In OpenAxiom one should be able to write a function that returns a 'Category':

but we get the error message:
   Internal Error
   Interpreter code generation failed for expression
      (IF (= |#1| 0) |SetCategory| |Type|)


This is ok for functions that return 'Domain':



... --Bill Page,  Wed, 28 May 2008 17:07:17 -0700 reply
Axiom Version:  => /usr/local/lib/open-axiom/x86_64-unknown-linux/1.2.0-2008-05-25 

category valued functions --gdr,  Wed, 28 May 2008 17:52:23 -0700 reply
Because the function of categories is to oversee domains,
it is much much harder to have category valued functions
with the current compilation scheme.  

However, in the interpreter we should probably try to
accomodate for as much as we can because we can also
do a small step semantics, e.g. interpret literally the codes.
Going back to your problem, an issue here is with what the type of
Type should be.  Currently, OpenAxiom says that Type has type Type, 
instead of Category:

Another option might be to say that Type has type Category.  That
would make your function OK.  Note that the following works fine
?; Ring)
ST2 0
ST2 1
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fixed --gdr,  Wed, 28 May 2008 22:48:49 -0700 reply
Bill, your original example now works.

declarations require domains --Bill Page,  Thu, 29 May 2008 14:36:02 -0700 reply
Something is still inconsistent here:
  (1) -> ST(x:Integer):Category == (x=0 => SetCategory;Type)
   Function declaration ST : Integer -> Category has been added to
      workspace.
                                            Type: Void
  (2) -> A:=ST(0)
   Compiling function ST with type Integer -> Category

  ;;;     ***       |*1;ST;1;frame1392| REDEFINED
  ; (DEFUN |*1;ST;1;frame1392| ...) is being compiled.
  ;; The variable |*1;ST;1;frame1392;MV| is undefined.
  ;; The compiler will assume this variable is a global.

   (2)  SetCategory
                                            Type: Category
  (3) -> B:=ST(1)

   (3)  Type
                                            Type: Category
  (4) -> C:Category

   Category is a category, not a domain, and declarations require
      domains.
  (4) -> C:Category:=Ring

   Category is a category, not a domain, and declarations require
      domains.

  (4) -> C:=Ring

   (4)  Ring
                                               Type: Category

  (5) -> )display type C

   Type of value of C: Category

  (5) -> X:Domain:=Ring   -- Ring is not a domain

   (5)  Ring
                                               Type: Category


-------
If the type of a category-valued variable can be implicitly
made to be Category, it should also be possible to declare
this to be so.
... --gdr,  Thu, 29 May 2008 17:13:56 -0700 reply
well, that is the original restriction I inherited :-)

... --gdr,  Thu, 29 May 2008 17:15:33 -0700 reply
Status: open => fixed somewhere 

The code generation failure is fixed.  So, I don't
think is an issue any more.
Fixed --gdr,  Sun, 10 Aug 2008 15:27:15 -0700 reply
Status: fixed somewhere => closed 

This is OpenAxiom specific issue that is fixed.

Error: export AXIOM=/usr/local/lib/open-axiom/x86_64-unknown-linux/1.2.0-2008-05-25; export ALDORROOT=/usr/local/aldor/linux/1.1.0; export PATH=PATH; export HOME=/var/zope2/var/LatexWiki; ulimit -t 240; $AXIOM/bin/AXIOMsys < /var/zope2/var/LatexWiki/2099996685253644054-25px.axm
/bin/sh: /usr/local/lib/open-axiom/x86_64-unknown-linux/1.2.0-2008-05-25/bin/AXIOMsys: not found