Abstract
A description in the Jacobs and Langen domain is a set of sharing groups where each sharing group is a set of program variables. The presence of a sharing group in a description indicates that all the variables in the group can be bound to terms that contain a common variable. The expressiveness of the domain, alas, is compromised by its intractability. Not only are descriptions potentially exponential in size, but abstract unification is formulated in terms of an operation, called closure under union, that is also exponential. This paper shows how abstract unification can be reformulated so that closures can be collapsed in two senses. Firstly, one closure operation can be folded into another so as to reduce the total number of closures that need to be computed. Secondly, the remaining closures can be applied to smaller descriptions. Therefore, although the operation remains exponential, the overhead of closure calculation is reduced. Experimental evaluation suggests that the cost of analysis can be substantially reduced by collapsing closures.
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References
Bagnara, R., Gori, R., Hill, P., Zaffanella, E.: Finite-Tree Analysis for Constraint Logic-Based Languages. Information and Computation 193(2), 84–116 (2004)
Bagnara, R., Hill, P., Zaffanella, E.: Set-Sharing is Redundant for Pair-Sharing. Theoretical Computer Science 277(1-2), 3–46 (2002)
Bagnara, R., Zaffanella, E., Hill, P.: Enhanced Sharing Analysis Techniques: A Comprehensive Evaluation. Theory and Practice of Logic Programming 5 (2005)
Bossi, A., Gabbrielli, M., Levi, G., Martelli, M.: The s-Semantics Approach: Theory and Applications. The Journal of Logic Programming 19, 149–197 (1994)
Bruynooghe, M.: A Practical Framework for the Abstract Interpretation of Logic Programs. The Journal of Logic Programming 10(2), 91–124 (1991)
Bueno, F., GarcÃa de la Banda, M.: Set-Sharing Is Not Always Redundant for Pair-Sharing. In: Kameyama, Y., Stuckey, P.J. (eds.) FLOPS 2004. LNCS, vol. 2998, pp. 117–131. Springer, Heidelberg (2004)
Codish, M.: Efficient Goal Directed Bottom-Up Evaluation of Logic Programs. The Journal of Logic Programming 38(3), 355–370 (1999)
Codish, M., Lagoon, V., Bueno, F.: An Algebraic Approach to Sharing Analysis of Logic Programs. The Journal of Logic Programming 42(2), 111–149 (2000)
Codish, M., Mulkers, A., Bruynooghe, M., GarcÃa de la Banda, M., Hermenegildo, M.: Improving Abstract Interpretations by Combining Domains. ACM TOPLAS 17(1), 28–44 (1995)
Codish, M., Søndergaard, H., Stuckey, P.: Sharing and Groundness Dependencies in Logic Programs. ACM TOPLAS 21(5), 948–976 (1999)
Falaschi, M., Levi, G., Palamidessi, C., Martelli, M.: Declarative Modeling of the Operational Behavior of Logic Languages. Theoretical Computer Science 69(3), 289–318 (1989)
Gallagher, J.: A Bottom-Up Analysis Toolkit. Technical Report 95-016, Department of Computer Science, University of Bristol (Invited paper at WAILL) (1995)
Hans, W., Winkler, S.: Aliasing and Groundness Analysis of Logic Programs through Abstract Interpretation and its Safety. Technical Report Nr. 92-27, RWTH Aachen, Lehrstuhl für Informatik II Ahornstraße 55, W-5100 Aachen (1992)
Jacobs, D., Langen, A.: Static Analysis of Logic Programs for Independent And-Parallelism. The Journal of Logic Programming 13(2 & 3), 291–314 (1992)
Li, X., King, A., Lu, L.: Correctness of Closure Collapsing. Technical Report 2-06, University of Kent (2006), http://www.cs.kent.ac.uk/pubs/2006/2370
Li, X., King, A., Lu, L.: Lazy Set-Sharing Analysis. In: Hagiya, M., Wadler, P. (eds.) FLOPS 2006. LNCS, vol. 3945, pp. 177–191. Springer, Heidelberg (2006)
Muthukumar, K., Hermenegildo, M.: Compile-Time Derivation of Variable Dependency Using Abstract Interpretation. The Journal of Logic Programming 13(2-3), 315–347 (1992)
Schachte, P., Søndergaard, H.: Closure Operators for ROBDDs. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 1–16. Springer, Heidelberg (2005)
Søndergaard, H.: An Application of Abstract Interpretation of Logic Programs: Occur Check Reduction. In: Robinet, B., Wilhelm, R. (eds.) ESOP 1986. LNCS, vol. 213, pp. 327–338. Springer, Heidelberg (1986)
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Li, X., King, A., Lu, L. (2006). Collapsing Closures. In: Etalle, S., Truszczyński, M. (eds) Logic Programming. ICLP 2006. Lecture Notes in Computer Science, vol 4079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11799573_13
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DOI: https://doi.org/10.1007/11799573_13
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