In the paper we discuss some of the problems. This class includes all domains, but also the ordered group of integer numbers and the ordered semigroup of natural numbers, and some other domains. We show, however, that these results cannot be transferred to arbitrary infinite states. We prove that safe -programs do not have any effective syntax. Open questions 1.
Further work needs to be done for integer numbers.
In general, we conjecture that if, for an expansion of or another expanded domain, the first order theory of the expanded domain is decidable and locally generic extended queries do not express more than restricted ones, then there is an effective translation algorithm. We conjecture that if, in an expansion of , locally generic extended queries express more than restricted ones, the first order theory of the expanded domain is undecidable. A specific open problem is, can it be done for linear constraints with at least one constant over rational or real numbers.