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Coalgebras and Monads in the Semantics of Java
 Theoretical Computer Science
, 2002
"... This paper describes the basic structures in the denotational and axiomatic semantics of sequential Java, both from a monadic and a coalgebraic perspective. This semantics is an abstraction of the one used for the verification of (sequential) Java programs using proof tools in the LOOP project at th ..."
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This paper describes the basic structures in the denotational and axiomatic semantics of sequential Java, both from a monadic and a coalgebraic perspective. This semantics is an abstraction of the one used for the verification of (sequential) Java programs using proof tools in the LOOP project at the University of Nijmegen. It is shown how the monadic perspective gives rise to the relevant computational structure in Java (composition, extension and repetition), and how the coalgebraic perspective o#ers an associated program logic (with invariants, bisimulations, and Hoare logics) for reasoning about the computational structure provided by the monad.
Similarity Quotients as Final Coalgebras
"... Abstract. We give a general framework relating a branching time relation on nodes of a transition system to a final coalgebra for a suitable endofunctor. Examples of relations treated by our theory include bisimilarity (a well known example), similarity, upper and lower similarity for transition sys ..."
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Abstract. We give a general framework relating a branching time relation on nodes of a transition system to a final coalgebra for a suitable endofunctor. Examples of relations treated by our theory include bisimilarity (a well known example), similarity, upper and lower similarity for transition systems with divergence, and nested similarity. Our results describe firstly how to characterize the relation in terms of a given final coalgebra, and secondly how to construct a final coalgebra using the relation. Our theory uses a notion of “relator ” based on earlier work of Thijs. But whereas a relator must preserve binary composition in Thijs ’ framework, it only laxly preserves composition in ours. It is this weaker requirement that allows nested similarity to be an example. 1
Semantic Principles in the . . .
, 2001
"... Coalgebras for a functor on the category of sets subsume many formulations of the notion of transition system, including labelled transition systems, Kripke models, Kripke frames and many types of automata. This paper presents a multimodal language which is bisimulation invariant and (under a natur ..."
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Coalgebras for a functor on the category of sets subsume many formulations of the notion of transition system, including labelled transition systems, Kripke models, Kripke frames and many types of automata. This paper presents a multimodal language which is bisimulation invariant and (under a natural completeness condition) expressive enough to characterise elements of the underlying state space up to bisimulation. Like Moss' coalgebraic logic, the theory can be applied to an arbitrary signature functor on the category of sets. Also, an upper bound for the size of conjunctions and disjunctions needed to obtain characteristic formulas is given.
MSc in Logic
, 2011
"... In this thesis we study relation liftings in the context of coalgebraic modal logic. ..."
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In this thesis we study relation liftings in the context of coalgebraic modal logic.
Abstract Coalgebras and Monads in the Semantics of Java ⋆
"... This paper describes the basic structures in the denotational and axiomatic semantics of sequential Java, both from a monadic and a coalgebraic perspective. This semantics is an abstraction of the one used for the verification of (sequential) Java programs using proof tools in the LOOP project at th ..."
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This paper describes the basic structures in the denotational and axiomatic semantics of sequential Java, both from a monadic and a coalgebraic perspective. This semantics is an abstraction of the one used for the verification of (sequential) Java programs using proof tools in the LOOP project at the University of Nijmegen. It is shown how the monadic perspective gives rise to the relevant computational structure in Java (composition, extension and repetition), and how the coalgebraic perspective offers an associated program logic (with invariants, bisimulations, and Hoare logics) for reasoning about the computational structure provided by the monad.
Stone Coalgebras
"... In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue ..."
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In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue
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"... to the power set functor on the category of sets.We prove that the socalled descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. Thisyields a duality between the category of modal algebras and that of coalgebra ..."
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to the power set functor on the category of sets.We prove that the socalled descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. Thisyields a duality between the category of modal algebras and that of coalgebras over the Vietoris functor.Building on this idea, we introduce the notion of a Vietoris polynomial functor over the category of Stone spaces. For each such functor T we provide an adjunction between thecategory of Tsorted Boolean algebras with operators and the category of Stone coalgebrasover T. Since the unit of this adjunction is an isomorphism, this shows that Coalg(T)op isa full reflective subcategory of
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"... analogue to the power set functor. We prove that the socalled descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. This yields a duality between the category of modal algebras and that of coalgebras over the Vi ..."
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analogue to the power set functor. We prove that the socalled descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. This yields a duality between the category of modal algebras and that of coalgebras over the Vietoris functor. Building on this