Theoretical Computer Science - Special issue: Fourth workshop on mathematical foundations of programming semantics, Boulder, CO, May 1988
Categorical fixed point semantics
Theoretical Computer Science - Special issue: Fourth workshop on mathematical foundations of programming semantics, Boulder, CO, May 1988
Notions of computation and monads
Information and Computation
A characterisation of the least-fixed-point operator by dinaturality
Theoretical Computer Science
Handbook of logic in computer science (vol. 3): semantic structures
Handbook of logic in computer science (vol. 3): semantic structures
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Retracting Some Paths in Process Algebra
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
Proceedings of the First Imperial College Department of Computing Workshop on Theory and Formal Methods
Complete Axioms for Categorical Fixed-Point Operators
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Mathematical Structures in Computer Science
Traces for coalgebraic components
Mathematical Structures in Computer Science
A coinductive calculus for asynchronous side-effecting processes
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
A coinductive calculus for asynchronous side-effecting processes
Information and Computation
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Simulations between processes can be understood in terms of coalgebra homomorphisms, with homomorphisms to the final coalgebra exactly identifying bisimilar processes. The elements of the final coalgebra are thus natural representatives of bisimilarity classes, and a denotational semantics of processes can be developed in a final-coalgebra-enriched category where arrows are processes, canonically represented. In the present paper, we describe a general framework for building final-coalgebra-enriched categories. Every such category is constructed from a multivariant functor representing a notion of process, much like Moggi's categories of computations arising from monads as notions of computation. The "notion of process" functors are intended to capture different flavors of processes as dynamically extended computations. These functors may involve a computational (co)monad, so that a process category in many cases contains an associated computational category as a retract. We further discuss categories of resumptions and of hyperfunctions, which are the main examples of process categories. Very informally, the resumptions can be understood as computations extended in time, whereas hypercomputations are extended in space.