@article{RUTTEN2001358,
    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.},
    Author = {Rutten, J.J.M.M.},
    File = {Elements of Stream Calculus - 1-s2.0-S1571066104809721-main - a.pdf},
    ISSN = {1571-0661},
    Journal = {Electronic Notes in Theoretical Computer Science},
    Keywords = {Coinduction, coalgebra, finality, stream, derivative, differential equation, difference equation, Euler formula, counting, formal power series, weighted automaton},
    Note = {MFPS 2001,Seventeenth Conference on the Mathematical Foundations of Programming Semantics},
    Pages = {358-423},
    Title = {Elements of Stream Calculus: (An Extensive Exercise in Coinduction)},
    URL = {https://www.sciencedirect.com/science/article/pii/S1571066104809721},
    Volume = {45},
    Year = {2001},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S1571066104809721},
    bdsk-url-2 = {https://doi.org/10.1016/S1571-0661(04)80972-1},
    date-added = {2023-03-25 19:38:39 +0100},
    date-modified = {2023-03-25 19:38:39 +0100},
    doi = {10.1016/S1571-0661(04)80972-1}
}

@article{RUTTEN2001358, 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.}, Author = {Rutten, J.J.M.M.}, File = {Elements of Stream Calculus - 1-s2.0-S1571066104809721-main - a.pdf}, ISSN = {1571-0661}, Journal = {Electronic Notes in Theoretical Computer Science}, Keywords = {Coinduction, coalgebra, finality, stream, derivative, differential equation, difference equation, Euler formula, counting, formal power series, weighted automaton}, Note = {MFPS 2001,Seventeenth Conference on the Mathematical Foundations of Programming Semantics}, Pages = {358-423}, Title = {Elements of Stream Calculus: (An Extensive Exercise in Coinduction)}, URL = {https://www.sciencedirect.com/science/article/pii/S1571066104809721}, Volume = {45}, Year = {2001}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S1571066104809721}, bdsk-url-2 = {https://doi.org/10.1016/S1571-0661(04)80972-1}, date-added = {2023-03-25 19:38:39 +0100}, date-modified = {2023-03-25 19:38:39 +0100}, doi = {10.1016/S1571-0661(04)80972-1} }