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32
A CurryHoward foundation for functional computation with control
 In Proceedings of ACM SIGPLANSIGACT Symposium on Principle of Programming Languages
, 1997
"... We introduce the type theory ¯ v , a callbyvalue variant of Parigot's ¯calculus, as a CurryHoward representation theory of classical propositional proofs. The associated rewrite system is ChurchRosser and strongly normalizing, and definitional equality of the type theory is consistent, com ..."
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Cited by 90 (3 self)
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We introduce the type theory ¯ v , a callbyvalue variant of Parigot's ¯calculus, as a CurryHoward representation theory of classical propositional proofs. The associated rewrite system is ChurchRosser and strongly normalizing, and definitional equality of the type theory is consistent, compatible with cut, congruent and decidable. The attendant callbyvalue programming language ¯pcf v is obtained from ¯ v by augmenting it by basic arithmetic, conditionals and fixpoints. We study the behavioural properties of ¯pcf v and show that, though simple, it is a very general language for functional computation with control: it can express all the main control constructs such as exceptions and firstclass continuations. Prooftheoretically the dual ¯ v constructs of naming and ¯abstraction witness the introduction and elimination rules of absurdity respectively. Computationally they give succinct expression to a kind of generic (forward) "jump" operator, which may be regarded as a unif...
Full Abstraction for Functional Languages with Control
 In Proceedings, Twelfth Annual IEEE Symposium on Logic in Computer Science
, 1997
"... This paper considers the consequences of relaxing the bracketing condition on `dialogue games', showing that this leads to a category of games which can be `factorized' into a wellbracketed substructure, and a set of classically typed morphisms. These are shown to be sound denotations for ..."
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Cited by 86 (7 self)
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This paper considers the consequences of relaxing the bracketing condition on `dialogue games', showing that this leads to a category of games which can be `factorized' into a wellbracketed substructure, and a set of classically typed morphisms. These are shown to be sound denotations for control operators, allowing the factorization to be used to extend the definability result for PCF to one for PCF with control operators at atomic types. Thus we define a fully abstract and effectively presentable model of a functional language with nonlocal control as part of a modular approach to modelling nonfunctional features using games. 1.
A Semantic analysis of control
, 1998
"... This thesis examines the use of denotational semantics to reason about control flow in sequential, basically functional languages. It extends recent work in game semantics, in which programs are interpreted as strategies for computation by interaction with an environment. Abramsky has suggested that ..."
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Cited by 38 (6 self)
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This thesis examines the use of denotational semantics to reason about control flow in sequential, basically functional languages. It extends recent work in game semantics, in which programs are interpreted as strategies for computation by interaction with an environment. Abramsky has suggested that an intensional hierarchy of computational features such as state, and their fully abstract models, can be captured as violations of the constraints on strategies in the basic functional model. Nonlocal control flow is shown to fit into this framework as the violation of strong and weak ‘bracketing ’ conditions, related to linear behaviour. The language µPCF (Parigot’s λµ with constants and recursion) is adopted as a simple basis for highertype, sequential computation with access to the flow of control. A simple operational semantics for both callbyname and callbyvalue evaluation is described. It is shown that dropping the bracketing condition on games models of PCF yields fully abstract models of µPCF.
Sequentiality vs. Concurrency in Games and Logic
 Math. Structures Comput. Sci
, 2001
"... Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic. ..."
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Cited by 19 (0 self)
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Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.
Callbyvalue is dual to callbyname reloaded
 In Term rewriting and applications. Lecture Notes in Comput. Sci
, 2005
"... Abstract. We consider the relation of the dual calculus of Wadler (2003) to the λµcalculus of Parigot (1992). We give translations from the λµcalculus into the dual calculus and back again. The translations form an equational correspondence as defined by Sabry and Felleisen (1993). In particular, ..."
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Cited by 15 (0 self)
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Abstract. We consider the relation of the dual calculus of Wadler (2003) to the λµcalculus of Parigot (1992). We give translations from the λµcalculus into the dual calculus and back again. The translations form an equational correspondence as defined by Sabry and Felleisen (1993). In particular, translating from λµ to dual and then ‘reloading ’ from dual back into λµ yields a term equal to the original term. Composing the translations with duality on the dual calculus yields an involutive notion of duality on the λµcalculus. A previous notion of duality on the λµcalculus has been suggested by Selinger (2001), but it is not involutive. Note This paper uses color to clarify the relation of types and terms, and of source and target calculi. If the URL below is not in blue please download the color version from
Relational parametricity and control
 Logical Methods in Computer Science
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A classical linear lambdacalculus
, 1996
"... This paper proposes and studies a typed calculus for classical linear logic. I shall give an explanation of a multipleconclusion formulation for classical logic due to Parigot and compare it to more traditional treatments by Prawitz and others. I shall use Parigot's method to devise a natural ..."
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Cited by 9 (0 self)
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This paper proposes and studies a typed calculus for classical linear logic. I shall give an explanation of a multipleconclusion formulation for classical logic due to Parigot and compare it to more traditional treatments by Prawitz and others. I shall use Parigot's method to devise a natural deduction formulation of classical linear logic. This formulation is compared in detail to the sequent calculus formulation. In an appendix I shall also demonstrate a somewhat hidden connexion with the paradigm of control operators for functional languages which gives a new computational interpretation of Parigot's techniques.
Environments, Continuation Semantics and Indexed Categories
 Theoretical Aspects of Computer Software, number 1281 in Lect. Notes Comp. Sci
, 1997
"... . There have traditionally been two approaches to modelling environments, one by use of ønite products in Cartesian closed categories, the other by use of the base categories of indexed categories with structure. Recently, there have been more general deønitions along both of these lines: the ørst g ..."
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Cited by 7 (2 self)
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. There have traditionally been two approaches to modelling environments, one by use of ønite products in Cartesian closed categories, the other by use of the base categories of indexed categories with structure. Recently, there have been more general deønitions along both of these lines: the ørst generalising from Cartesian to symmetric premonoidal categories, the second generalising from indexed categories with speciøed structure to categories. The added generality is not of the purely mathematical kind; in fact it is necessary to extend semantics from the logical calculi studied in, say, Type Theory to more realistic programming language fragments. In this paper, we establish an equivalence between these two recent notions. We then use that equivalence to study semantics for continuations. We give three category theoretic semantics for modelling continuations and show the relationships between them. The ørst is given by a continuations monad. The second is based on a symmetric prem...
Type Theories for Autonomous and *Autonomous Categories: I. Type Theories and Rewrite Systems  II. Internal Languages and Coherence Theorems
, 1998
"... We introduce a family of type theories as internal languages for autonomous (or symmetric monoidal closed) and autonomous categories, in the same sense that simplytyped calculus (augmented by appropriate constructs for products and the terminal object) is the internal language for cartesian clos ..."
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Cited by 5 (4 self)
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We introduce a family of type theories as internal languages for autonomous (or symmetric monoidal closed) and autonomous categories, in the same sense that simplytyped calculus (augmented by appropriate constructs for products and the terminal object) is the internal language for cartesian closed categories. The rules are presented in the style of Gentzen's Sequent Calculus. A key feature is the systematic treatment of naturality conditions by explicitly representing the categorical composition, or cut in the type theory, by explicit substitution, and the introduction of new letconstructs, one for each of the three type constructors ?;\Omega and (, and a Parigotstyle ¯abstraction to give expression to the involutive negation. The commutation congruences of these theories are precisely those imposed by the naturality conditions. In particular the type theory for autonomous categories may be regarded as a term assignment system for the multiplicative (\Omega ; (;?;?)fragmen...
Games And Definability For FPC
 Bulletin of Symbolic Logic
, 1997
"... . A new games model of the language FPC, a type theory with products, sums, function spaces and recursive types, is described. A definability result is proved, showing that every finite element of the model is the interpretation of some term of the language. 1. Introduction. The work of Lorenzen [2 ..."
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. A new games model of the language FPC, a type theory with products, sums, function spaces and recursive types, is described. A definability result is proved, showing that every finite element of the model is the interpretation of some term of the language. 1. Introduction. The work of Lorenzen [24, 23] proposed dialogue games as a foundation for intuitionistic logic. The idea is simple: associated to a formula A is a set of moves for two players, each of which is either an attack on Aan attempt to refute its validityor a defence. The players, O who wants to refute A and P who wants to prove A, take turns to make moves according to some rules. The rules determine which player has won when play ends, and the formula A is semantically valid if there is a strategy by which P can always win: a winning strategy. More recently, games of this kind have been applied in computer science to give programming languages a new kind of semantics with a strong intensional flavour. The game in...