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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 103 (18 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.
Algorithmic Game Semantics
 In Schichtenberg and Steinbruggen [16
, 2001
"... Introduction SAMSON ABRAMSKY (samson@comlab.ox.ac.uk) Oxford University Computing Laboratory 1. Introduction Game Semantics has emerged as a powerful paradigm for giving semantics to a variety of programming languages and logical systems. It has been used to construct the first syntaxindependen ..."
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Cited by 47 (3 self)
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Introduction SAMSON ABRAMSKY (samson@comlab.ox.ac.uk) Oxford University Computing Laboratory 1. Introduction Game Semantics has emerged as a powerful paradigm for giving semantics to a variety of programming languages and logical systems. It has been used to construct the first syntaxindependent fully abstract models for a spectrum of programming languages ranging from purely functional languages to languages with nonfunctional features such as control operators and locallyscoped references [4, 21, 5, 19, 2, 22, 17, 11]. A substantial survey of the state of the art of Game Semantics circa 1997 was given in a previous Marktoberdorf volume [6]. Our aim in this tutorial presentation is to give a first indication of how Game Semantics can be developed in a new, algorithmic direction, with a view to applications in computerassisted verification and program analysis. Some promising steps have already been taken in this
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 fully ab ..."
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Cited by 34 (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...
A View on Implementing Processes: Categories of Circuits
, 1996
"... . We construct a category of circuits: the objects are alphabets and the morphisms are deterministic automata. The construction differs in several respects from the bicategories of circuits appearing previously in the literature: it is parameterized by a monad which allows flexibility in the emergen ..."
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Cited by 7 (1 self)
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. We construct a category of circuits: the objects are alphabets and the morphisms are deterministic automata. The construction differs in several respects from the bicategories of circuits appearing previously in the literature: it is parameterized by a monad which allows flexibility in the emergent notion of process. We focus on the circuits which arise from a distributive category and the exception monad. These circuits are partial in that they may, based on their state, choose to abort on some inputs. Consequently, certain circuits determine languages, and safety and liveness properties with respect to these languages are captured by circuit equations. Actually, the notions of safety and liveness arise abstractly in any copy category. Extracting the category of circuits which are both safe and live corresponds to the extensive completion of a distributive copy category. Partial circuits coincide with elements of the terminal coalgebra of a specific datatype. The coinduction princ...
Semantics for Interoperability: relating ontologies and schemata
 and Expert Systems Applications, 14th International Conference, DEXA 2003
, 2002
"... Any builder of an information system, whether a database or a knowledge based system, will start from some conceptualisation of the domain, which will embody a number of fundamental assumptions about the domain. Often these underlying assumptions... ..."
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Cited by 5 (0 self)
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Any builder of an information system, whether a database or a knowledge based system, will start from some conceptualisation of the domain, which will embody a number of fundamental assumptions about the domain. Often these underlying assumptions...
COMPACTLY ACCESSIBLE CATEGORIES AND QUANTUM KEY DISTRIBUTION
"... Abstract. Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finitedimensional, they cannot accomodate (co)limitbased constructions. For example, they cannot capture protocols such as quantum key distribution, that rely on the law of large n ..."
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Abstract. Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finitedimensional, they cannot accomodate (co)limitbased constructions. For example, they cannot capture protocols such as quantum key distribution, that rely on the law of large numbers. To overcome this limitation, we introduce the notion of a compactly accessible category, relying on the extra structure of a factorisation system. This notion allows for infinite dimension while retaining key properties of compact categories: the main technical result is that the choiceofduals functor on the compact
Final Coalgebras
"... That is, makes the diagram C R 1 oo 2 // D TC TR T1 oo T2 // TD 1 commute. We call a pair (c; d) 2 C D bisimilar, if 9R C D. R bisimulation and (c; d) 2 R. If c and d are bisimilar, this is denoted by c  d. 2 On Bisimulation If f : A ! B is a function, denote its Graph b ..."
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That is, makes the diagram C R 1 oo 2 // D TC TR T1 oo T2 // TD 1 commute. We call a pair (c; d) 2 C D bisimilar, if 9R C D. R bisimulation and (c; d) 2 R. If c and d are bisimilar, this is denoted by c  d. 2 On Bisimulation If f : A ! B is a function, denote its Graph by G(f) = f(a; f(a)) j a 2<F12.2
J. GoubaultLarrecq
, 2002
"... We describe a construction of coequalizers in the category Cpo Cpo Cpo of complete partial orders and continuous maps, showing that this category is cocomplete. This is not new: Meseguer proved it in 1977, using fairly abstract categorytheoretic tools, and Fiech reproved it in 1996, using fairly ..."
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We describe a construction of coequalizers in the category Cpo Cpo Cpo of complete partial orders and continuous maps, showing that this category is cocomplete. This is not new: Meseguer proved it in 1977, using fairly abstract categorytheoretic tools, and Fiech reproved it in 1996, using fairly intricate byhand constructions. We hope to give a clearer and better structured presentation of the construction.
Talk I: Final Coalgebras
, 2003
"... For the remainder of this exposition assume that T: Set! Set is an endofunctor. Unless otherwise stated, the results and proofs of the material presented is taken from Rutten [10]. 1 Preliminaries Deo/nition 1.1. (i) A Tcoalgebra (Tsystem) is pair (C; fl) where C is a set and fl: C! T C. (ii) If ( ..."
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For the remainder of this exposition assume that T: Set! Set is an endofunctor. Unless otherwise stated, the results and proofs of the material presented is taken from Rutten [10]. 1 Preliminaries Deo/nition 1.1. (i) A Tcoalgebra (Tsystem) is pair (C; fl) where C is a set and fl: C! T C. (ii) If (C; fl) and (D; ffi) are Tsystems, then f: C! D is a Tcoalgebra homomorphism (Tmorphism), if ffi ffi f = T f ffi fl, that is, if the diagram C fl fflffl f // D