Meta-circular Abstract Interpretation in Prolog

We give an introduction to the meta-circular approach to the abstract interpretation of logic programs. This approach is particularly useful for prototyping and for introductory classes on abstract interpretation. Using interpreters, students can immediately write, adapt, and experiment with interpreters and working dataflow analysers. We use a simple meta-circular interpreter, based on a “non-ground T_P” semantics, as a generic analysis engine. Instantiating the engine is a matter of providing an appropriate domain of approximations, together with definitions of “abstract” unification and disjunction. Small changes of the interpreter let us vary both what can be “observed” by an analyser, and how fixed point computation is done. Amongst the dataflow analyses used to exemplify this approach are a parity analysis, groundness dependency analysis, call patterns, depth-k analysis, and a “pattern” analysis to establish most specific generalisations of calls and success sets.