.lsp
   Issuing )library command for 5624154441249846913-25px004
   Reading /var/zope2/var/LatexWiki/5624154441249846913-25px004.asy
   AldorDomain is now explicitly exposed in frame initial 
   AldorDomain will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/5624154441249846913-25px004

axiom
aInteger:=make()$AldorDomain(Integer)

(2)

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

aldor
#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/zope2/var/LatexWiki/domain.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 ./domain.lsp
   Issuing )library command for domain
   Reading /var/zope2/var/LatexWiki/domain.asy
   Domain is now explicitly exposed in frame initial 
   Domain will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/domain

And it nearly solves the problem!

axiom
a:=(Integer,Float)

(3)

Except:

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

causes Axiom to abort.