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32
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 192 (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.
A system of interaction and structure
 ACM TRANSACTIONS ON COMPUTATIONAL LOGIC
, 2004
"... This paper introduces a logical system, called BV, which extends multiplicative linear logic by a noncommutative selfdual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, call ..."
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Cited by 87 (15 self)
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This paper introduces a logical system, called BV, which extends multiplicative linear logic by a noncommutative selfdual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulae subject to certain equational laws typical of sequents. The calculus of structures is obtained by generalising the sequent calculus in such a way that a new topdown symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allowing the design of BV, yield a modular proof of cut elimination.
Noncommutativity and MELL in the Calculus of Structures
 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2001
"... We introduce the calculus of structures: it is more general than the sequent calculus and it allows for cut elimination and the subformula property. We show a simple extension of multiplicative linear logic, by a selfdual noncommutative operator inspired by CCS, that seems not to be expressible in ..."
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Cited by 58 (22 self)
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We introduce the calculus of structures: it is more general than the sequent calculus and it allows for cut elimination and the subformula property. We show a simple extension of multiplicative linear logic, by a selfdual noncommutative operator inspired by CCS, that seems not to be expressible in the sequent calculus. Then we show that multiplicative exponential linear logic benefits from its presentation in the calculus of structures, especially because we can replace the ordinary, global promotion rule by a local version. These formal systems, for which we prove cut elimination, outline a range of techniques and properties that were not previously available. Contrarily to what happens in the sequent calculus, the cut elimination proof is modular.
A Judgmental Analysis of Linear Logic
, 2003
"... We reexamine the foundations of linear logic, developing a system of natural deduction following MartinL of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, ext ..."
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Cited by 49 (27 self)
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We reexamine the foundations of linear logic, developing a system of natural deduction following MartinL of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva's full intuitionistic linear logic. We also provide a corresponding sequent calculus that admits a simple proof of the admissibility of cut by a single structural induction. Finally, we show how to interpret classical linear logic (with or without the MIX rule) in our system, employing a form of doublenegation translation.
Focusing the inverse method for linear logic
 Proceedings of CSL 2005
, 2005
"... 1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10 ..."
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Cited by 38 (11 self)
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1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10
A NonCommutative Extension of MELL
, 2002
"... We extend multiplicative exponential linear logic (MELL) by a noncommutative, selfdual logical operator. The extended system, called NEL, is defined in the formalism of the calculus of structures, which is a generalisation of the sequent calculus and provides a more refined analysis of proofs. We ..."
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Cited by 27 (12 self)
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We extend multiplicative exponential linear logic (MELL) by a noncommutative, selfdual logical operator. The extended system, called NEL, is defined in the formalism of the calculus of structures, which is a generalisation of the sequent calculus and provides a more refined analysis of proofs. We should then be able to extend the range of applications of MELL, by modelling a broad notion of sequentiality and providing new properties of proofs. We show some proof theoretical results: decomposition and cut elimination. The new operator represents a significant challenge: to get our results we use here for the first time some novel techniques, which constitute a uniform and modular approach to cut elimination, contrary to what is possible in the sequent calculus.
A Purely Logical Account of Sequentiality in Proof Search
, 2002
"... A strict correspondence between the proofsearch space of a logical formal system and computations in a simple process algebra is established. Sewuential ..."
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Cited by 24 (3 self)
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A strict correspondence between the proofsearch space of a logical formal system and computations in a simple process algebra is established. Sewuential
Full completeness of the multiplicative linear logic of chu spaces
 Proc. IEEE Logic in Computer Science 14
, 1999
"... We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cutfree proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on ..."
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Cited by 22 (8 self)
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We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cutfree proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on a twoletter alphabet. This is the online version of the paper of the same title appearing in the LICS’99 proceedings. 1
Games for Recursive Types
 Theory and Formal Methods of Computing 1994: Proceedings of the Second Imperial College Department of Computing Workshop on Theory and Formal Methods. Imperial
, 1994
"... We present results concerning the solution of recursive domain equations in the category G of games, which is a modified version of the category presented in [AJM94]. New constructions corresponding to lifting and separated sum for games are presented, and are used to generate games for two simple r ..."
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Cited by 16 (4 self)
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We present results concerning the solution of recursive domain equations in the category G of games, which is a modified version of the category presented in [AJM94]. New constructions corresponding to lifting and separated sum for games are presented, and are used to generate games for two simple recursive types: the vertical and lazy natural numbers. Recently, the "game semantics" paradigm has been used to model the multiplicative fragment of linear logic [AJ94], and to provide a solution to the full abstraction problem for PCF [AJM94, HO94], where the intensional structure of the games model captures both the sequential and functional nature of the language. In the light of these results, it is natural to ask whether recursive types can be handled in this setting. Here we show that they can: for a wide class of functors \Phi, including all of the usual type constructors, the equation D ' \Phi(D) has a (canonical) solution. In fact we solve this equation up to identity, and the solut...
Timeless Games
 Computer Science Logic: 11th International Workshop Proceedings, volume 1414 of Lecture Notes in Computer Science. EACSL
, 1998
"... . Two models of classical linear logic are set up. First our recent version of AJM games model which will be our source model. Then the target model, polarized pointed relations, a variant of the plain relational model which is constructed in two steps: first the model of pointed relations, then the ..."
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Cited by 14 (1 self)
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. Two models of classical linear logic are set up. First our recent version of AJM games model which will be our source model. Then the target model, polarized pointed relations, a variant of the plain relational model which is constructed in two steps: first the model of pointed relations, then the additional polarization structure which yields a proper duality. Then the natural timeforgetting map is shown to generate a lax functor from the source to the target. Finally a further refinement of the target model using bipolarities is sketched, giving a closer link with the games model for the interpretation of syntax. Thus a bridge is constructed that goes from a dynamic model to a static model of evaluation. 1 Introduction The basic mathematical reflex was to model types, programs, evaluation with sets, functions, composition. As years went by, denotational semantics pictured the syntactic triple with increasingly sophisticated tools: lattices, posets, concrete data structures, coher...