The syntax for declarations which have multiple variables is given on page 142 of the Axiom book. However, using this syntax inside a function results in the compiler failing.

The first time an attempt is made to compile a function which uses this syntax, no diagnostic is produced. However, the libraries needed by the function being compiled are not loaded, and the function itself is not executed (or at least it doesn't produce any output). If a second attempt is made to execute the function, a "System error" results.

The following session transcript demonstrates the problem. It attempts to execute two functions. The first of these, named "bug", demonstrates the behavior described above. The second function, named "nonbug", is identical to "bug" except that the declaration containing two variables has been replaced by two declarations each containing a single variable. Axiom handles the "nonbug" function correctly, demonstrating that the problem is triggered by a declaration containing multiple variables. The transcript follows:

$ axiom
                        AXIOM Computer Algebra System 
                         Version: Axiom (April 2006)
               Timestamp: Wednesday June 21, 2006 at 03:45:56 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------
   Re-reading compress.daase   Re-reading interp.daase
   Re-reading operation.daase
   Re-reading category.daase
   Re-reading browse.daase
(1) -> 
(1) -> bug(x) == (local a, b; (a, b) : Integer; 1)
                                                                   Type: Void
(2) -> bug(1)
   Compiling function bug with type PositiveInteger -> PositiveInteger 
(2) -> bug(1)
   >> System error:
   (|Tuple| |a| |b|) is not of type SYMBOL.

(2) -> nonbug(x) == (local c, d; c : Integer; d : Integer; 1)
                                                                   Type: Void
(3) -> nonbug(1)
   Compiling function nonbug with type PositiveInteger -> 
      PositiveInteger 
   Loading /home/ka/w/axiom/mnt/linux/algebra/PI.o for domain 
      PositiveInteger 
   Loading /home/ka/w/axiom/mnt/linux/algebra/NNI.o for domain 
      NonNegativeInteger 
   Loading /home/ka/w/axiom/mnt/linux/algebra/INT.o for domain Integer 
   Loading /home/ka/w/axiom/mnt/linux/algebra/OUTFORM.o for domain 
      OutputForm 
   Loading /home/ka/w/axiom/mnt/linux/algebra/LIST.o for domain List 
   (3)  1
                                                        Type: PositiveInteger
(4) -> )quit

nobug(x) == (local a, b; a, b : Integer; a:=b:=1; a+b)

nobug(1)

Compiling function nobug with type PositiveInteger -> Integer

(1)

bug(x) == (local a, b; (a, b) : Tuple Integer; a:=b:=1; a+b)

bug(1)

   Cannot convert right-hand side of assignment
   1

      to an object of the type Tuple(Integer) of the left-hand side.

Also, when I tried this in my Windows version, I got:

                        AXIOM Computer Algebra System
              Version of Tuesday November 30, 2004 at 21:11:14
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave AXIOM and return to shell.
-----------------------------------------------------------------------------

(1) -> bug(x) == (local a, b; (a, b) : Integer; 1)
                                                                   Type: Void
(2) ->   bug(1)
   Compiling function bug with type PositiveInteger -> PositiveInteger
   >> System error:
   (|Tuple| |a| |b|) is not of type SYMBOL.

protected-symbol-warn called with (NIL)

So the older version caught the syntax error on first compile and run. Your example seems to me to be a syntax error that was not caught in the current version on first compile and run (I was not able to find the (a,b):Integer in the Axiom book.) since (a,b) is a tuple. Correct syntax is a, b:Integer for multivariable declarations. Note that (a,b):Tuple Integer is incorrect syntax also, since (a,b) is not an indentifier.

(a,b):POLY INT

a:= 11

(2)

typeOf a

(3)

b:= 12

(4)

a+b

(5)

c,d:POLY INT

 LISP output:
(() ())

c:=11

(6)

d:=12

(7)

c+d

(8)

Why does c,d:POLY INT produce a Lisp output? and of type Tuple Void?

c,d: POLY INT

 LISP output:
(() ())

is a tuple, consisting of a symbol `c' and a declaration `d: POLY INT'. However, a declaration has type `Void', and since a Tuple is a homogeneous container, both component must be brought to a common type, which is `Void'. Thus we get a Tuple Void. But, a `Void' is not coercible to OutputForm?, therefore we get the LISP output. Try

2,3

(9)

My preference would be that we reject the declaration `(a,b): Integer' - which is invalid based on the above explanation. And we also reject `(a,b): Tuple Integer' because, if we do accept it, then we should logically -- for consistency -- accept `(a,b): Tuple Integer := tupleExpression'. But we have, in general, no way to know that the initializer has exactly two components, so we have an invitation for subtle errors.

Opinions?