Rational series and their languages
Rational series and their languages
The algebra of stream processing functions
Theoretical Computer Science
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
Automatic Sequences: Theory, Applications, Generalizations
Automatic Sequences: Theory, Applications, Generalizations
Behavioural differential equations: a coinductive calculus of streams, automata, and power series
Theoretical Computer Science
Reo: a channel-based coordination model for component composition
Mathematical Structures in Computer Science
A coinductive calculus of streams
Mathematical Structures in Computer Science
A tutorial on coinductive stream calculus and signal flow graphs
Theoretical Computer Science - Formal methods for components and objects
Comonadic Notions of Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Coinductive Properties of Causal Maps
AMAST 2008 Proceedings of the 12th international conference on Algebraic Methodology and Software Technology
CIRC: a circular coinductive prover
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
Scans and convolutions: a calculational proof of Moessner's theorem
IFL'08 Proceedings of the 20th international conference on Implementation and application of functional languages
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We study various operations for splitting, partitioning, projecting and merging streams of data. These operations are motivated by their use in dataflow programming and stream processing languages. We use the framework of stream calculus and stream circuits for defining and proving properties of such operations using behavioural differential equations and coinduction proof principles. As a featured example we give proofs of results, observed by Moessner, from elementary number theory using our framework. We study the invariance of certain well patterned classes of streams, namely rational and algebraic streams, under splitting and merging. Finally we show that stream circuits extended with gates for dyadic split and merge are expressive enough to realise some non-rational algebraic streams, thereby going beyond ordinary stream circuits.