CSP, partial automata, and coalgebras
Theoretical Computer Science
A coalgebraic equational approach to specifying observational structures
Theoretical Computer Science
Coalgebra morphisms subsume open maps
Theoretical Computer Science
Compositional SOS and beyond: a coalgebraic view of open systems
Theoretical Computer Science
Bisimulation indexes and their applications
Theoretical Computer Science
Annals of Mathematics and Artificial Intelligence
pi-Calculus, Structured Coalgebras, and Minimal HD-Automata
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Semantic Constructions for Hidden Algebra
WADT '98 Selected papers from the 13th International Workshop on Recent Trends in Algebraic Development Techniques
Categorical Programming with Abstract Data Types
AMAST '98 Proceedings of the 7th International Conference on Algebraic Methodology and Software Technology
Automata, Power Series, and Coinduction: Taking Input Derivatives Seriously
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Semantical Principles in the Modal Logic of Coalgebras
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
A Complete Coinductive Logical System for Bisimulation Equivalence on Circular Objects
FoSSaCS '99 Proceedings of the Second International Conference on Foundations of Software Science and Computation Structure, Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS'99
The Demonic Product of Probabilistic Relations
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Minimizing Transition Systems for Name Passing Calculi: A Co-algebraic Formulation
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Tile Transition Systems as Structured Coalgebras
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
Bisimulation for labelled Markov processes
Information and Computation - Special issue: LICS'97
Simply Observable Behavioral Specification
APSEC '99 Proceedings of the Sixth Asia Pacific Software Engineering Conference
Coinductive characterizations of applicative structures
Mathematical Structures in Computer Science
Hidden coinduction: behavioural correctness proofs for objects
Mathematical Structures in Computer Science
A comonadic account of behavioural covarieties of coalgebras
Mathematical Structures in Computer Science
Abstract behavior types: a foundation model for components and their composition
Science of Computer Programming - Formal methods for components and objects pragmatic aspects and applications
Stacking cycles: functional transformation of circular data
IFL'02 Proceedings of the 14th international conference on Implementation of functional languages
IS=DBS+interaction: towards principles of information system design
ER'00 Proceedings of the 19th international conference on Conceptual modeling
UML'00 Proceedings of the 3rd international conference on The unified modeling language: advancing the standard
Behavioural constructor implementation for regular algebras
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
Cofree coalgebras for signature morphisms
Formal Methods in Software and Systems Modeling
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In the semantics of programming, finite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with infinite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (1988) on a theory of non-wellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages (Milner, 1980; Park, 1981). Using the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras (Aczel and Mendler, 1989). Thus the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to: coalgebra, homomorphism of coalgebras, and bisimulation, respectively. In this paper, the latter are taken as the basic ingredients of a theory called universal coalgebra. Some standard results from universal algebra are reformulated (using the afore mentioned correspondence) and proved for a large class of coalgebras, leading to a series of results on, e.g., the lattices of subcoalgebras and bisimulations, simple coalgebras and coinduction, and a covariety theorem for coalgebras similar to Birkhoff''s variety theorem.