A general framework for semantics-based bottom-up abstract interpretation of logic programs

The theory of abstract interpretation provides a formal framework to develop advanced dataflow analysis tools. The idea is to define a nonstandard semantics which is able to compute, in finite time, an approximated model of the program. In this paper, we define an abstract interpretation framework based on a fixpoint approach to the semantics. This leads to the definition, by means of a suitable set of operators, of an abstract fixpoint characterization of a model associated with the program. Thus, we obtain a specializable abstract framework for bottom-up abstract interpretations of definite logic programs. The specialization of the framework is shown on two examples, namely, gound-dependence analysis and depth-kanalysis.