Closures on CPOs Form Complete Lattices

Information and Computation

Volumn 152, Issue 2, 1999, Pages 236-249

  Ranzato, Francesco ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Abstract interpretation; Closure operator; Complete lattice; CPO; Domain theory

Indexed keywords

EID: 0347565240     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1006/inco.1999.2801     Document Type: Article

References (32)

1. Abramsky, S. (1999), Personal communication, March.
2. Abramsky, S., and Jung, A. (1994), Domain theory, in "Handbook of Logic in Computer Science" (S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, Eds.), Vol. 3, pp. 1-168, Clarendon, Oxford.
3. Abramsky, S., and Melliès, P.-A. (1999), Concurrent games and full completeness, in "Proc. of the 14th IEEE Symp. on Logic in Computer Science (LICS '99)," IEEE Comput. Soc. Press, Los Alamitos, CA.
4. Borceux, F., and Kelly, G. M. (1987), On locales and localizations, J. Pure Appl. Algebra 46, 1-34.
5. Cortesi, A., Filé, G., Giacobazzi, R., Palamidessi, C., and Ranzato, F. (1997), Complementation in abstract interpretation, ACM Trans. Program. Lang. Syst. 19(1), 7-47.
6. Cousot, P. (1996), Abstract interpretation, ACM Comput. Surv. 28(2), 324-328.
7. Cousot, P., and Cousot, R. (1977), Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints, in "Conference Record of the 4th ACM Symp. on Principles of Programming Languages (POPL '77)," pp. 238-252, ACM Press, New York.
8. Cousot, P., and Cousot, R. (1979a), A constructive characterization of the lattices of all retractions, preclosure, quasi-closure and closure operators on a complete lattice, Portugal. Math. 38(2), 185-198.
9. Cousot, P., and Cousot, R. (1979b), Systematic design of program analysis frameworks, in "Conference Record of the 6th ACM Symp. on Principles of Programming Languages (POPL '79)," pp. 269-282, ACM Press, New York.
10. Davey, B. A., and Priestley, H. A. (1990), "Introduction to Lattices and Order," Cambridge Univ. Press, Cambridge, UK.
11. Escardó, M. H. (1998), Properly injective spaces and function spaces, Topology Appl. 75(1-2), 75-120.
12. Falaschi, M., Gabbrielli, M., Marriott, K., and Palamidessi, C. (1997), Constraint logic programming with dynamic scheduling: a semantics based on closure operators, Inform. and Comput. 137(1), 41-67.
13. Filé, G., Giacobazzi, R., and Ranzato, F. (1996), A unifying view of abstract domain design, ACM Comput. Surv. 28(2) 333-336.
14. Filé, G., and Ranzato, F. (1996), Complementation of abstract domains made easy, in "Proc. of the 1996 Joint Internat. Conf. and Symp. on Logic Programming (JIC SLP '96)" (M. Maher, Ed.), pp. 348-362, The MIT Press, Cambridge, MA.
15. Germano, G. M., and Mazzanti, S. (1991), Closure functions and general iterates as reflectors (Fundamental Study), Theoret. Comput. Sci. 82, 215-252.
16. Giacobazzi, R., Palamidessi, C., and Ranzato, F. (1996), Weak relative pseudo-complements of closure operators, Algebra Universalis 36(3), 405-412.
17. Giacobazzi, R., and Ranzato, F. (1998a), Optimal domains for disjunctive abstract interpretation, Sci. Comput. Program. 32(1-3), 177-210.
18. Giacobazzi, R., and Ranzato, F. (1998b), Uniform closures: order-theoretically reconstructing logic program semantics and abstract domain refinements, Inform. and Comput. 145(2), 153-190.
19. Giacobazzi, R., Ranzato, F., and Scozzari, F. (1998), Complete abstract interpretations made constructive, in "Proc. of the 23rd Internat. Symp. on Mathematical Foundations of Computer Science (MFCS '98)" (L. Brim, J. Gruska, and J. Zlatuška, Eds.), Lecture Notes in Computer Science, Vol. 1450, pp. 366-377, Springer-Verlag, Berlin.
20. Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M., and Scott, D. S. (1980), "A Compendium of Continuous Lattices," Springer-Verlag, Berlin.
21. Hawrylycz, M., and Reiner, V. (1993), The lattice of closure relations on a poset, Algebra Universalis 30(3), 301-310.
22. Jensen, T. (1997), Disjunctive program analysis for algebraic data types, ACM Trans. Program. Lang. Syst. 19(5), 751-803.
23. Monteiro, A., and Ribeiro, H. (1942), L'opération de fermeture et ses invariants dans les systèmes partiellement ordonnés, Portugal. Math. 3(3), 171-184.
24. Morgado, J. (1960), Some results on the closure operators of partially ordered sets, Portugal. Math. 19(2), 101-139.
25. Mycroft, A. (1981), "Abstract Interpretation and Optimising Transformations for Applicative Programs," Ph.D. thesis, CST-15-81, Univ. of Edinburgh, Edinburgh, Scotland.
26. Mycroft, A., and Nielson, F. (1983), Strong abstract interpretation using power domains, in "Proc. of the 10th Internat. Colloq. on Automata, Languages and Programming (ICALP '83)" (J. Díaz, Ed.), Lecture Notes in Computer Science, Vol. 154, pp. 536-547, Springer-Verlag, Berlin.
27. Nielson, F. (1984), "Abstract Interpretation Using Domain Theory," Ph.D. thesis, CST-31-84, Univ. of Edinburgh, Edinburgh, Scotland.
28. Pataraia, D. (1997), A constructive proof of the fixed-point theorem for CPOs, unpublished talk, given at the "65th Meeting of the Peripathetic Seminar on Sheaves and Logic (PSSL65), Aarhus, Denmark."
29. Plotkin, G. D. (1977), A powerdomain construction, SIAM J. Comput. 5(3), 452-487.
30. Ranzato, F. (1998), On Morgado's notion of relative quasi-infimum, manuscript, Dipartimento di Matematica, Università di Padova, Italy.
31. Sanchis, L. E. (1977), Data types as lattices: retractions, closures and projections, RAIRO Informat. Théor. 11(4), 329-344.
32. Ward, M. (1942), The closures operators of a lattices, Ann. of Math. 43(2), 191-196.