Algebra of programming
Objects and classes, co-algebraically
Object orientation with parallelism and persistence
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Components as processes: an exercise in coalgebraic modeling
Fourth International Conference on Formal methods for open object-based distributed systems IV
Data Refinement: Model-Oriented Proof Methods and Their Comparison
Data Refinement: Model-Oriented Proof Methods and Their Comparison
Defining Equations in Terminal Coalgebras
Selected papers from the 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop on Recent Trends in Data Type Specification
Polynomial Relators (Extended Abstract)
AMAST '91 Proceedings of the Second International Conference on Methodology and Software Technology: Algebraic Methodology and Software Technology
Behaviour-Refinement of Coalgebraic Specifications with Coinductive Correctness Proofs
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Exercises in Coalgebraic Specification
Revised Lectures from the International Summer School and Workshop on Algebraic and Coalgebraic Methods in the Mathematics of Program Construction
On the Refinement and Simulation of Data Types and Processes
IFM '99 Proceedings of the 1st International Conference on Integrated Formal Methods
Mathematical Structures in Computer Science
Safety of abstract interpretations for free, via logical relations and Galois connections
Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
Components as coalgebras: the refinement dimension
Theoretical Computer Science - Algebraic methodology and software technology
Transposing partial components: an exercise on coalgebraic refinement
Theoretical Computer Science - Components and objects
Pointfree factorization of operation refinement
FM'06 Proceedings of the 14th international conference on Formal Methods
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A transition system can be presented either as a binary relation or as a coalgebra for the powerset functor, each representation being obtained from the other by transposition. More generally, a coalgebra for a functor F generalises transition systems in the sense that a shape for transitions is determined by F, typically encoding a signature of methods and observers. This paper explores such a duality to frame in purely relational terms coalgebraic refinement, showing that relational (data) refinement of transition relations, in its two variants, downward and upward (functional) simulations, is equivalent to coalgebraic refinement based on backward and forward morphisms, respectively. Going deeper, it is also shown that downward simulation provides a complete relational rule to prove coalgebraic refinement. With such a single rule the paper defines a pre-ordered calculus for refinement of coalgebras, with bisimilarity as the induced equivalence. The calculus is monotonic with respect to the main relational operators and arbitrary relator F, therefore providing a framework for structural reasoning about refinement.