Computing Abstract Distances in Logic Programs

Abstract interpretation is a well-established technique for performing static analyses of logic programs. However, choosing the abstract domain, widening, fixpoint, etc. that provides the best precision-cost trade-off remains an open problem. This is in a good part because of the challenges involved in measuring and comparing the precision of different analyses. We propose a new approach for measuring such precision, based on defining distances in abstract domains and extending them to distances between whole analyses of a given program, thus allowing comparing precision across different analyses. We survey and extend existing proposals for distances and metrics in lattices or abstract domains, and we propose metrics for some common domains used in logic program analysis, as well as extensions of those metrics to the space of whole program analyses. We implement those metrics within the CiaoPP framework and apply them to measure the precision of different analyses on both benchmarks and a realistic program.