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72
Full Abstraction for PCF
 INFORMATION AND COMPUTATION
, 1996
"... An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "historyfree" strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable i ..."
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Cited by 255 (16 self)
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An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "historyfree" strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable in a certain simple extension of PCF. We then introduce an intrinsic preorder on strategies, and show that it satisfies some remarkable properties, such that the intrinsic preorder on function types coincides with the pointwise preorder. We then obtain an orderextensional fully abstract model of PCF by quotienting the intensional model by the intrinsic preorder. This is the first syntaxindependent description of the fully abstract model for PCF. (Hyland and Ong have obtained very similar results by a somewhat different route, independently and at the same time.) We then consider the effective version of our model, and prove a Universality Theorem: every element of the effective extensional model is definable in PCF. Equivalently, every recursive strategy is definable up to observational equivalence.
logic: its syntax and semantics
 Advances in Linear Logic
, 1995
"... Linear logic is not an alternative logic; it should rather be seen as an extension of usual logic. Since there is no hope to modify the extant classical or intuitionistic connectives 1, linear logic introduces new connectives. 1.1.1 Exponentials: actions vs situations Classical and intuitionistic lo ..."
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Cited by 192 (1 self)
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Linear logic is not an alternative logic; it should rather be seen as an extension of usual logic. Since there is no hope to modify the extant classical or intuitionistic connectives 1, linear logic introduces new connectives. 1.1.1 Exponentials: actions vs situations Classical and intuitionistic logics deal with stable truths: if A and A ⇒ B, then B, but A still holds. This is perfect in mathematics, but wrong in real life, since real implication is causal. A causal implication cannot be iterated since the conditions are modified after its use; this process of modification of the premises (conditions) is known in physics as reaction. For instance, if A is to spend $1 on a pack of cigarettes and B is to get them, you lose $1 in this process, and you cannot do it a second time. The reaction here was that $1 went out of your pocket. The first objection to that view is that there are in mathematics, in real life, cases where reaction does not exist or can be neglected: think of a lemma which is forever true, or of a Mr. Soros, who has almost an infinite amount of dollars.
Games and Full Abstraction for the Lazy lambdacalculus
 In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science
, 1995
"... ion for the Lazy calculus Samson Abramsky Guy McCusker Department of Computing Imperial College of Science, Technology and Medicine 180 Queen's Gate London SW7 2BZ United Kingdom Abstract We define a category of games G, and its extensional quotient E . A model of the lazy calculus, a typ ..."
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Cited by 149 (9 self)
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ion for the Lazy calculus Samson Abramsky Guy McCusker Department of Computing Imperial College of Science, Technology and Medicine 180 Queen's Gate London SW7 2BZ United Kingdom Abstract We define a category of games G, and its extensional quotient E . A model of the lazy calculus, a typefree functional language based on evaluation to weak head normal form, is given in G, yielding an extensional model in E . This model is shown to be fully abstract with respect to applicative simulation. This is, so far as we know, the first purely semantic construction of a fully abstract model for a reflexivelytyped sequential language. 1 Introduction Full Abstraction is a key concept in programming language semantics [9, 12, 23, 26]. The ingredients are as follows. We are given a language L, with an `observational preorder'  on terms in L such that P  Q means that every observable property of P is also satisfied by Q; and a denotational model MJ\DeltaK. The model M is then said to be f...
Glueing and Orthogonality for Models of Linear Logic
 Theoretical Computer Science
, 2003
"... We present the general theory of the method of glueing and associated technique of orthogonality for constructing categorical models of all the structure of linear logic: in particular we treat the exponentials in detail. We indicate simple applications of the methods and show that they cover famili ..."
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Cited by 41 (6 self)
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We present the general theory of the method of glueing and associated technique of orthogonality for constructing categorical models of all the structure of linear logic: in particular we treat the exponentials in detail. We indicate simple applications of the methods and show that they cover familiar examples. 1
Kripke Logical Relations and PCF
 Information and Computation
, 1995
"... Sieber has described a model of PCF consisting of continuous functions that are invariant under certain (finitary) logical relations, and shown that it is fully abstract for closed terms of up to thirdorder types. We show that one may achieve full abstraction at all types using a form of "Krip ..."
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Cited by 35 (3 self)
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Sieber has described a model of PCF consisting of continuous functions that are invariant under certain (finitary) logical relations, and shown that it is fully abstract for closed terms of up to thirdorder types. We show that one may achieve full abstraction at all types using a form of "Kripke logical relations" introduced by Jung and Tiuryn to characterize definability. To appear in Information and Computation. (Accepted, October 1994) Supported by NSF grant CCR92110829. 1 Introduction The nature of sequential functional computation has fascinated computer scientists ever since Scott remarked on a curious incompleteness phenomenon when he introduced LCF (Logic for Computable Functions) and its continuous function model in 1969 (Scott, 1993). Scott noted that although the functionals definable by terms in PCFthe term language of LCFadmitted a sequential evaluation strategy, there were functions in the model that seemed to require a parallel evaluation strategy. "Sequen...
Compositional and Inductive Semantic Definitions in Fixpoint, Equational, Constraint, Closurecondition, Rulebased and GameTheoretic Form
, 1995
"... We present a language and semanticsindependent, compositional and inductive method for specifying formal semantics or semantic properties of programs in equivalent fixpoint, equational, constraint, closurecondition, rulebased and gametheoretc form. The definitional method is obtained by extendin ..."
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Cited by 26 (10 self)
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We present a language and semanticsindependent, compositional and inductive method for specifying formal semantics or semantic properties of programs in equivalent fixpoint, equational, constraint, closurecondition, rulebased and gametheoretc form. The definitional method is obtained by extending settheoretic definitions in the context of partial orders. It is parameterized by the language syntax, by the semantic domains and by the semantic transformers corresponding to atomic and compound program components. The definitional method is shown to be preserved by abstract interpretation in either fixpoint, equational, constraint, closurecondition, rulebased or gametheoretic form. The features common to all possible instantiations are factored out thus allowing for results of general scope such as welldefinedness, semantic equivalence, soundness and relative completeness of abstract interpretations, etc. to be proved compositionally in a general language and semanticsindependent framework.
Nondeterministic Games and Program Analysis: An application to security (Extended Abstract)
 Proceedings of the Fourteenth International Symposium on Logic in Computer Science, Computer Society Press of the IEEE
"... Pasquale Malacaria and Chris Hankin Dept. of Computing Imperial College LONDON SW7 2BZ pm5,clh@doc.ic.ac.uk Abstract We present a unifying framework for using game semantics as a basis for program analysis. Also, we present a case study of the techniques. The unifying framework presents games ..."
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Cited by 24 (4 self)
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Pasquale Malacaria and Chris Hankin Dept. of Computing Imperial College LONDON SW7 2BZ pm5,clh@doc.ic.ac.uk Abstract We present a unifying framework for using game semantics as a basis for program analysis. Also, we present a case study of the techniques. The unifying framework presents gamesbased program analysis as an abstract interpretation of an appropriate games category in the category of nondeterministic games. The case study concerns an application to security.
A Structural Approach to Reversible Computation
 Theoretical Computer Science
, 2001
"... Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on simulations of lowlevel machine models. By contrast, we develop ..."
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Cited by 24 (3 self)
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Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on simulations of lowlevel machine models. By contrast, we develop a more structural approach. We show how highlevel functional programs can be mapped compositionally (i.e. in a syntaxdirected fashion) into a simple kind of automata which are immediately seen to be reversible. The size of the automaton is linear in the size of the functional term. In mathematical terms, we are building a concrete model of functional computation. This construction stems directly from ideas arising in Geometry of Interaction and Linear Logic—but can be understood without any knowledge of these topics. In fact, it serves as an excellent introduction to them. At the same time, an interesting logical delineation between reversible and irreversible forms of computation emerges from our analysis. 1