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27
Computational Interpretations of Linear Logic
 Theoretical Computer Science
, 1993
"... We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the CurryHoward isomorphism. In the case of Intuitionistic Linear Logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluation an ..."
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Cited by 282 (3 self)
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We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the CurryHoward isomorphism. In the case of Intuitionistic Linear Logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluation and storage allocation, while maintaining the logical content of programs as proofs, and computation as cutelimination.
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 209 (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.
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 in a certai ..."
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Cited by 194 (14 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.
Full Abstraction for PCF (Extended Abstract)
 THEORETICAL ASPECTS OF COMPUTER SOFTWARE. INTERNATIONAL SYMPOSIUM TACS'94, NUMBER 789 IN LECTURE NOTES IN COMPUTER SCIENCE
, 1994
"... The Full Abstraction Problem for PCF [23, 20, 7, 11] is one of the longeststanding problems in the semantics of programming languages. There is quite widespread agreement that it is one of the most difficult; there is much less agreement as to what exactly the problem is, or more particularly as ..."
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Cited by 66 (11 self)
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The Full Abstraction Problem for PCF [23, 20, 7, 11] is one of the longeststanding problems in the semantics of programming languages. There is quite widespread agreement that it is one of the most difficult; there is much less agreement as to what exactly the problem is, or more particularly as to the precise criteria for a solution. The usual formulation is that one wants a "semantic characterization" of the fully abstract model (by which we mean the inequationally fully abstract orderextensional model, which Milner proved to be uniquely specified up to isomorphism by these properties [20]). The problem is to understand what should be meant by a "semantic characterization". Our view is that the essential content of the problem, what makes it important, is that it calls for a semantic characterization of sequential, functional computation at hig...
Proof Nets for Intuitionistic Linear Logic
 Essential Nets, Research Report
"... Abstract. We present a class of proof nets that are specially designed for Intuitionistic Linear Logic, for which we give a correctness criterion, as well as a cutelimination procedure. The proof of sequentialization uses a special kind of oriented paths. In this paper we present a class of proof o ..."
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Cited by 34 (1 self)
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Abstract. We present a class of proof nets that are specially designed for Intuitionistic Linear Logic, for which we give a correctness criterion, as well as a cutelimination procedure. The proof of sequentialization uses a special kind of oriented paths. In this paper we present a class of proof objects for intuitionistic linear logic with the connectives ⊗, ⊸, � and! 1; in particular we can interpret the simply typed lambda calculus, with or without product types. We call these proof nets essential nets. We will formulate a correctness criterion for them: there is an intrinsic property that characterizes the essential nets that do come from proofs in the sequent calculus; it turns out that every such (correct) essential net represents a large number of sequent proofs that differ by inessential details. Thus essential nets, as should be the case for proof nets in general, have the power of eliminating a lot of the bureaucracy in the sequent calculus. We will give a cutelimination procedure for essential nets which is based on that correctness criterion. That procedure is not one that can be said to be
Interaction Nets and Term Rewriting Systems
, 1998
"... Term rewriting systems provide a framework in which it is possible to specify and program in a traditional syntax (oriented equations). Interaction nets, on the other hand, provide a graphical syntax for the same purpose, but can be regarded as being closer to an implementation since the reductio ..."
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Cited by 13 (7 self)
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Term rewriting systems provide a framework in which it is possible to specify and program in a traditional syntax (oriented equations). Interaction nets, on the other hand, provide a graphical syntax for the same purpose, but can be regarded as being closer to an implementation since the reduction process is local and asynchronous, and all the operations are made explicit, including discarding and copying of data. Our aim is to bridge the gap between the above formalisms by showing how to understand interaction nets in a term rewriting framework. This allows us to transfer results from one paradigm to the other, deriving syntactical properties of interaction nets from the (wellstudied) properties of term rewriting systems; in particular concerning termination and modularity. Keywords: term rewriting, interaction nets, termination, modularity. 1 Introduction Term rewriting systems provide a general framework for specifying and reasoning about computation. They can be regarde...
Causality and True Concurrency: A Dataflow Analysis of the PiCalculus (Extended Abstract)
, 1995
"... ) (Appeared in the Proceedings of the Fourth International Conference on Algebraic Methodology and Software Technology, July 1995 Lecture Notes in Computer Science, Volume 936) Lalita Jategaonkar Jagadeesan Software Production Research Dept. AT&T Bell Laboratories Naperville, IL 60566 (USA) lalita ..."
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Cited by 12 (0 self)
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) (Appeared in the Proceedings of the Fourth International Conference on Algebraic Methodology and Software Technology, July 1995 Lecture Notes in Computer Science, Volume 936) Lalita Jategaonkar Jagadeesan Software Production Research Dept. AT&T Bell Laboratories Naperville, IL 60566 (USA) lalita@research.att.com Radha Jagadeesan ? Math. Sciences Loyola University Chicago, IL 60626 (USA) radha@math.luc.edu 1 Introduction The picalculus [18, 17] is a process algebra for describing networks of processes with dynamically evolving communication structure. The key idea underlying the picalculus is the notion of naming: names are used to refer to channels  the links between processes, and can be dynamically created or hidden. Names together with a rich algebra of process combinators that includes parallel composition, allow the picalculus to encode asynchronous networks of processes that evolve dynamically. In turn, mobility  this ability to change the network configuratio...
Local and asynchronous betareduction (an analysis of Girard's EX formula)
, 1992
"... We build a confluent, local, asynchronous reduction on terms, using infinite objects (partial injections of Girard's algebra L*), which is simple (only one move), intelligible (semantic setting of the reduction), general (based on a largescale decomposition of fi), and may be mechanized. ' Equipe d ..."
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Cited by 12 (0 self)
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We build a confluent, local, asynchronous reduction on terms, using infinite objects (partial injections of Girard's algebra L*), which is simple (only one move), intelligible (semantic setting of the reduction), general (based on a largescale decomposition of fi), and may be mechanized. ' Equipe de Logique Math'ematique UFR de math'ematiques Couloir 4555, 5`eme 'etage Universit'e de Paris 7 2 place Jussieu 75251 Paris Cedex 05 FRANCE Phone: (331) 43 29 77 26 Introduction Captatio Benevolentiae. calculus certainly is the simplest syntax ever developed for proof denotation & normalization in intuitionistic logic. Discovered by Church, rediscovered by Gentzen (under the guise of natural deduction), turned into a functional language by McCarthy (LISP), and nowadays clearly seen to be extendable to classical logic as well,  calculus is a fair syntax. Longing for a mathematical account of fireduction. Albeit the computation rule of  calculus, fireduction, is simple, understood...
The geometry of linear higherorder recursion
 In Logic in Computer Science, 20th International Symposium, Proceedings
, 2005
"... Linearity and ramification constraints have been widely used to weaken higherorder (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions, as the works by Leivant, Hofmann and others show. This paper shows that finetuning these two cons ..."
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Cited by 9 (4 self)
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Linearity and ramification constraints have been widely used to weaken higherorder (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions, as the works by Leivant, Hofmann and others show. This paper shows that finetuning these two constraints leads to different expressive strengths, some of them lying well beyond polynomial time. This is done by introducing a new semantics, called algebraic context semantics. The framework stems from Gonthier’s original work and turns out to be a versatile and powerful tool for the quantitative analysis of normalization in the lambdacalculus with constants and higherorder recursion. 1
The Effects of
 Artificial Sources of Water on Rangeland Biodiversity. Environment Australia and CSIRO
, 1997
"... “Turing hoped that his abstractedpapertape model was so simple, so transparent and well defined, that it would not depend on any assumptions about physics that could conceivably be falsified, and therefore that it could become the basis of an abstract theory of computation that was independent of ..."
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Cited by 9 (5 self)
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“Turing hoped that his abstractedpapertape model was so simple, so transparent and well defined, that it would not depend on any assumptions about physics that could conceivably be falsified, and therefore that it could become the basis of an abstract theory of computation that was independent of the underlying physics. ‘He thought, ’ as Feynman once put it, ‘that he understood paper. ’ But he was mistaken. Real, quantummechanical paper is wildly different from the abstract stuff that the Turing machine uses. The Turing machine is entirely classical...”