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13
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 298 (31 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 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
Towards a Mathematical Operational Semantics
 In Proc. 12 th LICS Conf
, 1997
"... We present a categorical theory of `wellbehaved' operational semantics which aims at complementing the established theory of domains and denotational semantics to form a coherent whole. It is shown that, if the operational rules of a programming language can be modelled as a natural transformation ..."
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Cited by 134 (9 self)
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We present a categorical theory of `wellbehaved' operational semantics which aims at complementing the established theory of domains and denotational semantics to form a coherent whole. It is shown that, if the operational rules of a programming language can be modelled as a natural transformation of a suitable general form, depending on functorial notions of syntax and behaviour, then one gets both an operational model and a canonical, internally fully abstract denotational model for free; moreover, both models satisfy the operational rules. The theory is based on distributive laws and bialgebras; it specialises to the known classes of wellbehaved rules for structural operational semantics, such as GSOS.
On the Foundations of Final Coalgebra Semantics: nonwellfounded sets, partial orders, metric spaces
, 1998
"... ..."
On the Origins of Bisimulation and Coinduction
"... The origins of bisimulation and bisimilarity are examined, in the three fields where they have been ..."
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Cited by 21 (0 self)
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The origins of bisimulation and bisimilarity are examined, in the three fields where they have been
Semantics for Finite Delay
 Theoretical Computer Science
, 1997
"... We produce a fully abstract model for a notion of process equivalence taking into account issues of fairness, called by Milner fair bisimilarity. The model uses Aczel's antifoundation axiom and it is constructed along the lines of the antifounded model for SCCS given by Aczel. We revisit Aczel's s ..."
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Cited by 4 (2 self)
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We produce a fully abstract model for a notion of process equivalence taking into account issues of fairness, called by Milner fair bisimilarity. The model uses Aczel's antifoundation axiom and it is constructed along the lines of the antifounded model for SCCS given by Aczel. We revisit Aczel's semantics for SCCS where we prove a unique fixpoint theorem under the assumption of guarded recursion. Then we consider Milner's extension of SCCS to include a finite delay operator ". Working with fair bisimilarity we construct a fully abstract model, which is also fully abstract for fortification. We discuss the solution of recursive equations in the model. The paper is concluded with an investigation of the algebraic theory of fair bisimilarity. Keywords: fairness, antifoundation, finite delay, parallelism, fair bisimilarity, fortification. This paper was composed while I was unemployed and an unofficial visitor at the Department of Mathematics, University of Ioannina, Greece. My than...
Coinductive Interpreters for Process Calculi
 In Sixth International Symposium on Functional and Logic Programming, volume 2441 of LNCS
, 2002
"... This paper suggests functional programming languages with coinductive types as suitable devices for prototyping process calculi. The proposed approach is independent of any particular process calculus and makes explicit the dierent ingredients present in the design of any such calculi. In partic ..."
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Cited by 3 (1 self)
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This paper suggests functional programming languages with coinductive types as suitable devices for prototyping process calculi. The proposed approach is independent of any particular process calculus and makes explicit the dierent ingredients present in the design of any such calculi. In particular structural aspects of the underlying behaviour model become clearly separated from the interaction structure which de nes the synchronisation discipline. The approach is illustrated by the detailed development in Charity of an interpreter for a family of process languages.
Lectures on Semantics: The initial algebra and final coalgebra perspectives
"... These lectures give a nonstandard introduction, for computer science students, to the mathematical semantics of formal languages. We do not attempt to give a balanced treatment, but instead focus on some key general ideas, illustrated with simple examples. The ideas are formulated using some elemen ..."
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Cited by 3 (0 self)
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These lectures give a nonstandard introduction, for computer science students, to the mathematical semantics of formal languages. We do not attempt to give a balanced treatment, but instead focus on some key general ideas, illustrated with simple examples. The ideas are formulated using some elementary category theoretic notions. All the required category theory is introduced in the lectures. In addition to the familiar initial algebra approach to syntax and semantics we examine the less familiar final coalgebra approach to operational semantics. Our treatment of formal semantics is intended to complement a more standard introduction.
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 ..."
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Cited by 2 (2 self)
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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.
Adding Enrichments to Refined Interleavings: A New Model for the πCalculus
, 1999
"... The question of how to model πcalculus name passing has attracted significant interest. Here, this topic is approached with a new fully abstract interleaving model. Its central feature: Every semantic object contains all its transformations under injective name replacements. It is shown how this en ..."
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The question of how to model πcalculus name passing has attracted significant interest. Here, this topic is approached with a new fully abstract interleaving model. Its central feature: Every semantic object contains all its transformations under injective name replacements. It is shown how this enrichment can be used, in a systematic way, to obtain compositional interpretations of the constructors of the πcalculus. The theory of nonwellfounded sets serves as the mathematical basis. Moreover, category theory is used in the form of coalgebras of endofunctors. Not more is needed since transformations under name replacements are not regarded as arrows of a category of partial orders of (unenriched) semantic objects. This approach is a hallmark of previous interleaving models of the πcalculus. It seems to require a lot more category theory than is used here. Also, unlike other related work, the present one does not employ type theory.