Semantics of a sequential language for exact real-number computation

Proceedings - Symposium on Logic in Computer Science

Volumn 19, Issue , 2004, Pages 426-435

  Marcial Romero, J Raymundo ^a   Escardó, Martín H ^a  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ABSTRACTING; BOOLEAN FUNCTIONS; COMPUTATIONAL METHODS; DATA STRUCTURES; NUMBER THEORY; PROBLEM SOLVING; SEMANTICS;

REAL NUMBERS; SEQUENTIAL LANGUAGES;

COMPUTER PROGRAMMING LANGUAGES;

EID: 4544263677     PISSN: 10436871     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/lics.2004.1319637     Document Type: Conference Paper

References (29)

1. S. Abramsky and A. Jung. Domain theory. In S. Abram-sky, D. Gabbay, and T. S. E. Maibaum, editors, Handbook of Logic in Computer Science Volume 3, pages 1-168. Oxford University Press, 1994.
2. E. Bishop and D. Bridges. Constructive Analysis. Springer, Berlin, 1985.
3. H. Boehm and R. Cartwright. Exact real arithmetic: Formulating real numbres as functions. In Turner. D., editor, Research Topics in Functional Programming, pages 43-64, 1990.
4. P. Buneman, S. Davidson, and A. Watters. A semantics for complex objects and approximate queries. pages 305-314, 1988.
5. A. Edalat, P. J. Potts, and P. Sünderhauf. Lazy computation with exact real numbers. In International Conference on Functional Programming, pages 185-194, 1998.
6. M. H. Escardó. PCF extended with real numbers. Theoretical Computer Science, 162(1):79-115, 1996.
7. M. H. Escardó. Real PCF extended with ∃ is universal. In A. Edalat, S. Jourdan, and G. McCusker, editors, Advances in Theory and Formal Methods of Computing: Proceedings of the Third Imperial College Workshop, April 1996, pages 13-24, Christ Church, Oxford, 1996. IC Press.
8. M. H. Escardó, M. Hofmann, and T. Streicher. On the non-sequential nature of the interval-domain model of exact real-number computation. Mathematical Structures in Computer Science. Accepted for publication (2002).
9. M. H. Escardó and T. Streicher. Induction and recursion on the partial real line with applications to Real PCF. Theoretical Computer Science, 210(1):121-157, 1999.
10. A. Farjudian. Sequentially and piece-wise affinity in segments of real-pcf. ENTCS (to appear).
11. P. D. Gianantonio. A Functional Approach to Computability on Real Numbers. PhD thesis, Udine, 1993.
12. P. D. Gianantonio. An abstract data type for real numbers. Theoretical Computer Science, 221(1-2):295-326, 1999.
13. G. Gierz and et al. Continuous lattices and domains. Cambridge University Press, 2003.
14. C. A. Gunter. The mixed powerdomain. Theoretical Computer Science, 103(2):311-334, 1992.
15. C. A. Gunter and D. S. Scott. Semantic domains. Handbook of Theoretical Computer Science, B:633-674, 1990. edited by J. van Leeuwen, North Holland.
16. R. Heckmann. Power domain constructions. Science of Computer Programming, 17(1-3):77-117, 1991.
17. K.Weihrauch. Computable Analysis. Springer-Verlag, 2000.
18. H. Luckhardt. A fundamental effect in computations on real numbers. Theoretical Computer Science, 5(3):321-324, 1977/78.
19. E. Manes. Monads of sets. In M. Hazewinkel, editor, Handbook of Algebra, volume 3, pages 67-153. Elsevier Science, 2003.
20. D. Normann. Exact real number computations relative to hereditarily total functionals. Theoretical Computer Science, 284(2):437-453, 2002.
21. G. D. Plotkin. A powerdomain construction. SIAM Journal on Computing, 5(3):452-487, 1976.
22. G. D. Plotkin. Lcf considered as a programming language. Theoretical Computer Science, 5(1):223-255, 1977.
23. G. D. Plotkin. Domains. Post-graduate Lecture in Advanced Domain Theory Univesity of Edinburgh, Departament of Computer Science. Available from the author's web page, page 116, 1983.
24. th IEEE Symposium on Logic in Computer Science, pages 248-257, 1997.
25. D. Scott. Lattice theory, data type and semantics. In In Randall Rustin, editor, Formal Semantics of Algorithmic Languages, pages 65-106. Prentice Hall, 1972.
26. M. B. Smyth. Power domains. Journal of Computer and System Science, 16:23-36, 1978.
27. M. B. Smyth. Powerdomains and predicate transformers: A topological view. In ICALP '83, LNCS, volume 154, pages 662-675. Springer, 1983.
28. M. B. Smyth. Topology. In S. Abramsky,D.M. Gabbay, and T.S.E Maibaum, editors, Handbook on Logic in Computer Science, 1:641-761, 1992.
29. S. Vickers. Topology Via Logic. Cambridge University Press, Cambridge, 1989.