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A coinductive calculus of streams

Published online by Cambridge University Press:  28 January 2005

J.J.M.M. RUTTEN
J.J.M.M. RUTTEN
Affiliation:
CWI and VUA, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands Email: janr@cwi.nl, URL: www.cwi.nl/~janr
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Abstract

We develop a coinductive calculus of streams based on the presence of a final coalgebra structure on the set of streams (infinite sequences of real numbers). The main ingredient is the notion of stream derivative, which can be used to formulate both coinductive proofs and definitions. In close analogy to classical analysis, the latter are presented as behavioural differential equations. A number of applications of the calculus are presented, including difference equations, analytical differential equations, continued fractions, and some problems from discrete mathematics and combinatorics.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 15 , Issue 1 , February 2005 , pp. 93 - 147
Copyright
2005 Cambridge University Press

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