Results 1 
9 of
9
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 ..."
Abstract

Cited by 298 (31 self)
 Add to MetaCart
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 certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (NonWellFounded sets, CSLI Leethre Notes, Vol. 14, center for the study of Languages and information, Stanford, 1988) on a theory of nonwellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages. Using the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras. Thus, the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to coalgebra, homomorphism of coalgebras, and bisimulation, respectively. In this paper, the latter are taken
A Tutorial on (Co)Algebras and (Co)Induction
 EATCS Bulletin
, 1997
"... . Algebraic structures which are generated by a collection of constructors like natural numbers (generated by a zero and a successor) or finite lists and trees are of wellestablished importance in computer science. Formally, they are initial algebras. Induction is used both as a definition pr ..."
Abstract

Cited by 228 (34 self)
 Add to MetaCart
. Algebraic structures which are generated by a collection of constructors like natural numbers (generated by a zero and a successor) or finite lists and trees are of wellestablished importance in computer science. Formally, they are initial algebras. Induction is used both as a definition principle, and as a proof principle for such structures. But there are also important dual "coalgebraic" structures, which do not come equipped with constructor operations but with what are sometimes called "destructor" operations (also called observers, accessors, transition maps, or mutators). Spaces of infinite data (including, for example, infinite lists, and nonwellfounded sets) are generally of this kind. In general, dynamical systems with a hidden, blackbox state space, to which a user only has limited access via specified (observer or mutator) operations, are coalgebras of various kinds. Such coalgebraic systems are common in computer science. And "coinduction" is the appropriate te...
On the Foundations of Final Coalgebra Semantics: nonwellfounded sets, partial orders, metric spaces
, 1998
"... ..."
On the Foundations of Corecursion
 Logic Journal of the IGPL
, 1997
"... We consider foundational questions related to the definition of functions by corecursion. This method is especially suited to functions into the greatest fixed point of some monotone operator, and it is most applicable in the context of nonwellfounded sets. We review the work on the Special Final C ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
We consider foundational questions related to the definition of functions by corecursion. This method is especially suited to functions into the greatest fixed point of some monotone operator, and it is most applicable in the context of nonwellfounded sets. We review the work on the Special Final Coalgebra Theorem of Aczel [1] and the Corecursion Theorem of Barwise and Moss [4]. We offer a condition weaker than Aczel's condition of uniformity on maps, and then we prove a result relating the operators satisfying the new condition to the smooth operators of [4]. Keywords: corecursion, coalgebra, operator on sets 1 Introduction By a stream of natural numbers we mean a pair hn; si where n 2 N and s is again a stream of natural numbers. Let f : N ! N . Consider the following function which purports to define a function from N into the streams: iter f (n) = hn; iter f f(n)i (1.1) For each n, iter f (n) is a stream, so iter f itself is a function from numbers to streams. This is an examp...
Semantical Analysis of Perpetual Strategies in λcalculus
, 1998
"... this paper we carry out a semantical investigation of perpetual strategies in ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
this paper we carry out a semantical investigation of perpetual strategies in
Final Semantics for the picalculus
, 1998
"... In this paper we discuss final semantics for the calculus, a process algebra which models systems that can dynamically change the topology of the channels. We show that the final semantics paradigm, originated by Aczel and Rutten for CCSlike languages, can be successfully applied also here. This i ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
In this paper we discuss final semantics for the calculus, a process algebra which models systems that can dynamically change the topology of the channels. We show that the final semantics paradigm, originated by Aczel and Rutten for CCSlike languages, can be successfully applied also here. This is achieved by suitably generalizing the standard techniques so as to accommodate the mechanism of name creation and the behaviour of the binding operators peculiar to the calculus. As a preliminary step, we give a higher order presentation of the calculus using as metalanguage LF , a logical framework based on typed calculus. Such a presentation highlights the nature of the binding operators and elucidates the role of free and bound channels. The final semantics is defined making use of this higher order presentation, within a category of hypersets.
The Fine Structure of Game Lambda Models
"... . We study models of the untyped lambda calculus in the setting of game semantics. In particular, we show that, in the category of games G, introduced by Abramsky, Jagadeesan and Malacaria, all  models can be partitioned in three disjoint classes, and each model in a class induces the same theory ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
. We study models of the untyped lambda calculus in the setting of game semantics. In particular, we show that, in the category of games G, introduced by Abramsky, Jagadeesan and Malacaria, all  models can be partitioned in three disjoint classes, and each model in a class induces the same theory (i.e. the set of equations between terms), that are the theory H , the theory which identies two terms i they have the same Bohm tree and the theory which identies all the terms which have the same LevyLongo tree. Key Words: Games Semantics, Lambda Calculus, Bohmtrees Introduction In this paper we explore the methodology for giving denotational semantics based on games, recently introduced by Abramsky, Jagadeesan, Malacaria and Hyland, Ong (see [AJM96,HO00]). We use game semantics to build models of the untyped calculus, focusing on which theories can be modeled. theories are congruences over terms, which extend pure conversion. Their interest lies in the fact that t...
Parametric Parameter Passing λcalculus
, 2003
"... this paper we propose a new calculus, the Vcalculus, which is parametric with respect to a subset V of terms that we call input values. The Vcalculus is a callbyvalue calculus, in the sense that the reduction rule is a kind of conditioned  rule, ring just in case the argument belong to V. In ..."
Abstract
 Add to MetaCart
this paper we propose a new calculus, the Vcalculus, which is parametric with respect to a subset V of terms that we call input values. The Vcalculus is a callbyvalue calculus, in the sense that the reduction rule is a kind of conditioned  rule, ring just in case the argument belong to V. Informally, input values represent partially evaluated terms, that can be passed as parameters. Callbyname and callbyvalue parameter passing can be seen as the two most radical choices: in the former policy parameters are not evaluated, while in the latter they are evaluated until an output result is reached. The only conditions we ask on the set V is to be closed under substitution and reduction: these conditions are quite natural, in order to preserve the status of an input, during the computation