Results 1  10
of
10
Products of coalgebras
, 2001
"... We prove that the category of Fcoalgebras is complete, that is products and equalizers exist, provided that the type functor F is bounded or preserves mono sources. This generalizes and simplifies a result of Worrell ([Wor98]). We also describe the relationship between the product A × B and the lar ..."
Abstract

Cited by 21 (5 self)
 Add to MetaCart
(Show Context)
We prove that the category of Fcoalgebras is complete, that is products and equalizers exist, provided that the type functor F is bounded or preserves mono sources. This generalizes and simplifies a result of Worrell ([Wor98]). We also describe the relationship between the product A × B and the largest bisimulation ∼ A,B between A and B and find an example of two finite coalgebras whose product is infinite.
From Settheoretic Coinduction to Coalgebraic Coinduction: some results, some problems
, 1999
"... ..."
Covarieties and Complete Covarieties
, 1999
"... We present two ways to de ne covarieties and complete covarieties, i.e. covarieties that are closed under total bisimulation: by closure operators and by subcoalgebras of coalgebras. ..."
Abstract

Cited by 14 (3 self)
 Add to MetaCart
We present two ways to de ne covarieties and complete covarieties, i.e. covarieties that are closed under total bisimulation: by closure operators and by subcoalgebras of coalgebras.
Equational and implicational classes of coalgebras (Extended Abstract)
"... If T: Set! Set is a functor which is bounded and preserves weak pullbacks then a class of Tcoalgebras is acovariety, i.e closed under H (homomorphic images), S (subcoalgebras) and (sums), if and only if it can be de ned by a set of "coequations". Similarly, classes closed under H and can ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
If T: Set! Set is a functor which is bounded and preserves weak pullbacks then a class of Tcoalgebras is acovariety, i.e closed under H (homomorphic images), S (subcoalgebras) and (sums), if and only if it can be de ned by a set of "coequations". Similarly, classes closed under H and can be characterized by implications of coequations. These results are analogous to the theorems of G.Birkhoff and of A.I.Mal'cev in classical universal algebra.
Finitary coalgebraic multisemilattices and multilatticesI,II
"... In this paper we continue the coalgebraization of the structure of multilattice. Specifically, we introduce a coalgebraic characterization of the notion of finitary multi(semi)lattice, a generalization of that of semilattice which arises naturally in several areas of computer science and provides t ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
In this paper we continue the coalgebraization of the structure of multilattice. Specifically, we introduce a coalgebraic characterization of the notion of finitary multi(semi)lattice, a generalization of that of semilattice which arises naturally in several areas of computer science and provides the possibility of handling nondeterminism.
Algebraic Semantics of Statements of Sequential Java
, 2003
"... Formal semantics of some representative expressions and statements of sequential Java in the context of the statebased algebraic model of the language proposed by the authors is given. ..."
Abstract
 Add to MetaCart
Formal semantics of some representative expressions and statements of sequential Java in the context of the statebased algebraic model of the language proposed by the authors is given.
On Understanding Data . . .
, 2009
"... In 1985 Luca Cardelli and Peter Wegner, my advisor, published an ACM Computing Surveys paper called “On understanding types, data abstraction, and polymorphism”. Their work kicked off a flood of research on semantics and type theory for objectoriented programming, which continues to this day. Despi ..."
Abstract
 Add to MetaCart
In 1985 Luca Cardelli and Peter Wegner, my advisor, published an ACM Computing Surveys paper called “On understanding types, data abstraction, and polymorphism”. Their work kicked off a flood of research on semantics and type theory for objectoriented programming, which continues to this day. Despite 25 years of research, there is still widespread confusion about the two forms of data abstraction, abstract data types and objects. This essay attempts to explain the differences and also why the differences matter.
General Terms
"... This paper describes how to use the Microsoft DSL Tools to construct the Interactive Television Applications system as an ..."
Abstract
 Add to MetaCart
This paper describes how to use the Microsoft DSL Tools to construct the Interactive Television Applications system as an
Coalgebraic Description of Generalized Binary Methods
, 2005
"... We extend the ReichelJacobs coalgebraic account of specification and refinement of objects and classes in Object Oriented Programming to (generalized) binary methods. These are methods that take more than one parameter of a class type. Class types include sums and (possibly infinite) products type ..."
Abstract
 Add to MetaCart
(Show Context)
We extend the ReichelJacobs coalgebraic account of specification and refinement of objects and classes in Object Oriented Programming to (generalized) binary methods. These are methods that take more than one parameter of a class type. Class types include sums and (possibly infinite) products type constructors. We study and compare two solutions for modeling generalized binary methods, which use purely covariant functors. In the first solution, which applies when we already have a class implementation, we reduce the behaviour of a generalized binary method to that of a bunch of unary methods. These are obtained by freezing the types of the extra class parameters to constant types. The bisimulation behavioural equivalence induced on objects by this model amounts to the greatest congruence w.r.t method application. Alternatively, we treat binary methods as graphs instead of functions, thus turning contravariant occurrences in the functor into covariant ones.