G'erard Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20:265--321, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by games on graphs. This is a very concrete model which differs from previous models in that the strategies (programs) operate on the position (data) reached and not on the details of how the data was obtained. In this it is faithful to the concrete data structure conception of computation (see [2, 9]) In [7] we explained the connections with abstract games. Here we concentrate on the sequential algorithms point of view, and connections with the Longley Conjecture. 2 Graph Games While traditionally games have been formalized via game trees, there is a way of using graphs as the underlying ....

....opening O move to which P may respond by playing any natural number. We define N g for higher types inductively via g = N g ( g N ( g ) N and similarly for N t . Note that the type structure N is the sequential algorithms model of Berry and Curien (see [2]) As models for this type structure, the category of regulated graph games and that of tree games are very closely connected. Theorem 3.8 The functor T induces an isomorphism TN for all types . 4 An extensional exponential By working with graph games we aim to force a degree of ....

G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20:265--321, 1982.

....the #y.x false. V responds by picking a value he claims makes x true. F tries to show this false by picking one side of the conjunction which he claims does not hold, and so on. Game Semantics: an Overview Sequential sequential algorithms models [4] are the first use of the interactive approach in denotational semantics of programs. A sequential algorithm describes the response of the program to partial input data from the environment. This was the first model to capture precisely a notion of sequential, ....

G erard Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20:265--321, 1982.

....to be transferable, in principle, to object languages. In a later exposition we wish to report how the proposed typed syntax can be a powerful tool for language analysis when coupled with process theoretic reasoning techniques. From the viewpoint of the semantic study of sequentiality [6, 10, 29], our work positions sequentiality as a sub class of the general universe of name passing interactive behaviour. This characterisation allows us to delineate sequentiality against the background of a broad computational universe which, among others, includes concurrency and non determinism, ....

Berry, G. and Curien, P. L., Sequential algorithms on concrete data structures TCS, 20(3), 265-321, North-Holland, 1982. 16

....F (f) can observe properties of the process computing its argument f , rather than only the extensional properties of the function f , and make its output depend on these properties. For this reason, attempts by Kleene [18 21] in his work on higher type recursion theory, and by Berry and Curien [9] in their work on sequential algorithms, failed to yield a characterization. Similarly, while there were encodings of the calculus into various process calculi such as the calculus [27] there was no characterization of which processes arose from these encodings. The more refined tools provided ....

G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20:265--321, 1982.

.... Three are domain theoretic: the standard model based on Scott continuous functions [Plo77] Berry s bidomains model based on stable functions [Ber79] and the Bucciarelli Ehrhard model based on strongly stable functions [BE91] The fourth is the Berry Curien model based on sequential algorithms [BC82]. Of these, we can say that the standard Cartwright and Felleisen s model without error values turns out to be equivalent to the sequential algorithms model [CF92, Cur92a] The main result in [CF92, Cur92a] is that the sequential algorithms model with errors is fully abstract for SPCF, an ....

Gerard Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20:265-321, 1982.

.... give a representation of Berry s cartesian closed category of dIdomains and stable functions [2, 18] while Berry and Curien s category of sequential algorithms on Kahn and Plotkin s concrete datastructures provides a domain theory in which the method of computation is represented explicitly [3]. These two domain theories can be used to give models of PCF. But they do not give order extensional models; a model is orderextensional if elements of the function spaces are ordered according to the pointwise order. If we limit attention to extensional models, that is models where denotations ....

Berry, G.,and Curien, P-L., Sequential algorithms on concrete data structures. Theoretical Computer Science 20, pp.265-321, 1982.

.... because the event domains (in particular the concrete domains) that do not satisfy e, e, do not have the (dc) property (down closure) of the coherence spaces (used for prove the proposition above) We can see this in the following example (over concrete domains) given by Curien Berry in [BER 82, p. 271] Let 4 be the cds: where c 0 c 1 (c 0 , 0) c 1 , 0) c 2 (c 0 1) c 2 . The set of states is the following concrete domain: c 2 0 c 0 c 1 0 1 0 (c 0 , 0) c 1 , 1) c 1 , 0) c 0 , 1) c 2 , 0) c 0 , 0) c 1 , 0) c 0 , 1) c 1 , 0) c 0 , 0) c ....

BERRY, G.; CURIEN, P.L. Sequential Algorithms on Concrete Data Structures. In: Theoretical Computer Science, v.20, n.3, Amsterdam, North-Holland, p. 265-321, 1982.

....collapse of the unconstrained HO model of PCF is isomorphic to the strongly stable model, and to show that the de nability problem is soluble in the minimal model. 1 Introduction This paper is a study of the relationship between two models of functional computation; sequential algorithms [7, 11] and Hyland Ong games [19] These semantics have a good deal in common; both focus on the behaviour of programs in contrast with traditional denotational models based on sets and functions and both have been used as the basis of full abstraction results for sequential languages. Our aim ....

....(and more e ective than ) PCF sequentiality. The accuracy of this characterisation is witnessed by the fact that it yields a fully abstract (and e ectively presentable) model of SPCF with errors. It was subsequently discovered by Curien that sequential algorithms on sequential data structures [7] can be used as a more concrete representation of the observably sequential functions, and in particular, a fully abstract 3 model of SPCF (with or without errors) 10] was de ned by Cartwright, Curien and Felleisen [10] in a games like style. Although the original de nition of sequential ....

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G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20:265-321, 1982.

....for the same function) has to be explicitly incorporated into the definition at certain points. This intensional character is also an important aspect of much of the work in computer science on the semantics of higher type computation: for instance, Berry and Curien s sequential algorithms model [BC82], or the game models of PCF [AJM00, HO00, Nic94] Kleene s unimonotone semantics can be considered as one in which computable objects act only on computable objects, if computable here is understood to mean realized by some oracle. However, the behaviour of oracles is not required to be ....

....these referred in some way to the operational semantics of PCF and so were felt not to qualify as an independent mathematical characterization of sequentiality. Several other models for PCF were constructed: Berry s stable and bistable models [Ber78b] the Berry Curien sequential algorithms model [BC82, Cur93] based on Kahn and Plotkin s notion of concrete data structure [KP93] and the BucciarelliEhrhard strongly stable model [BE91b, Ehr93] For a detailed survey of this material and further references, we recommend [Ong95] This line of research gave much insight into the di#culty of the full ....

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G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20(3), 1982.

....domains) and he also observed that a subclass of these domains (coherence spaces) has very good properties with respect to stability. Hypercoherences: a strongly stable model of linear logic This work gave rise to the first proof theoretic model of classical linear logic. Berry and Curien (see [BC, C]) defined a CCC where morphisms are sequential, but are not functions; they are sequential algorithms. In [BE] a joint work with Antonio Bucciarelli, we introduced the notion of strong stability in order to build a CCC where, at first order, the morphisms are sequential functions. Our basic ....

G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theor. Comp. Sci. 20, 1982. Thomas Ehrhard

.... instance any expressive enough object oriented programming language) Precursors to these game theoretical models can be seen in [Jo77] where for the first time a category of games is defined, and in the work of Kleene on recursive functionals, and of Berry and Curien on sequential algorithms in [BeCu82]. In another line of research, game semantical methods have so far had a number of other applications, including in [AbrJag94] an alternative realization of the Geometry of interaction program (initiated in [Gir89] and developed in a series of papers) In this paper we would like to give an ....

G. Berry, P. L. Curien, Sequential algorithms on concrete data structures, Theoretical Computer Science 20 (1982), p. 265--321

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G. Berry and P.-L. Curien, Sequential algorithms on concrete data structures, Theoretical Computer Science 20, 265-321 (1982).

....of denotational semantics) and functions to a setting retaining more than the ordinary input output behaviour of programs. For example, the two above schedules for the logical and function are given di erent interpretations in the model. The insight resulted in the model of sequential algorithms [6], which I presented in 1978 in a Spring School on calculus in La Ch atre. In this model, morphisms are not functions but pairs of a function and a computation strategy for it, that speci es a schedule of interaction of the function with its argument. The model was then turned into syntax, and ....

G. Berry and P.-L. Curien, Sequential algorithms on concrete data structures, Theoretical Computer Science 20, 265-321 (1982).

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G'erard Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20:265--321, 1982.

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G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. In Theoretical Computer Science, 20:265-321, 1982.

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G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20:265-321, 1982.

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G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20:265-321, 1982.

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Berry, G. and Curien, P. L., Sequential algorithms on concrete data structures TCS, 20(3), 265-321, North-Holland, 1982.

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G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science, 20:265--321, 1982.

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G. Berry,P.L.Curien, Sequential algorithms on concrete data structures, Theoretical Computer Science 20 (1982), p. 265--321

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Berry, G. and Curien, P. L., Sequential algorithms on concrete data structures TCS, 20(3), 265-321, North-Holland, 1982.

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Berry, G. and Curien, P. L., Sequential algorithms on concrete data structures TCS, 20(3), 265-321, North-Holland, 1982.

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BERRY, G.; CURIEN, P.L. Sequential Algorithms on Concrete Data Structures. In: Theoretical Computer Science, v.20, n.3, Amsterdam, North-Holland, p. 265-321, 1982.

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G. Berry and P-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science 20, 1982.

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G. Berry and P.-L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science 20(1982), pp. 265-321.

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