Exact real arithmetic: a case study in higher order programming

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Exact real arithmetic: a case study in higher order programming

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Conference on LISP and Functional Programming archive
Proceedings of the 1986 ACM conference on LISP and functional programming table of contents

Cambridge, Massachusetts, United States

Pages: 162 - 173

Year of Publication: 1986

ISBN:0-89791-200-4

Authors

Hans-J. Boehm	Rice University
Robert Cartwright	Rice University
Mark Riggle	Rice University
Michael J. O'Donnell	University of Chicago

Sponsor

SIGPLAN: ACM Special Interest Group on Programming Languages

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 6, Downloads (12 Months): 52, Citation Count: 17

Additional Information:

references cited by collaborative colleagues

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	Avi 61	Avizienis, A., "Signed-Digit Number Representations for Fast Parallel Arithmetic", Institute of Radio Engineers Transactions on Electronic Computers, 1961, p. 389.
	Avi 64	Avizienis, A, "Binary-Compatible Signed-Digit Arithmetic", AFIPS Conference Proceedings 26, 1(1964), pp. 66,3-672
	Atk 75	Atkins, D. E., "Introduction to the Role of Redundancy m Computer Arithmetic, iEEE Computer 8, 6 (1975), pp. 74-76
	Bis 67	Bishop, Errett, Fosndationz o! Constructive Analyeis, McGraw-Hi!l, New York, 1967.
	Bri 79	Bridges, D. S., Oonstructive Functional Analysis, Pitman, London, 1979.
	Boe 85a	Boehm, Hans, Alan Demers, and James Donahue, "A Programmer's Introductwn to Russell", Technical Report 85-16, Department of Computer Science, Rice University.
	Boe 85b	Hans-Juergen Boehm , Alan Demers, Implementing RUSSELL, Proceedings of the 1986 SIGPLAN symposium on Compiler construction, p.186-195, June 25-27, 1986, Palo Alto, California, United States
	Card 84	Luca Cardelli, Compiling a functional language, Proceedings of the 1984 ACM Symposium on LISP and functional programming, p.208-217, August 06-08, 1984, Austin, Texas, United States [doi>10.1145/800055.802037]
	Cart 80	Robert Cartwright, A constructive alternative to axiomatic data type definitions, Proceedings of the 1980 ACM conference on LISP and functional programming, p.46-55, August 25-27, 1980, Stanford University, California, United States [doi>10.1145/800087.802789]
	Cart 81	Robert Cartwright, Formal program testing, Proceedings of the 8th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, p.125-132, January 26-28, 1981, Williamsburg, Virginia [doi>10.1145/567532.567546]
	Cart 82a	Robert Cartwright , James Donahue, The semantics of lazy (and industrious) evaluation, Proceedings of the 1982 ACM symposium on LISP and functional programming, p.253-264, August 15-18, 1982, Pittsburgh, Pennsylvania, United States [doi>10.1145/800068.802157]
	Cart 82b	Cartwright, Robert S, et al., "Rn: An Expertmental Computer Network to Support Numencal Computatwn", Technical Report, Mathematical Sciences Department, Rice University, 1982.
	Cart 83	Robert Cartwright, Recursive programs as definitions in first order logic, SIAM Journal on Computing, v.13 n.2, p.374-408, May 1984 [doi>10.1137/0213026]
	Dem 85	James Donahue , Alan Demers, Data types are values, ACM Transactions on Programming Languages and Systems (TOPLAS), v.7 n.3, p.426-445, July 1985 [doi>10.1145/3916.3987]
	Gol 83	Golub, Gene H., and Charles F. Van Loan, Matriz Computations, Johns Hopkins University Press, Baltimore, 1983.
	Knu 69	Donald E. Knuth, The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1997
	Myh 72	Myhill, J., "What is a Real Number?", American Mathematical Monthly 79, 7 (1972), pp. 748-754
	O’Do 85	Michael J. O'Donnell, Equational logic as a programming language, Massachusetts Institute of Technology, Cambridge, MA, 1985
	Owe 79	Robert Michael Owens , Mary Jane Irwin, On-line algorithms for the design of pipeline architectures, Proceedings of the 6th annual symposium on Computer architecture, p.12-19, April 23-25, 1979 [doi>10.1145/800090.802888]
	PJ 84	Peyton Jones, Simon L., "Arbitrary Preoslon Arithmetic Using Continued Fractions", INDRA Note 1530, Department of Computer Science, University College London, 1984
	Rog 67	Hartley Rogers, Jr., Theory of recursive functions and effective computability, MIT Press, Cambridge, MA, 1987
	Scot 81	D Scott, Lectures on a Mathematical Theory of Computation, Technical Monograph PRG-19, Oxford University Computing Laboratory, Oxford, 1981.
	Wie 80	Wiedmer, E., "Computing with Infinite Objects", Theoretical Computer Science 10 (1980), pp. 133-155
	Wil 65	J. H. Wilkinson, The algebraic eigenvalue problem, Oxford University Press, Inc., New York, NY, 1988

CITED BY 17

	Jean Vuillemin, Exact real computer arithmetic with continued fractions, Proceedings of the 1988 ACM conference on LISP and functional programming, p.14-27, July 25-27, 1988, Snowbird, Utah, United States
	Vernon A. Lee, Jr. , Hans-J. Boehm, Optimizing programs over the constructive reals, ACM SIGPLAN Notices, v.25 n.6, p.102-111, Jun. 1990
	Reinhold Heckmann, Contractivity of linear fractional transformations, Theoretical Computer Science, v.279 n.1-2, p.65-82, May 28, 2002
	Namhyun Hur , James H. Davenport, An exact real algebraic arithmetic with equality determination, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.169-174, July 2000, St. Andrews, Scotland
	Guy L. Steele, Jr. , Richard P. Gabriel, The evolution of Lisp, ACM SIGPLAN Notices, v.28 n.3, p.231-270, March 1993
	James H. Davenport, Equality in computer algebra and beyond, Journal of Symbolic Computation, v.34 n.4, p.259-270, October 2002
	Hideki Tsuiki, Real number computation through gray code embedding, Theoretical Computer Science, v.284 n.2, p.467-485, 28 July 2002
	J. Vuillemin, Exact Real Computer Arithmetic with Continued Fractions, IEEE Transactions on Computers, v.39 n.8, p.1087-1105, August 1990
	Guy L. Steele , Richard P. Gabriel, The evolution of Lisp, History of programming languages---II, ACM Press, New York, NY, 1996
	Keith Briggs, Implementing exact real arithmetic in python, C++ and C, Theoretical Computer Science, v.351 n.1, p.74-81, 14 February 2006
	Jesse Hughes , Milad Niqui, Admissible digit sets, Theoretical Computer Science, v.351 n.1, p.61-73, 14 February 2006
	Herman Geuvers , Milad Niqui , Bas Spitters , Freek Wiedijk, Constructive analysis, types and exact real numbers, Mathematical Structures in Computer Science, v.17 n.1, p.3-36, February 2007
	Yves Bertot, Affine functions and series with co-inductive real numbers, Mathematical Structures in Computer Science, v.17 n.1, p.37-63, February 2007
	Russell O'connor, A monadic, functional implementation of real numbers, Mathematical Structures in Computer Science, v.17 n.1, p.129-159, February 2007
	B. B. Chase , R. T. Hood, Selective interpretation as a technique for debugging computationally intensive programs, ACM SIGPLAN Notices, v.22 n.7, p.113-124, July 1987
	H. J. Boehm, Constructive real interpretation of numerical programs, ACM SIGPLAN Notices, v.22 n.7, p.214-221, July 1987
	Xiaolin Qin , Yong Feng , Jingwei Chen , Jingzhong Zhang, Finding exact minimal polynomial by approximations, Proceedings of the 2009 conference on Symbolic numeric computation, August 03-05, 2009, Kyoto, Japan

Collaborative Colleagues:

Hans-J. Boehm: colleagues

Robert Cartwright: colleagues

Mark Riggle: colleagues

Michael J. O'Donnell: colleagues

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