The relationship between Hyland-Ong-style games and Berry-Curien sequential algorithms is investigated, with the object of describing semantic solutions to two problems | to characterise eectively the \minimal models" of the simply-typed -calculus and the fully abstract model of PCF with control operators | which are shown to be equivalent.

It is a fact of experience from the study of higher type computability that a wide range of approaches to defining a class of (hereditarily) total functionals over N leads in practice to a relatively small handful of distinct type structures. Among these are the type structure C of Kleene-Kreisel continuous functionals, its effective substructure C eff, and the type structure HEO of the hereditarily effective operations. However, the proofs of the relevant equivalences are often non-trivial, and it is not immediately clear why these particular type structures should arise so ubiquitously. In this paper we present some new results which go some way towards explaining this phenomenon. Our results show that a large class of extensional collapse constructions always give rise to C, C eff or HEO (as appropriate). We obtain versions of our results for both the “standard” and “modified” extensional collapse constructions. The proofs make essential use of a technique due to Normann. Many new results, as well as some previously known ones, can be obtained as instances of our theorems, but more importantly, the proofs apply uniformly to a whole family of constructions, and provide strong evidence that the above three type structures are highly canonical mathematical objects.

Abstract. We give a fully abstract game model for Idealized Algol with non-local control flow. In contrast to most previous papers on game semantics, we do not need to include the bad-variable constructor mkvar to obtain full abstraction. Using the model we show that, unlike in the “control-free ” case, the presence of mkvar does affect observational equivalence. We conclude by discussing the effect of mkvar on nondeterministic and probabilistic variants of Idealized Algol. 1

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We present a process semantics for the purely additive fragment of linear logic in which formulas denote protocols and (equivalence classes of) proofs denote multi-channel concurrent processes. The polycategorical model induced by this process semantics is shown to be equivalent to the free polycategory based on the syntax (i.e., it is full and faithfully complete). This establishes that the additive fragment of linear logic provides a semantics of concurrent processes. Another property of this semantics is that it gives a canonical representation of proofs in additive linear logic.

Abstract. Safety is a syntactic condition of higher-order grammars that constrains occurrences of variables in the production rules according to their type-theoretic order. In this paper, we introduce the safe lambda calculus, which is obtained by transposing (and generalizing) the safety condition to the setting of the simply-typed lambda calculus. In contrast to the original definition of safety, our calculus does not constrain types (to be homogeneous). We show that in the safe lambda calculus, there is no need to rename bound variables when performing substitution, as variable capture is guaranteed not to happen. We also propose an adequate notion of β-reduction that preserves safety. In the same vein as Schwichtenberg’s 1976 characterization of the simply-typed lambda calculus, we show that the numeric functions representable in the safe lambda calculus are exactly the multivariate polynomials; thus conditional is not definable. We also give a characterization of representable word functions. We then study the complexity of deciding beta-eta equality of two safe simply-typed terms and show that this problem is PSPACE-hard. Finally we give a game-semantic analysis of safety: We show that safe terms are denoted by P-incrementally justified strategies. Consequently pointers in the game semantics of safe λ-terms are only necessary from order 4 onwards.

This article opens a series of papers on asynchronous games semantics, which aims at a concurrent and geometric account of interference and states in programming languages. In order to develop our theory, we need to reformulate arena games in a simpler algebraic vocabulary, inspired by Girard's Geometry of Interaction and Abramsky, Jagadeesan and Malacaria (AJM) token games. This is precisely the task of this article, which prepares the field for the positional / homotopic account of innocence in (Mellies 2004). 1.

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Formal framework for reasoning about programs are important not only for automated tools but also for programmers. Type systems have proven an enormously popular framework for validating static analyses of programs, as well as for documenting their interfaces for programmers. However, most type systems used in practice today fail to capture many essential aspect of p behavior dependencie of programs The considerabl c i pas twenty years int developing that captu e information I pape examin compa contrast connec mbe o highly influentia p ototy ica system capturing dependencies Specifically w classi e typ system a onceive fo l canonical example o pendenc system system information-flow di moda systems c (co)monadi e fec dependenc discipline linear system p e- easonin abou state esou Finally als esen calculus provide insight possibili fo a unified account for all of these systems.

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