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Title:Comparing Functional Paradigms for Exact Real-number Computation
Authors: Alexander Simpson ; Andrej Bauer ; Martin Escardo
Date:Jul 2002
Publication Title:Proceedings of ICALP 2002
Publication Type:Conference Paper Publication Status:Published
Page Nos:488-500
We compare the definability of total functionals over the reals in two functional-programming approaches to exact real-number computation: the extensional approach, in which one has an abstract datatype of real numbers; and the intensional approach, in which one encodes real numbers using ordinary datatypes. We show that the type hierarchies coincide up to second-order types, and we relate this fact to an analogous comparison of type hierarchies over the external and internal real numbers in Dana Scott's category of equilogical spaces. We do not know whether similar coincidences hold at third-order types. However, we relate this question to a purely topological conjecture about the Kleene-Kreisel continuous functionals over the natural numbers. Finally, although it is known that, in the extensional approach, parallel primitives are necessary for programming total first-order functions, we demonstrate that, in the intensional approach, such primitives are not needed for second-order types and below.
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Bibtex format
author = { Alexander Simpson and Andrej Bauer and Martin Escardo },
title = {Comparing Functional Paradigms for Exact Real-number Computation},
book title = {Proceedings of ICALP 2002},
publisher = {Springer},
year = 2002,
month = {Jul},
pages = {488-500},

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