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Constructive analysis, types and exact real numbers

Published online by Cambridge University Press:  01 February 2007

HERMAN GEUVERS ,
MILAD NIQUI ,
BAS SPITTERS  and
FREEK WIEDIJK
HERMAN GEUVERS
Affiliation:
Radboud University Nijmegen, the Netherlands Email: spitters@cs.ru.nl
MILAD NIQUI
Affiliation:
Radboud University Nijmegen, the Netherlands Email: spitters@cs.ru.nl
BAS SPITTERS
Affiliation:
Radboud University Nijmegen, the Netherlands Email: spitters@cs.ru.nl
FREEK WIEDIJK
Affiliation:
Radboud University Nijmegen, the Netherlands Email: spitters@cs.ru.nl
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Abstract

In this paper we will discuss various aspects of computable/constructive analysis, namely semantics, proofs and computations. We will present some of the problems and solutions of exact real arithmetic varying from concrete implementations, representation and algorithms to various models for real computation. We then put these models in a uniform framework using realisability, which opens the door to the use of type theoretic and coalgebraic constructions both in computing and reasoning about these computations. We will indicate that it is often natural to use constructive logic to reason about these computations.

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Paper
Information
Mathematical Structures in Computer Science , Volume 17 , Issue 1 , February 2007 , pp. 3 - 36
Copyright
Copyright © Cambridge University Press 2007

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