  This paper describes an approach to the methodology of answer set programming
(ASP) that can facilitate the design of encodings that are easy to understand
and provably correct. Under this approach, after appending a rule or a small
group of rules to the emerging program we include a comment that states what
has been "achieved" so far. This strategy allows us to set out our
understanding of the design of the program by describing the roles of small
parts of the program in a mathematically precise way.
