Analysis of Downward Closed Properties of Logic Programs
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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.
KeywordsAbstract interpretation domain theory linear refinement type theory type analysis logic programming
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- 2.G. Birkhoff. Lattice Theory. In AMS Colloquium Publication, third ed., 1967.Google Scholar
- 3.M. Codish and B. Demoen. Deriving Polymorphic Type Dependencies for Logic Programs Using Multiple Incarnations of Prop. In Proc. of the first International Symposium on Static Analysis, volume 864 of Lecture Notes in Computer Science, pages 281–296. Springer-Verlag, 1994.Google Scholar
- 4.M. Codish and V. Lagoon. Type Dependencies for Logic Programs Using ACI-Unification. In Proceedings of the 1996 Israeli Symposium on Theory of Computing and Systems, pages 136–145. IEEE Press, June 1996. Extended version to appear in Theoretical Computer Science.Google Scholar
- 5.A. Cortesi, G. Filè, and W. Winsborough. Prop Revisited: Propositional Formula as Abstract Domain for Groundness Analysis. In Proc. Sixth IEEE Symp. on Logic In Computer Science, pages 322–327. IEEE Computer Society Press, 1991.Google Scholar
- 7.P. Cousot and R. Cousot. Systematic Design of Program Analysis Frameworks. In Proc. 6th ACM Symp. on Principles of Programming Languages, pages 269–282, 1979.Google Scholar
- 9.N.J. Cutland. Computability: An Introduction to Recursive Function Theory. Cambridge University Press, 1980.Google Scholar
- 11.R. Giacobazzi, F. Ranzato, and F. Scozzari. Building Complete Abstract Interpretations in a Linear Logic-based Setting. In G. Levi, editor, Static Analysis, Proceedings of the 5th International Static Analysis Symposium SAS 98, volume 1503 of Lecture Notes in Computer Science, pages 215–229. Springer-Verlag, 1998.Google Scholar
- 12.Giorgio Levi and Fausto Spoto. An Experiment in Domain Refinement: Type Domains and Type Representations for Logic Programs. In Catuscia Palamidessi, Hugh Glaser, and Karl Meinke, editors, Principles of Declarative Programming, volume 1490 of Lecture Notes in Computer Science, pages 152–169, Pisa, Italy, September 1998. ©Springer-Verlag.CrossRefGoogle Scholar
- 15.F. Scozzari. Logical Optimality of Groundness Analysis. In P. Van Hentenryck, editor, Proceedings of the 4th International Static Analysis Symposium SAS’97, volume 1302 of Lecture Notes in Computer Science, pages 83–97. Springer-Verlag, 1997.Google Scholar
- 16.Jan-Georg Smaus, Patricia Hill, and Andy King. Mode Analysis for Typed Logic Programs. In Proc. of the LOPSTR’99 Workshop, pages 163–170, Venice, Italy, September 1999.Google Scholar