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43
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 325 (32 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
Games and Full Completeness for Multiplicative Linear Logic
 JOURNAL OF SYMBOLIC LOGIC
, 1994
"... We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the den ..."
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Cited by 215 (26 self)
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We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear Logic with the MIX rule: every winning strategy is the denotation of a unique cutfree proof net. A key role is played by the notion of historyfree strategy; strong connections are made between historyfree strategies and the Geometry of Interaction. Our semantics incorporates a natural notion of polarity, leading to a refined treatment of the additives. We make comparisons with related work by Joyal, Blass et al.
Linearity, Sharing and State: a fully abstract game semantics for Idealized Algol with active expressions
 ALGOLLIKE LANGUAGES
, 1997
"... The manipulation of objects with state which changes over time is allpervasive in computing. Perhaps the simplest example of such objects are the program variables of classical imperative languages. An important strand of work within the study of such languages, pioneered by John Reynolds, focusses ..."
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Cited by 105 (19 self)
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The manipulation of objects with state which changes over time is allpervasive in computing. Perhaps the simplest example of such objects are the program variables of classical imperative languages. An important strand of work within the study of such languages, pioneered by John Reynolds, focusses on "Idealized Algol", an elegant synthesis of imperative and functional features. We present a novel semantics for Idealized Algol using games, which is quite unlike traditional denotational models of state. The model takes into account the irreversibility of changes in state, and makes explicit the difference between copying and sharing of entities. As a formal measure of the accuracy of our model, we obtain a full abstraction theorem for Idealized Algol with active expressions.
A brief history of process algebra
 Theor. Comput. Sci
, 2004
"... Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The a ..."
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Cited by 62 (1 self)
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Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.
Interactive Foundations of Computing
, 1997
"... : The claim that interactive systems have richer behavior than algorithms is surprisingly easy to prove: Turing machines cannot model interaction machines because: interaction is not expressible by a finite initial input string. Interaction machines extend the Chomsky hierarchy, are modeled by inte ..."
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Cited by 50 (6 self)
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: The claim that interactive systems have richer behavior than algorithms is surprisingly easy to prove: Turing machines cannot model interaction machines because: interaction is not expressible by a finite initial input string. Interaction machines extend the Chomsky hierarchy, are modeled by interaction grammars, and precisely capture fuzzy concepts like open systems and empirical computer science. Part I of this paper examines extensions to interactive models for algorithms, machines, grammars, and semantics, while part II considers the expressiveness of different forms of interaction. Interactive identity machines are already more powerful than Turing machines, while noninteractive parallelism and distribution are algorithmic. The extension of Turing to interaction machines parallels that of the lambda to the pi calculus, but the ability to model shared state allows interaction machines to express more powerful behavior than calculi. Asynchronous and nonserializable interaction ar...
Geometry of Interaction and Linear Combinatory Algebras
, 2000
"... this paper was quite di#erent, stemming from the axiomatics of categories of tangles (although the authors were aware of possible connections to iteration theories. In fact, similar axiomatics in the symmetric case, motivated by flowcharts and "flownomials" had been developed some years ea ..."
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Cited by 42 (10 self)
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this paper was quite di#erent, stemming from the axiomatics of categories of tangles (although the authors were aware of possible connections to iteration theories. In fact, similar axiomatics in the symmetric case, motivated by flowcharts and "flownomials" had been developed some years earlier by Stefanescu (Stefanescu 2000).) However, the first author realized, following a stimulating discussion with Gordon Plotkin, that traced monoidal categories provided a common denominator for the axiomatics of both the Girardstyle and AbramskyJagadeesanstyle versions of the Geometry of Interaction, at the basic level of the multiplicatives. This insight was presented in (Abramsky 1996), in which Girardstyle GoI was dubbed "particlestyle", since it concerns information particles or tokens flowing around a network, while the AbramskyJagadeesan style GoI was dubbed "wavestyle", since it concerns the evolution of a global information state or "wave". Formally, this distinction is based on whether the tensor product (i.e. the symmetric monoidal structure) in the underlying category is interpreted as a coproduct (particle style) or as a product (wave style). This computational distinction between coproduct and product interpretations of the same underlying network geometry turned out to have been partially anticipated, in a rather di#erent context, in a pioneering paper by E. S. Bainbridge (Bainbridge 1976), as observed by Dusko Pavlovic. These two forms of interpretation, and ways of combining them, have also been studied recently in (Stefanescu 2000). He uses the terminology "additive" for coproductbased (i.e. our "particlestyle") and "multiplicative" for productbased (i.e. our "wavestyle"); this is not suitable for our purposes, because of the clash with Linear Logic term...
Full Abstraction for Idealized Algol with Passive Expressions
, 1998
"... ion for Idealized Algol with Passive Expressions Samson Abramsky University of Edinburgh Department of Computer Science James Clerk Maxwell Building Edinburgh EH9 3JZ Scotland samson@dcs.ed.ac.uk Guy McCusker St John's College Oxford OX1 3JP, England mccusker@comlab.ox.ac.uk Abstract A ful ..."
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Cited by 38 (7 self)
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ion for Idealized Algol with Passive Expressions Samson Abramsky University of Edinburgh Department of Computer Science James Clerk Maxwell Building Edinburgh EH9 3JZ Scotland samson@dcs.ed.ac.uk Guy McCusker St John's College Oxford OX1 3JP, England mccusker@comlab.ox.ac.uk Abstract A fully abstract games model of Reynolds' Idealized Algol is described. The model gives a semantic account of the distinction between active types, such as commands, which admit sideeffecting behaviour, and passive types, such as expressions, which do not. Keywords: Algollike languages, game semantics, full abstraction. 1 Introduction Our aim in this paper is to give the first syntaxindependent construction of a fully abstract model for Idealized Algol. John Reynolds proposed Idealized Algol as capturing the essence of Algol 60 [32]; it is an elegant synthesis of the features of a simple blockstructured imperative programming language with those of higherorder functional programming. As such it...
InformationFlow Security for Interactive Programs
"... Interactive programs allow users to engage in input and output throughout execution. The ubiquity of such programs motivates the development of models for reasoning about their informationflow security, yet no such models seem to exist for imperative programming languages. Further, existing langua ..."
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Cited by 29 (9 self)
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Interactive programs allow users to engage in input and output throughout execution. The ubiquity of such programs motivates the development of models for reasoning about their informationflow security, yet no such models seem to exist for imperative programming languages. Further, existing languagebased security conditions founded on noninteractive models permit insecure information flows in interactive imperative programs. This paper formulates new strategybased informationflow security conditions for a simple imperative programming language that includes input and output operators. The semantics of the language enables a finegrained approach to the resolution of nondeterministic choices. The security conditions leverage this approach to prohibit refinement attacks while still permitting observable nondeterminism. Extending the language with probabilistic choice yields a corresponding definition of probabilistic noninterference. A soundness theorem demonstrates the feasibility of statically enforcing the security conditions via a simple type system. These results constitute a step toward understanding and enforcing informationflow security in realworld programming languages, which include similar input and output operators.
Algebraic Approaches to Nondeterminism  an Overview
 ACM Computing Surveys
, 1997
"... this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University ..."
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Cited by 24 (3 self)
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this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University
Correspondence between Operational and Denotational Semantics
 Handbook of Logic in Computer Science
, 1995
"... This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational ..."
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Cited by 23 (0 self)
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This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational semantics of PCF induced by an interpretation; (standard) Scott model, adequacy, weak adequacy and its proof (by a computability predicate) Domain Theory up to SFP and Scott domains; non full abstraction of the standard model, definability of compact elements and full abstraction for PCFP (PCF + parallel or), properties of orderextensional (continuous) models of PCF, Milner's model and Mulmuley's construction (excluding proofs) Additional topics (time permitting): results on pure simplytyped lambda calculus, Friedman 's Completeness Theorem, minimal model, logical relations and definability, undecidability of lambda definability (excluding proof), dIdomains and stable functions Homepa...