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6,213
Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
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Cited by 400 (42 self)
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In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models
Coalgebraic Logic
 Annals of Pure and Applied Logic
, 1999
"... We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that infinitary modal logic contains characterizing formulas. That is, every modelworld pair is characterized up to bisimulation by an infinitary formula. The ..."
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Cited by 109 (0 self)
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logics. We then apply the characterization result to get representation theorems for final coalgebras in terms of maximal elements of ordered algebras. The end result is that the formulas of coalgebraic logics can be viewed as approximations to the elements of the final coalgebra. Keywords: infinitary
On Tree Coalgebras and Coalgebra Presentations
"... For deterministic systems, expressed as coalgebras over polynomial functors, every tree t (an element of the final coalgebra) turns out to represent a new coalgebra At. The universal property of these coalgebras, resembling freeness, is that for every state s of every system S there exists a unique ..."
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For deterministic systems, expressed as coalgebras over polynomial functors, every tree t (an element of the final coalgebra) turns out to represent a new coalgebra At. The universal property of these coalgebras, resembling freeness, is that for every state s of every system S there exists a unique
A Coalgebraic Semantics of Subtyping
, 2000
"... Coalgebras have been proposed as formal basis for the semantics of objects in the sense of objectoriented programming. This paper shows that this semantics provides a smooth interpretation for subtyping, a central notion in objectoriented programming. We show that different characterisations of be ..."
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Cited by 8 (1 self)
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of behavioural subtyping found in the literature can conveniently be expressed in coalgebraic terms. We also investigate the subtle difference between behavioural subtyping and refinement.
Coalgebraic Monads
, 2002
"... This paper introduces coalgebraic monads as a unified model of term algebras covering fundamental examples such as initial algebras, final coalgebras, rational terms and term graphs. We develop a general method for obtaining finitary coalgebraic monads which allows us to generalise the notion of rat ..."
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Cited by 7 (5 self)
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This paper introduces coalgebraic monads as a unified model of term algebras covering fundamental examples such as initial algebras, final coalgebras, rational terms and term graphs. We develop a general method for obtaining finitary coalgebraic monads which allows us to generalise the notion
Simulations in Coalgebra
 THEOR. COMP. SCI
, 2003
"... A new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive. Such an order forms a basic building block for a "lax relation lifting", or "relator" as used by other authors. Simulations appear as coalgebras of thi ..."
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Cited by 24 (2 self)
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A new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive. Such an order forms a basic building block for a "lax relation lifting", or "relator" as used by other authors. Simulations appear as coalgebras
Objects and Classes, Coalgebraically
 ObjectOrientation with Parallelism and Persistence
, 1995
"... The coalgebraic perspective on objects and classes in objectoriented programming is elaborated: objects consist of a (unique) identifier, a local state, and a collection of methods described as a coalgebra; classes are coalgebraic (behavioural) specifications of objects. The creation of a "n ..."
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Cited by 73 (18 self)
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;new" object of a class is described in terms of the terminal coalgebra satisfying the specification. We present a notion of "totally specified" class, which leads to particularly simple terminal coalgebras. We further describe local and global operational semantics for objects. Associated
Comprehension for Coalgebras
 SIAM J. Matrix Anal. Appl
, 2002
"... The notion of an endofunctor having "greatest subcoalgebras" is introduced as a form of comprehension. This notion is shown to be instrumental in giving a systematic and abstract proof of the existence of limits for coalgebras  proved earlier by Worrell and by Gumm & Schroder. These ..."
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Cited by 1 (0 self)
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. These insights, in dual form, are used to reinvestigate colimits for algebras in terms of "least quotient algebras"  leading to a uniform approach to limits of coalgebras and colimits of algebras. Finally, at an abstract level of fibrations, an equivalence is established between having greatest
ON MINIMAL COALGEBRAS
"... Abstract. We define an outdegree for Fcoalgebras and show that the coalgebras of outdegree at most κ form a covariety. As a subcategory of all Fcoalgebras, this class has a terminal object, which for many problems can stand in for the terminal Fcoalgebra, which need not exist in general. As exam ..."
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Cited by 4 (1 self)
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Abstract. We define an outdegree for Fcoalgebras and show that the coalgebras of outdegree at most κ form a covariety. As a subcategory of all Fcoalgebras, this class has a terminal object, which for many problems can stand in for the terminal Fcoalgebra, which need not exist in general
Coalgebraic Multigames?
"... Abstract. Coalgebraic games have been recently introduced as a generalization of Conway games and other notions of games arising in different contexts. Using coalgebraic methods, games can be viewed as elements of a final coalgebra for a suitable functor, and operations on games can be analyzed in ..."
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in terms of (generalized) coiteration schemata. Coalgebraic games are sequential in nature, i.e. at each step either the Left (L) or the Right (R) player moves (global polarization), moreover only a single move can be performed at each step. Recently, in the context of Game Semantics, concurrent games have
Results 1  10
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6,213