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Practical coinduction

Published online by Cambridge University Press:  09 February 2016

DEXTER KOZEN  and
ALEXANDRA SILVA
DEXTER KOZEN
Affiliation:
Computer Science, Cornell University, Ithaca, New York 14853-7501, U.S.A. Email: kozen@cs.cornell.edu
ALEXANDRA SILVA
Affiliation:
Intelligent Systems, Radboud University Nijmegen, Postbus 9010, 6500 GL Nijmegen, the Netherlands Email: alexandra@cs.ru.nl
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Abstract

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Induction is a well-established proof principle that is taught in most undergraduate programs in mathematics and computer science. In computer science, it is used primarily to reason about inductively defined datatypes such as finite lists, finite trees and the natural numbers. Coinduction is the dual principle that can be used to reason about coinductive datatypes such as infinite streams or trees, but it is not as widespread or as well understood. In this paper, we illustrate through several examples the use of coinduction in informal mathematical arguments. Our aim is to promote the principle as a useful tool for the working mathematician and to bring it to a level of familiarity on par with induction. We show that coinduction is not only about bisimilarity and equality of behaviors, but also applicable to a variety of functions and relations defined on coinductive datatypes.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 7: Special Issue: Coalgebraic Logic , October 2017 , pp. 1132 - 1152
Copyright
Copyright © Cambridge University Press 2016 

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