The Law and Hilbert's tenth problem
-----------------------------------

If we can verify the object version of the Law at compile-time,
we have an algorithm for Hilbert's tenth problem 
(given a multivariable polynomial,
is there a solution in the integers) which
is known to be undecidable. Therefore, the object version of the
Law cannot be checked at compile-time.

Consider: 

; A = <x> B.
(defmethod (A :m) ()
  (send (send self ':get-x a1 a2 ... an) ':m))

;METHOD (self : A, a1, a2, ... , an : $integer) : B.
(defmethod (A :get-x) (a1 a2 ... an)
  (if (= (poly a1 a2 ... an) 0) then (send *p* ':y) else x))
; *p* is an instance of P = <y> B ...
; poly is a polynomial in n variables with integer coefficients.
; we assume there are no shared objects

Note that if the method get-x is in good style then
the polynomial does not have any zeros in the integers.

I suggest that we put a summary of this into the OOPSLA paper as
the motivation for the current formulation.

-- Karl