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International Symposium on Logic-Based Program Synthesis and Transformation

LOPSTR 2019: Logic-Based Program Synthesis and Transformation pp 57–72Cite as

Computing Abstract Distances in Logic Programs

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12042)

Abstract

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.

Keywords

  • Abstract interpretation
  • Static analysis
  • Logic programming
  • Metrics
  • Distances
  • Complete lattices
  • Program semantics

Research partially funded by MINECO TIN2015-67522-C3-1-R TRACES project, and the Madrid P2018/TCS-4339 BLOQUES-CM program. We are also grateful to the anonymous reviewers for their useful comments.

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Notes

  1. 1.

    Some of these attempts (and others) are further explained in the related work section (Sect. 6).

  2. 2.

    Actually that only guarantees that \(d'\) is a pseudo-metric. Proving that it is indeed a metric is more involved and not really relevant to our discussion.

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Authors and Affiliations

  1. IMDEA Software Institute, Madrid, Spain

    Ignacio Casso, José F. Morales, Pedro López-García, Roberto Giacobazzi & Manuel V. Hermenegildo

  2. T. University of Madrid (UPM), Madrid, Spain

    Ignacio Casso & Manuel V. Hermenegildo

  3. Spanish Council for Scientific Research (CSIC), Madrid, Spain

    Pedro López-García

  4. University of Verona, Verona, Italy

    Roberto Giacobazzi

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  1. Ignacio Casso
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  5. Manuel V. Hermenegildo
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Correspondence to Ignacio Casso .

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  1. University of Bologna, Bologna, Italy

    Prof. Dr. Maurizio Gabbrielli

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Casso, I., Morales, J.F., López-García, P., Giacobazzi, R., Hermenegildo, M.V. (2020). Computing Abstract Distances in Logic Programs. In: Gabbrielli, M. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2019. Lecture Notes in Computer Science(), vol 12042. Springer, Cham. https://doi.org/10.1007/978-3-030-45260-5_4

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