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Abstract: Real PCF is an extension of the programming language PCF with a data type for real numbers. Although a Real PCF definable real number cannot be computed in finitely many steps, it is possible to compute an arbitrarily small rational interval containing the real number in a sufficiently large number of steps. Based on a domain-theoretic approach to integration, we show how to define integration in Real PCF. We propose two approaches to integration in Real PCF. One consists in adding integration... (Update)
Context of citations to this paper: More
...this paper. 1. 1 Embedding spaces into domains In applications of domain theory [2] to denotational semantics [16, 13] and integration [8, 11], one starts by implicitly or explicitly embedding given spaces X , Y , Z, into appropriate domains C, D, E, endowed with the...
...is universal. Several proofs have been omitted due to lack of space. For a full version of this paper containing all proofs see [13]. 2. Real PCF In this section we summarize the results of [16, 14] needed in this paper. We assume familiarity with PCF [23, 19] We...
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BibTeX entry: (Update)
A. Edalat and M. Escard'o. Integration in real PCF. In Eleventh Annual IEEE Symposium on Logic in Computer Science (LICS),. IEEE, 1996. http://citeseer.ist.psu.edu/edalat96integration.html More
@article{ edalat00integration,
author = "Abbas Edalat and Martin Hotzel Escardo",
title = "Integration in Real {PCF}",
journal = "Information and Computation",
volume = "160",
number = "1-2",
pages = "128-166",
year = "2000",
url = "citeseer.ist.psu.edu/edalat96integration.html" }
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306 LCF considered as a programming language (context) - Plotkin - 1977 DBLP
245 A Compendium of Continuous Lattices (context) - Gierz, Hofmann et al. - 1980
224 Semantics of Programming Languages -- Structures and Techniq.. (context) - Gunter - 1992
213 a theory of computation andcomplexity over the real numbers (context) - Blum, Shub et al. - 1989
211 Domain theory - Abramsky, Jung - 1994 ACM
75 Constructive Analysis (context) - Bishop, Bridges - 1985
44 Theoretical Computer Science (context) - Edalat, integration - 1995 ACM
41 Notes on Constructive Mathematics (context) - Martin-Loef - 1970
34 Exact real arithmetic: A case study in higher order programm.. (context) - Boehm, Cartwright et al. - 1986 ACM DBLP
32 Exact real arithmetic: Formulating real numbers as functions (context) - Boehm, Cartwright - 1990
27 Springer-Verlag (context) - Weihrauch - 1987
20 Power domains and iterated function systems - Edalat - 1996 ACM DBLP
20 A simple introduction to computable analysis (context) - Weihrauch - 1995
17 Computing with infinite objects (context) - Wiedmer - 1980 DBLP
13 Integration in Real PCF - Edalat, Escardo - 1995 ACM DBLP
12 A Functional Approach to Computability on Real Numbers - di Gianantonio - 1993
10 Computability and noncomputability in classical analysis (context) - Pour-el, Richards - 1983
9 Exact real arithmetic with continued fractions (context) - Vuillemin - 1988
9 Domain theory in stochastic processes - Edalat - 1995 ACM DBLP
9 Domain theory in learning processes - Edalat - 1995 DBLP
9 PCF extended with real numbers - Escardo - 1996 ACM DBLP
6 Scott domain theory as a foundation for interval analysis (context) - Escardoand, Claudio - 1993
5 Complexitity Theory of Real Functions (context) - Ko - 1991
2 Real PCF extended with 9 is universal (context) - Escardo
1 measuresand fractals via domain theory (context) - Edalat - 1995
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