Optimal domains for disjunctive abstract interpretation

Science of Computer Programming

Volumn 32, Issue 1-3, 1998, Pages 177-210

  Giacobazzi, Roberto ^a   Ranzato, Francesco ^b  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Abstract interpretation; Closure operator; Disjunctive abstract domain; Functional and logic programming; Least disjunctive basis

Indexed keywords

LOGIC PROGRAMMING; MATHEMATICAL OPERATORS; OPTIMIZATION;

ABSTRACT INTERPRETATION THEORY; FUNCTIONAL PROGRAMMING;

COMPUTER PROGRAMMING LANGUAGES;

EID: 0032163337     PISSN: 01676423     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-6423(97)00034-8     Document Type: Article

References (37)

1. T. Armstrong, K. Marriott, P. Schachte, H. Søndergaard, Boolean functions for dependency analysis: algebraic properties and efficient representation, in: B. Le Charlier (Ed.), Proc. 1st Internat. Static Analysis Symp. (SAS '94), Lecture Notes in Computer Science, Vol. 864, Springer, Berlin, 1994, pp. 266-280.
2. R. Balbes, P. Dwinger, Distributive Lattices, University of Missouri Press, Columbia, Missouri, 1974.
3. R. Barbuti, R. Giacobazzi, G. Levi, A general framework for semantics-based bottom-up abstract interpretation of logic programs, ACM Trans. Program. Lang. Syst. 15 (1) (1993) 133-181.
4. G. Birkhoff, Lattice Theory, 3rd ed., AMS Colloquium Publication, Providence, RI, 1967.
5. A. Cortesi, G. Filé, R. Giacobazzi, C. Palamidessi, F. Ranzato, Complementation in abstract interpretation, ACM Trans. Program. Lang. Syst. 19 (1) (1997) 7-47. A preliminary version appeared in Proc. SAS '95.
6. A. Cortesi, G. Filé, W. Winsborough, Optimal groundness analysis using propositional logic, J. Logic Programming 27 (2) (1996) 137-167.
7. P. Cousot, Méthodes itératives de construction et d'approximation de points fixes d'opérateurs monotones sur un treillis, analyse sémantique des programmes, Ph.D. Thesis, Université Scientifique et Médicale de Grenoble, 1978.
8. P. Cousot, Abstract interpretation, ACM Comput. Survey 28 (2) (1996) 324-328.
9. P. Cousot, Program analysis: the abstract interpretation perspective, ACM Comput. Survey 28 (4) (1996).
10. P. Cousot, Types as abstract interpretations (invited paper), in: Conf. Record of the 24th ACM Symp. on Principles of Programming Languages (POPL '97), ACM Press, New York, 1997, pp. 316-331.
11. P. Cousot, R. Cousot, Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints, in: Conf. Record of the 4th ACM Symp. on Principles of Programming Languages (POPL '77), ACM Press, New York, 1977, pp. 238-252.
12. P. Cousot, R. Cousot, Systematic design of program analysis frameworks, in: Conference Record of the 6th ACM Symp. on Principles of Programming Languages (POPL '79), ACM Press, New York, 1979, pp. 269-282.
13. P. Cousot, R. Cousot, Abstract interpretation and application to logic programs, J. Logic Programming 13 (2-3) (1992) 103-179.
14. P. Cousot, R. Cousot, Inductive definitions, semantics and abstract interpretation, in: Conf. Record of the 19th ACM Symp. on Principles of Programming Languages (POPL '92), ACM Press, New York, 1992, pp. 83-94.
15. P. Cousot, R. Cousot, Higher-order abstract interpretation (and application to comportment analysis generalizing strictness, termination, projection and PER analysis of functional languages), in: Proc. IEEE Internat. Conf. on Computer Languages (ICCL '94), IEEE Computer Society Press, Los Alamitos, CA, 1994, pp. 95-112.
16. P. Dart, On derived dependencies and connected databases, J. Logic Programming 11 (2) (1991) 163-188.
17. G. Filé, R. Giacobazzi, F. Ranzato, A unifying view of abstract domain design, ACM Comput. Survey 28 (2) (1996) 333-336.
18. G. Filé, F. Ranzato, Improving abstract interpretations by systematic lifting to the powerset, in: M. Bruynooghe (Ed.), Proc. 1994 Internat. Logic Programming Symp. (ILPS '94), MIT Press, Cambridge, MA, 1994, pp. 655-669.
19. G. Filé, F. Ranzato, The powerset operator on abstract interpretations, Theor. Comput. Sci., to appear.
20. G. Filé, F. Ranzato, Complementation of abstract domains made easy, in: M. Maher (Ed.), Proc. 1996 Joint Internat. Conf. and Symp. on Logic Programming (JICSLP '96), MIT Press, Cambridge, MA, 1996, pp. 348-362.
21. R. Giacobazzi, C. Palamidessi, F. Ranzato, Weak relative pseudo-complements of closure operators, Algebra Universalis 36 (3) (1996) 405-412.
22. R. Giacobazzi, F. Ranzato, Functional dependencies and Moore-set completions of abstract interpretations and semantics, in: J. Lloyd (Ed.), Proc. 1995 Internat. Logic Programming Symp. (ILPS '95), MIT Press, Cambridge, MA, 1995, pp. 321-335.
23. R. Giacobazzi, F. Ranzato, Complementing logic program semantics, in: M. Hanus, M. Rodríguez Artalejo (Eds.), Proc. 5th Internat. Conf. on Algebraic and Logic Programming (ALP '96), Lecture Notes in Computer Science, Vol. 1139, Springer, Berlin, 1996, pp. 238-253.
24. G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, D.S. Scott, A Compendium of Continuous Lattices, Springer, Berlin, 1980.
25. S. Hunt, PERs generalize projections for strictness analysis, in: S.P. Jones, G. Hutton, C.K. Holst, (Eds.), Proc. 1990 Glasgow Functional Programming Workshop, Workshops in Computing, Springer, Berlin, 1990, pp. 156-168.
26. T.P. Jensen, Disjunctive strictness analysis, in: Proc. 7th IEEE Symp. on Logic in Computer Science (LICS '92), IEEE Computer Society Press, Los Alamitos, CA, 1992, pp. 174-185.
27. N.D. Jones, S.S. Muchnick, Complexity of flow analysis, inductive assertion synthesis and a language due to Dijkstra, in: S.S. Muchnick, N.D. Jones, (Eds.), Program Flow Analysis: Theory and Applications, Prentice-Hall, Englewood Cliffs, NJ, 1981, pp. 380-393.
28. K. Marriott, H. Søndergaard, Precise and efficient groundness analysis for logic programs, ACM Lett. Program. Lang. Syst. 2 (1-4) (1993) 181-196.
29. J. Morgado, Some results on the closure operators of partially ordered sets, Portug. Math. 19 (2) (1960) 101-139.
30. A. Mycroft, The theory and practice of transforming call-by-need into call-by-value, in: B. Robinet (Ed.), Proc. 4th Internat. Symp. on Programming, Lecture Notes in Computer Science, Vol. 83, Springer, Berlin, 1980, pp. 270-281.
31. A. Mycroft, Abstract Interpretation and Optimising Transformations for Applicative Programs, Ph.D. Thesis, CST-15/81, Univ. of Edinburgh, 1981.
32. A. Mycroft, F. Nielson, Strong abstract interpretation using power domains, in: J. Diaz (Ed.), Proc. 10th Internat. Colloq. on Automata, Languages and Programming (ICALP '83), Lecture Notes in Computer Science, Vol. 154, Springer, Berlin, 1983, pp. 536-547.
33. F. Nielson, Abstract interpretation using domain theory, Ph.D. Thesis, CST-31/84, Univ. of Edinburgh, 1984.
34. F. Nielson., Expected forms of data flow analysis, in: H. Ganzinger, N.D. Jones (Eds.), Programs as Data Objects, Lecture Notes in Computer Science, Vol. 217, Springer, Berlin, 1986, pp. 192-205.
35. P. Wadler, R.J.M. Hughes, Projections for strictness analysis, in: G. Kahn (Ed.), Proc. Internat. Conf. on Functional Programming Languages and Computer Architecture (FPCA '87), Lecture Notes in Computer Science, Vol. 274, Springer, Berlin, 1987, pp. 385-407.
36. M. Ward, The closure operators of a lattice, Ann. Math. 43 (2) (1942) 191-196.
37. K. Yi, W.L. Harrison, Automatic generation and management of interprocedural program analyses, in: Conf. Record of the 20th ACM Symp. on Principles of Programming Languages (POPL '93), ACM Press, New York, 1993, pp. 246-259.