Effective and sequential definition by cases on the reals via infinite signed-digit numerals

Electronic Notes in Theoretical Computer Science

Volumn 13, Issue , 1998, Pages 53-68

  Escardó, Martín Hötzel ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

Parallel conditional; Real number computation

Indexed keywords

ALGORITHMS; GRAPHIC METHODS; INTEGRATION; MATHEMATICAL OPERATORS; NUMBER THEORY; SET THEORY; THEOREM PROVING;

PARALLEL CONDITION; REAL NUMBER COMPUTATION; REAL NUMBERS; SIGNED-DIGIT NUMERALS;

COMPUTATION THEORY;

EID: 18944399783     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1571-0661(05)80214-2     Document Type: Conference Paper

References (30)

1. Abramsky S., Jung A. Domain theory. Abramsky S., Gabbay D.M., Maibaum T.S.E. Handbook of Logic in Computer Science. volume 3:1994;1-168 Clarendon Press, Oxford
2. A. Avizienis. Binary-compatible signed-digit arithmetic. In AFIPS Conference Proceedings, volume 1 of 26, pages 663-672, 1964.
3. Boehm H.J., Cartwright R. Exact real arithmetic: Formulating real numbers as functions. Turner D. Research Topics in Functional Programming. 1990;43-64 Addison - Wesley
4. Boehm H.J., Cartwright R., Riggle M., O'Donnel M.J. Exact real arithmetic: A case study in higher order programming. ACM Symposium on Lisp and Functional Programming. 1986
5. Brouwer L.E.J. Besitzt jede reelle Zahl eine Dezimalbruchentwicklung? Math Ann. 83:1920;201-210
6. Cauchy A. Sur les moyens d'éviter les erreurs dans les calculs numeriques. Comptes Rendus. 11:1840;789-798. Paris.
7. Republished in: Augustin Cauchy, (Evres complétes, lére série, Tome V 431-442
8. M.H. Escardó. PCF extended with real numbers: A domain-theoretic approach to higher-order exact real number computation. PhD thesis, Imperial College of the University of London, November 1996. Technical Report ECS-LFCS-97-374, Department of Computer Science, University of Edinburgh. Available at http://www.dcs.ed.ac.uk/lfcsreps/EXPORT/97/ECS-LFCS-97-374/index. html.
9. P. Di Gianantonio. A functional approach to computability on real numbers. PhD thesis, University of Pisa, 1993. Technical Report TD 6/93.
10. P. Di Gianantonio. A golden ratio notation for the real numbers. Technical Report CS-R9602, CWI Amsterdam, 1996.
11. Di Gianantonio P. Real number computability and domain theory. Information and Computation. 127:(1):1996;11-25
12. Gunter C.A. Semantics of Programming Languages - Structures and Techniques. 1992;The MIT Press, London
13. Kleene S.C. Introduction to Metamathematics. 1952;North-Holland, Amsterdam
14. Ker-I Ko. Complexitity Theory of Real Functions. 1991;Birkhauser, Boston
15. Leslie J. The Philosophy of Arithmetic. 1817;Edinburgh
16. N.Th. Müller. Subpolynomial complexity classes of real functions and real numbers. In Laurent Kott, editor, Proceedings of the 13th International Colloquium on Automata, Languages, and Programming, volume 226 of Lecture Notes in Computer Science, pages 284-293, Berlin, 1986. Springer.
17. Plotkin G.D. LCF considered as a programming language. Theoretical Computer Science. 5:(1):1977;223-255
18. ω as a universal domain. Journal of Computer and System Sciences. 17:1978;209-236
19. G.D. Plotkin. Domains. Post-graduate lectures in advanced domain theory, Department of Computer Science, University of Edinburgh. Available at http://hypatia.dcs.qmw.ac.uk/sites/other/domain.notes.other, 1983.
20. Rogers H. Theory of Recursive Functions and Effective Computability. 1967;McGraw-Hill, New York
21. Scott D.S. A type-theoretical alternative to CUCH, ISWIM and OWHY. Theoretical Computer Science. 121:1993;411-440. Reprint of a manuscript produced in 1969
22. A. Simpson. Lazy functional algorithms for exact real functionals. In Mathematical Foundations of Computer Science 1998. To appear. Available at http://www.dcs.ed.ac.uk/home/als/Research/.
23. Smyth M.B. Topology. Abramsky S., Gabbay D.M., Maibaum T.S.E. Handbook of Logic in Computer Science. volume 1:1992;641-761 Clarendon Press, Oxford
24. Sünderhauf Ph. Discrete Approximation of Spaces. 1994;PhD thesis, Technishe Hochschule Darmstadt
25. Turing A. A correction. The London Mathematical Society. 43:1937;544-546
26. Turing A. On computable numbers, with an application to the Entscheindungproblem. The London Mathematical Society. 42:1937;230-265
27. K. Weihrauch. A simple introduction to computable analysis. Technical Report 171-7/1995, FernUniversität, 1995.
28. K. Weihrauch. A foundation for computable analysis. In Douglas S. Bridges, Cristian S. Calude, Jeremy Gibbons, Steve Reeves, and Ian H. Witten, editors, Combinatorics, Complexity, and Logic, Discrete Mathematics and Theoretical Computer Science, pages 66-89, Singapore, 1997. Springer. Proceedings of DMTCS'96.
29. Weihrauch K., Kreitz C. Representations of the real numbers and the open subsets of the set of real numbers. Annals of Pure and Applied Logic. 35:1987;247-260
30. Wiedmer E. Computing with infinite objects. Theoretical Computer Science. 10:1980;133-155