Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Specifying coalgebras with modal logic
Theoretical Computer Science
From modal logic to terminal coalgebras
Theoretical Computer Science
PI-Calculus: A Theory of Mobile Processes
PI-Calculus: A Theory of Mobile Processes
Exercises in coalgebraic specification
Algebraic and coalgebraic methods in the mathematics of program construction
Coalgebraic modal logic: soundness, completeness and decidability of local consequence
Theoretical Computer Science
Mathematical Structures in Computer Science
On the bisimulation proof method
Mathematical Structures in Computer Science
On the origins of bisimulation and coinduction
ACM Transactions on Programming Languages and Systems (TOPLAS)
An Algebra for Kripke Polynomial Coalgebras
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
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Bisimulation is one of the fundamental concepts of the theory of coalgebras. However, it is difficult to verify whether a relation is a bisimulation. Although some categorical bisimulation proof methods for coalgebras have been proposed, they are not based on specification languages of coalgebras so that they are difficult to be used in practice. In this paper, a specification language based on paths of polynomial functors is proposed to specify polynomial coalgebras. Since bisimulation can be defined by paths, it is easy to transform Sangiorgi's bisimulation proof methods for labeled transition systems to reasoning rules in such a path-based specification language for polynomial coalgebras. The paper defines the notions of progressions and sound functions based on paths, then introduces the notion of faithful contexts for the language and presents a bisimulation-up-to context proof technique for polynomial coalgebras. Several examples are given to illustrate how to make use of the bisimulation proof methods in the language.