Algebraic approaches to program semantics
Algebraic approaches to program semantics
Rational series and their languages
Rational series and their languages
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Automatic Sequences: Theory, Applications, Generalizations
Automatic Sequences: Theory, Applications, Generalizations
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
Behavioural differential equations: a coinductive calculus of streams, automata, and power series
Theoretical Computer Science
A coinductive calculus of streams
Mathematical Structures in Computer Science
Concrete stream calculus: An extended study
Journal of Functional Programming
Proving the unique fixed-point principle correct: an adventure with category theory
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
Linear constraints over infinite trees
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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We study the set T"A of infinite binary trees with nodes labelled in a semiring A from a coalgebraic perspective. We present coinductive definition and proof principles based on the fact that T"A carries a final coalgebra structure. By viewing trees as formal power series, we develop a calculus where definitions are presented as behavioural differential equations. We present a general format for these equations that guarantees the existence and uniqueness of solutions. Although technically not very difficult, the resulting framework has surprisingly nice applications, which is illustrated by various concrete examples.