Analysis of Downward Closed Properties of Logic Programs

We study the analysis of downward closed properties of logic programs, which are a very abstract presentation of types. We generalise to a very large class of downward closed properties the construction of the traditional domains for groundness analysis in such a way that the results enjoy the good properties of that domain. Namely, we obtain abstract domains with a clear representation made of logical formulas and with optimal and well-known abstract operations. Moreover, they can be built using the linear refinement technique, and, therefore, are provably optimal and enjoy the condensing property, which is very important for a goal-independent analysis.