categories: preprint: Elements of stream calculus

[Jan Rutten <Jan.Rutten@cwi.nl>]

The following technical report is now
available at ftp.cwi.nl as pub/CWIreports/SEN/SEN-R0120.ps.Z
(also via my home page: http://www.cwi.nl/~janr):

J.J.M.M. Rutten
Elements of stream calculus (an extensive exercise in coinduction) 
Technical Report  SEN-R0120, CWI, Amsterdam, 2001.

Abstract:
Based on the presence of a final coalgebra structure on the set of streams
(infinite sequences of real numbers), a coinductive calculus of streams is
developed.  The main ingredient is the notion of stream derivative, with
which both coinductive proofs and definitions can be formulated. 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.

The report will also appear in Volume 45 of 
Elsevier's ENTCS series, which contains 
the proceedings of MFPS 17.