Communication and concurrency
Journal of the ACM (JACM)
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Theoretical Computer Science
Automata and Coinduction (An Exercise in Coalgebra)
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
Category Theory and Computer Science
Recursion schemes from comonads
Nordic Journal of Computing
Towards a Mathematical Operational Semantics
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Behavioural differential equations: a coinductive calculus of streams, automata, and power series
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On the bisimulation proof method
Mathematical Structures in Computer Science
Recursive coalgebras from comonads
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
A coalgebraic approach to the semantics of the ambient calculus
Theoretical Computer Science - Algebra and coalgebra in computer science
Proof Methods for Corecursive Programs
Fundamenta Informaticae - Program Transformation: Theoretical Foundations and Basic Techniques. Part 1
PSPACE bounds for rank-1 modal logics
ACM Transactions on Computational Logic (TOCL)
Recursive Coalgebras from Comonads
Electronic Notes in Theoretical Computer Science (ENTCS)
Recursive coalgebras from comonads
Information and Computation - Special issue: Seventh workshop on coalgebraic methods in computer science 2004
Bisimulation proof methods in a path-based specification language for polynomial coalgebras
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
The Recursion Scheme from the Cofree Recursive Comonad
Electronic Notes in Theoretical Computer Science (ENTCS)
Concrete stream calculus: An extended study
Journal of Functional Programming
A coinductive calculus for asynchronous side-effecting processes
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Proving the unique fixed-point principle correct: an adventure with category theory
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
Towards a coalgebraic semantics of the ambient calculus
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Incremental pattern-based coinduction for process algebra and its isabelle formalization
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
CIA structures and the semantics of recursion
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Generic programming with adjunctions
SSGIP'10 Proceedings of the 2010 international spring school conference on Generic and Indexed Programming
Proof Methods for Corecursive Programs
Fundamenta Informaticae - Program Transformation: Theoretical Foundations and Basic Techniques. Part 1
Unifying structured recursion schemes
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
Adjoint folds and unfolds-An extended study
Science of Computer Programming
A coinductive calculus for asynchronous side-effecting processes
Information and Computation
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We introduce the $\lambda-coiteration$ schema for a distributive law $\lambda$ of a functor $\Functor{T}$ over a functor $\Functor{F}$. Parameterised by $\Functor{T}$ and $\lambda$ it generalises the basic coiteration schema uniquely characterising functions into a final $\Functor{F}$-coalgebra. Furthermore, the same parameters are used to generalise the categorical notion of a bisimulation to that of a $\lambda-bisimulation$, while still giving rise to a proof technique for bisimilarity. We first present a theorem showing the validity of the resulting definition and proof principles for categories with countable coproducts.Our approach gives a unifying categorical presentation and justification of several extensions of the basic coinduction schemata that have been treated separately before, and some only for specific types of system. As examples, the duals of primitive recursion and course-of-value iteration, which are known extensions of coiteration, arise as instances of our framework.Moreover, we derive schemata involving auxiliary operators definable with GSOS-style specifications such as addition of streams, regular operators on languages, or parallel and sequential composition of processes. The argument is based on a variation of the theory in the setting of monads and copointed functors. The schemata justify guarded recursive definitions and an up-to-context proof technique for operators of the type mentioned. The latter can ease bisimilarity proofs considerably.