The Halting Problem for Deductive Synthesis of Logic Programs

Deductive synthesis methods derive programs in an incremental manner, and therefore pose a halting problem { when can synthesis stop with a correct program? We give a characterisation of this problem and state a halting principle as a solution. Another characteristic of deductive synthesis is that it may derive several correct programs, giving rise to another question { which correct programs are desirable? We show that the answer is related to the halting problem, via the notion of steadfast , or reusable, programs as desirable programs. Our work also reveals that Clark's idea of the completion of a program is central to deductive synthesis, since it is the basis of our halting principle and our notion of steadfast programs.