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Abstract: . We show how functional languages can be used to write programs for real-valued functionals in exact real arithmetic. We concentrate on two useful functionals: definite integration, and the functional returning the maximum value of a continuous function over a closed interval. The algorithms are a practical application of a method, due to Berger, for computing quantifiers over streams. Correctness proofs for the algorithms make essential use of domain theory. 1 Introduction In exact real... (Update)
Context of citations to this paper: More
...algorithms for numerical integration. There are strong indications that domain and proof theoretic methods can be very useful (see e.g. [52], where a domain theoretic algorithm from my thesis is used for developing a functional program for integration) Algorithms...
...at which many interesting functionals, including definite integration (f, a, b) f(x) dx : real real , reside. See [EE00] and [Sim98] for accounts of integration within the extensional and intensional approaches respectively. We prove Theorem 1 by relating it to an analogous...
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BibTeX entry: (Update)
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/. http://citeseer.ist.psu.edu/simpson98lazy.html More
@article{ simpson98lazy,
author = "Alex K. Simpson",
title = "Lazy Functional Algorithms for Exact Real Functionals",
journal = "Lecture Notes in Computer Science",
volume = "1450",
pages = "456--??",
year = "1998",
url = "citeseer.ist.psu.edu/simpson98lazy.html" }
Citations (may not include all citations):306 LCF considered as a programming language (context) - Plotkin - 1977
56 Complexity Theory of Real Functions (context) - Ko - 1991
34 Exact real arithmetic: a case study in higher order programm.. (context) - Boehm, Cartwright et al. - 1986
32 PCF extended with real numbers (context) - Escard'o - 1996
32 Exact real arithmetic: Formulating real numbers as functions (context) - Boehm, Cartwright - 1990
12 A Functional Approach to Computability on Real Numbers - Di Gianantonio - 1993
10 Arbitrary precision real arithmetic: Design and algorithms (context) - Menissier-Morain - 1996
9 Exact real arithmetic with continued fractions (context) - Vuillemin - 1990
7 Properly injective spaces and function spaces (context) - Escard'o - 1998
6 totality and PCF (context) - Plotkin - 1998
5 Real Numbers and Computers (context) - Bajard, Michelucci et al. - 1995
5 An abstract data type for real numbers (context) - Di Gianantonio - 1997
5 Information and Computation (context) - Edalat, Escard'o et al. - 1998
3 Total objects and sets in domain theory (context) - Berger - 1993
1 Totale Objecte und Mengen in Bereichstheorie (context) - Berger - 1990
1 Semantics of Programming (context) - Gunter - 1992
1 Presented at workshop: New Paradigms for Computation on Clas.. (context) - Edalat, Potts et al. - 1997
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.dcs.ed.ac.uk/home/als/Research/): More
Properties of Fixed Points in Axiomatic Domain Theory - Plotkin, Simpson (1998) (Correct)
A Uniform Approach to Domain Theory in Realizability Models - Longley, Simpson (1996) (Correct)
Elementary Axioms for Categories of Classes (Extended Abstract) - Simpson (Correct)
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