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14
CallbyValue Games
, 1997
"... . A general construction of models of callbyvalue from models of callbyname computation is described. The construction makes essential use of the properties of sum types in common denotational models of callbyname. When applied to categories of games, it yields fully abstract models of the cal ..."
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Cited by 77 (7 self)
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. A general construction of models of callbyvalue from models of callbyname computation is described. The construction makes essential use of the properties of sum types in common denotational models of callbyname. When applied to categories of games, it yields fully abstract models of the callbyvalue functional language PCFv , which can be extended to incorporate recursive types, and of a language with local references as in Standard ML. 1 Introduction In recent years game semantics has emerged as a novel and intuitively appealing approach to modelling programming languages. Its first success was in providing a syntaxfree description of a fully abstract model of PCF [10, 1, 15]; full abstraction results have also been obtained for untyped and recursively typed functional languages, as well as languages with imperative features [12, 3]. However, none of this work addressed the problem of modelling callbyvalue languagesa major shortcoming, given that many reallife langua...
Probabilistic Game Semantics
 Computer Science Society
, 2000
"... A category of HO/Nstyle games and probabilistic strategies is developedwhere the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A 2sided die is shown to be universal in this category, in the sense that any strategy breaks down into a ..."
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A category of HO/Nstyle games and probabilistic strategies is developedwhere the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A 2sided die is shown to be universal in this category, in the sense that any strategy breaks down into a composition between some deterministic strategy and that die. The interpretative power of the category is then demonstrated by delineating a Cartesian closed subcategory which provides a fully abstract model of a probabilistic extension of Idealized Algol.
Fully Complete Models for ML Polymorphic Types
, 1999
"... We present an axiomatic characterization of models fullycomplete for MLpolymorphic types of system F. This axiomatization is given for hyperdoctrine models, which arise as adjoint models, i.e. coKleisli categories of suitable linear categories. Examples of adjoint models can be obtained from cate ..."
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Cited by 6 (0 self)
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We present an axiomatic characterization of models fullycomplete for MLpolymorphic types of system F. This axiomatization is given for hyperdoctrine models, which arise as adjoint models, i.e. coKleisli categories of suitable linear categories. Examples of adjoint models can be obtained from categories of Partial Equivalence Relations over Linear Combinatory Algebras. We show that a special linear combinatory algebra of partial involutions induces an hyperdoctrine which satisfies our axiomatization, and hence it provides a fullycomplete model for MLtypes.
Full Abstraction by Translation
 Proc., 3rd Workshop in Theory and Formal Methods
, 1996
"... This paper shows how a fully abstract model for a rich metalanguage like FPC can be used to prove theorems about other languages. In particular, we use results obtained from a game semantics of FPC to show that the natural translation of the lazy calculus into the metalanguage is fully abstract, th ..."
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This paper shows how a fully abstract model for a rich metalanguage like FPC can be used to prove theorems about other languages. In particular, we use results obtained from a game semantics of FPC to show that the natural translation of the lazy calculus into the metalanguage is fully abstract, thus obtaining a new full abstraction result from an old one. The proofs involved are very easyall the hard work was done in giving the original games model. So far we have been unable to prove the completeness of our translation without recourse to the denotational model; we therefore have an indication of the worth of such fully abstract models. 1 Introduction Plotkin, in his CSLI notes [18], showed how denotational semantics can be viewed as a twostage process. First one defines a metalanguage which describes elements of the intended semantic model, usually some category of domains. Then to give semantics to a language L it suffices to translate it into the metalanguage. While this is ...
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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Cited by 5 (1 self)
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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...
An operational domaintheoretic treatment of recursive types
 in: TwentySecond Mathematical Foundations of Programming Semantics
, 2006
"... We develop a domain theory for treating recursive types with respect to contextual equivalence. The principal approach taken here deviates from classical domain theory in that we do not produce the recursive types via the usual inverse limits constructions we have it for free by working directly wi ..."
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We develop a domain theory for treating recursive types with respect to contextual equivalence. The principal approach taken here deviates from classical domain theory in that we do not produce the recursive types via the usual inverse limits constructions we have it for free by working directly with the operational semantics. By extending type expressions to endofunctors on a ‘syntactic ’ category, we establish algebraic compactness. To do this, we rely on an operational version of the minimal invariance property. In addition, we apply techniques developed herein to reason about FPC programs. Key words: Operational domain theory, recursive types, FPC, realisable functor, algebraic compactness, generic approximation lemma, denotational semantics 1
Approximating UNITY
 In Proceedings of the 2nd International Conference on Synchronization Models and Languages (COORDINATION'97), volume 1282 of LNCS
, 1997
"... . A framework for the stepwise refinement of UNITY programs with local variables is proposed. It is centered around two preorders. The first one compares program components with respect to a given context. Aside from being contextsensitive, this order also allows the introduction of local variables ..."
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Cited by 3 (2 self)
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. A framework for the stepwise refinement of UNITY programs with local variables is proposed. It is centered around two preorders. The first one compares program components with respect to a given context. Aside from being contextsensitive, this order also allows the introduction of local variables. The second preorder compares program contexts with respect to their discriminating power. Using these two relations, program refinement arises as a form of assumption/commitment reasoning. An example illustrates the use of the framework and presents some proof rules. The simple syntactic and semantic structure of UNITY allows for a natural gametheoretic characterization of the preorders used in the framework. 1 Introduction Since its invention UNITY [CM88] has been a popular design notation for concurrent programs. It features a simple syntax and semantics and yet exhibits all the intricacies of concurrent programming. The programming notation is complemented nicely by an equally simple...
A games semantics for reductive logic and proofsearch
 GaLoP 2005: Games for Logic and Programming Languages
, 2005
"... Abstract. Theorem proving, or algorithmic proofsearch, is an essential enabling technology throughout the computational sciences. We explain the mathematical basis of proofsearch as the combination of reductive logic together with a control régime. Then we present a games semantics for reductive l ..."
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Abstract. Theorem proving, or algorithmic proofsearch, is an essential enabling technology throughout the computational sciences. We explain the mathematical basis of proofsearch as the combination of reductive logic together with a control régime. Then we present a games semantics for reductive logic and show how it may be used to model two important examples of control, namely backtracking and uniform proof. 1 Introduction to reductive logic and proofsearch Theorem proving, or algorithmic proofsearch, is an essential enabling technology throughout the computational sciences. We explain the mathematical basis of proofsearch as the combination of reductive logic together with a control régime. Then we present a games semantics for reductive logic and show how it may be used to model two important
A Fully Complete PER Model for ML Polymorphic Types
 Proceedings of CSL 2000, Springer LNCS Volume 1862
, 2000
"... . We present a linear realizability technique for building Partial Equivalence Relations (PER) categories over Linear Combinatory Algebras. These PER categories turn out to be linear categories and to form an adjoint model with their coKleisli categories. We show that a special linear combinato ..."
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. We present a linear realizability technique for building Partial Equivalence Relations (PER) categories over Linear Combinatory Algebras. These PER categories turn out to be linear categories and to form an adjoint model with their coKleisli categories. We show that a special linear combinatory algebra of partial involutions, arising from Geometry of Interaction constructions, gives rise to a fully and faithfully complete model for ML polymorphic types of system F. Keywords: MLpolymorphic types, linear logic, PER models, Geometry of Interaction, full completeness. Introduction Recently, Game Semantics has been used to define fullycomplete models for various fragments of Linear Logic ([AJ94a,AM99]), and to give fullyabstract models for many programming languages, including PCF [AJM96,HO96,Nic94], richer functional languages [McC96], and languages with nonfunctional features such as reference types and nonlocal control constructs [AM97,Lai97]. All these results are cru...