G. Berry and P-L Curien, "Theory and practice of sequential algorithms: the kernel of the programming language CDS," in Algebraic Methods in Semantics. Cambridge, U.K.: Cambridge Univ. Press, 1988, pp. 35--88.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....B and D simultaneously, thus allowing Player to respond in D . 30 6. 4 Sequential Algorithms Lamarche [Lam92] and more recently, but independently, Curien [Cur92] have found linear decompositions of the Berry Curien category of sequential algorithms on (filiform) concrete data structures [BC85]. That is, they have described models of Linear Logic (Intuitionistic Linear Logic only, in Curien s case) such that the co Kleisli category is equivalent to the BerryCurien category. Moreover, these Linear categories have a game theoretic flavour. In fact, we have the correspondence: Game ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In J. C. Reynolds and M. Nivat, editors, Algebraic Semantics, pages 35--84. Cambridge University Press, 1985.

....first author s interaction categories. 3 Interaction Categories Interaction Categories [1, 3, 4, 6] are a new paradigm for the semantics of sequential and concurrent computation. This term encompasses certain known categories (the category of concrete data structures and sequential algorithms [12], categories of games [7] geometry of interaction categories [8] as well as several new categories for concurrency. The fundamental examples of concurrent interaction categories are SProc, the category of synchronous processes, and ASProc, the category of asynchronous processes. These categories ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In J. C. Reynolds and M. Nivat, editors, Algebraic Semantics, pages 35--84. Cambridge University Press, 1985.

....in E(x) or else we would have c 2 E(x) and c i c. Continuing, we find an infinite descending chain of cells. 2 In this report, we have chosen to state all properties and make all proofs for arbitrary cds, without relying on well foundness. That this is indeed possible is stated in [5] and [2]. Definition 5 A cds M is called stable or deterministic, if for any state x and any cell c, if x 0 c, x 0 0 c and x 0 x, x 0 0 x, then x 0 = x 0 0 . A deterministic cds is abbreviated dcds. 8 So any state of a dcds contains at most one enabling for any cell c. It seems that ....

....first the argument with number k, then catch(M) k. Then the algorithmic model A can be naturally extended to a model of PCF catch (by giving the right interpretation to catch) which is fully abstract. 36 Chapter 4 Deterministic Concrete Data Structures as a Programming Language Following [2], we shall sketch a programming language, called CDS0 after [2] which essentially provides syntax for dcds and states. The language CDS0, has two main parts: the language for specifying dcds and the language for specifying states. States of dcds of the form [M sa M 0 ] which are essentially ....

[Article contains additional citation context not shown here]

G. Berry, P.L. Curen, Theory and Practice of Sequential Algorithms: the Kernel of the Applicative Language CDS, in M. Nivat, J.C. Reynolds eds. Algebraic Methods in Semantics Cambridge University Press 1985

.... linear lambda calculus, and provides a justification of the fact, observed several times in the past, that currying in functional programming correspond to a sort of associativity (this happens in the implementation of abstract machines, as well as in the coding of lambda terms into Berry s CDS [3]) Our result confirms once more that Linear Logic is a looking glass through which fundamental properties of functional computation appear symetrized and simplified. It should also be remarked that the axiom links from Linear Logic play a similar role to the formula links originally introduced by ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In M. Nivat and J. Reynolds, editors, Algebraic methods in semantics, pages 35--87. Cambridge University Press, 1985.

....separation of logic and control; and identity of program logic with proof logic. In such a language, a high level description of what 3 a program does actually is a program; that is, one can execute it. Other logical programming languages include pure Prolog [17] pure Lisp [67] and CDS [4]; such languages can also be considered as efficiently executable specification languages. Some other languages that are based on algebraic semantics include Larch [51] Asspegique [5] Obscure [62] and Act One [19] it seems fair to say that they have all been significantly influenced by OBJ. ....

Gerrard Berry and Pierre-Luc Currien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In Algebraic Methods in Semantics, pages 35--88. Cambridge University Press, 1985.

....real concurrent languages. 1 Motivation Abramsky [1] has recently proposed a new paradigm for the semantics of sequential and concurrent computation: Interaction Categories. This term encompasses certain known categories (the category of concrete data structures and sequential algorithms [5], categories of games [2] as well as a new category SProc, with which we will be working in this paper. The distinguishing feature of Interaction Categories is that composition in them is a dynamic process of interaction, rather than the static one of function composition found in the familiar ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In J. C. Reynolds and M. Nivat, editors, Algebraic Semantics, pages 35--84. Cambridge University Press, 1985.

.... [10] 6 3 The Interaction Category SProc The theory of Interaction Categories has been proposed as a new paradigm for the semantics of sequential and concurrent computation [1,5,6] The term encompasses certain known categories (the category of concrete data structures and sequential algorithms [16], categories of games [10] geometry of interaction categories [11] as well as several new categories for concurrency. The fundamental examples of concurrent interaction categories are SProc [5] the category of synchronous processes, and ASProc [6] the category of asynchronous processes. The ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In J. C. Reynolds and M. Nivat, editors, Algebraic Semantics, pages 35--84. Cambridge University Press, 1985.

....functions, and yet avoid the complexity of concurrent programming. Our starting point is the observation that our goals can be reached if the programming language expresses physical processes as in Krishnan s distributed CCS [12] and exhibits a property found in Berry and Curien s CDS language [2]: the possibility for a program to use another program s meaning as data because functional arguments can be evaluated. Indeed network utilization, degree of parallelism and processor allocation are all visible parameters of a program, once the process decomposition of its meaning is explicit. If ....

....of dcds and sequential algorithms. This is indeed the case but the existence of a composition is not trivially true and was proved in [8] by separating the control strategy from the I O part of algorithms. From this category, Berry and Curien have built a sequential functional language called CDS [2] and proved a full abstraction result for it. Its types are dcds and programs denote algorithms, i.e. states of exponential dcds. The operations of CDS are those of ordinary typed functional languages except that functions are spelled out as sets of events. The auxiliary question of a more ....

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G'erard Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In J. C. Reynolds and M. Nivat, editors, Algebraic Semantics, pages 35--84. Cambridge University Press, 1985.

.... ] What is the programming language for which the model associated with the cartesian closed category of filiform dcdss and sequential algorithms gives a fully abstract semantics Berry and Curien introduced a rather unconventional functional language called CDS which is described in full in [ Berry and Curien, 1985 ] A distinctive feature of this language is that its computational observables are not restricted just to data of ground type. In fact, the call by need parameter passing mechanism allows the programmer to observe as much information about any program fragment as he wishes. A crucial consequence ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the programming language cds. In M. Nivat and J. Reynolds, editors, Algebraic Semantics. Cambridge University Press, 1985.

....incremental computation adequate for domains of data. This is the index structure which is (implicitly) present in Kahn and Plotkin s, Milner s and Vuillemin s definitions of sequentiality, as well as in Berry and Curien s sequential algorithms over concrete data structures and the language CDS0 [BC85, Cur86] it is also used by Bucciarelli and Ehrhard for defining sequentiality at first order. In PCF, however, computation over function spaces proceeds in an inherently different manner, and thus the use of data indices is not always appropriate; a suitable higher order notion of incremental ....

....domain. This corresponds to an operational assumption that incremental computation over a function space proceeds in the same way as incremental computation over data. This assumption is reasonable in some frameworks, such as concrete domains and sequential algorithms, and the language CDS0 [BC85, Cur86] However, this operational assumption is not appropriate for PCF, where information about a functional argument is essentially incremented by applying it. We thus perceive the need to employ a different, higher order, notion of sequentiality over the functional domains, that would ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS0. In M. Nivat and J. C. Reynolds, editors, Algebraic Methods in Semantics, chapter 2, pages 35--87. Cambridge University Press, 1985.

....Berry and Curien s definition of sequential algorithms. It seems likely that a sequential language that embodies such operational assumptions would be matched better by our sequential functions, much as Berry and Curien s sequential algorithms provided a fully abstract model for the language CDS0 [BC85, Cur86] It may be interesting to devise and study such a language. Still, our notion of sequentiality bears a close relationship to the sequentiality inherent in PCF s operational semantics. The sequentiality of PCF [Plo77, lemma 4.2 (Activity lemma) is perhaps best expressed by saying that the ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS0. In M. Nivat and J. C. Reynolds, editors, Algebraic Methods in Semantics, chapter 2, pages 35--87. Cambridge University Press, 1985.

....for concrete data structures, by replacing functions by a notion of sequential algorithms. The resulting category of deterministic concrete data structures (DCDSs) and sequential algorithms is cartesian closed. Furthermore, a notation for elements of DCDSs is a basis for a functional language CDS0 [BC85], for which the sequential algorithms model provides a semantics with several interesting properties: The semantics is fully abstract with respect to a notion of observability that is sensitive to computation strategy; the model is intensional rather than extensional; sequential algorithms, ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS0. In Maurice Nivat and John Reynolds, editors, Algebraic Methods in Semantics, chapter 2, pages 35--87. Cambridge University Press, 1985.

....with the answer. Thus, the operational interpreter is in full agreement with the denotational semantics of the given language. 35 Chapter 3 A New Class of Domains In this chapter, we develop the concept of observably sequential computation as an extensional refinement of sequential computation [BC85, KP93] Since observably sequential computation requires additional structure on the domains, we introduce the class of domains, called OS domains, in the following section. 3.1 Higher Order Computation In this section, we briefly review the intuitive model of computation corresponding to ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language cds. In J. Reynolds and M. Nivat, editors, Algebraic Methods in Semantics, pages 35--88. Cambridge University Press, London, 1985.

....both B and D simultaneously, thus allowing Player to respond in D . 6. 4 Sequential Algorithms Lamarche [Lam92] and more recently, but independently, Curien 2 [Cur92] have found linear decompositions of the Berry Curien category of sequential algorithms on (filiform) concrete data structures [BC85]. That is, they have described models of Linear Logic (Intuitionistic Linear Logic only, in Curien s case) such that the co Kleisli category is equivalent to the Berry Curien category. Moreover, these Linear categories have a game theoretic flavour. In fact, we have the correspondence: 2 ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In J. C. Reynolds and M. Nivat, editors, Algebraic Semantics, pages 35--84. Cambridge University Press, 1985.

....B and D simultaneously, thus allowing Player to respond in D . 6. 4 Sequential Algorithms Lamarche [Lam92] and more recently, but independently, Curien 2 [Cur92] have found linear decompositions of the Berry Curien category of sequential algorithms on (filiform) concrete data structures [BC85]. That is, they have described models of Linear Logic (Intuitionistic Linear Logic only, in Curien s case) such that the co Kleisli category is equivalent to the BerryCurien category. Moreover, these Linear categories have a game theoretic flavour. In fact, we have the correspondence: Game ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In J. C. Reynolds and M. Nivat, editors, Algebraic Semantics, pages 35--84. Cambridge University Press, 1985.

....fonctionnels appliqu ee au parall elisme en processus statiques [10] nous avons [7] introduit les s emantiques d enotationnelle et op erationnelle d un langage explicitement parall ele et purement fontionnel : CDS . Il est inspir e du langage s equentiel fonctionnel CDS de Berry et Curien [1, 4] mais utilise les structures de donn ees concr etes g en eralis ees de Brookes et Geva [3, 2] qui peuvent exprimer le parall elisme. Au contraire du langage ADS0 [8] bas e sur les structures de tableau de Hains et Mullins [9] la th eorie garantit l existence de types d efinis r ecursivement, mais ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS, In G. Reynolds and M. Nivat, Eds., Algebraic Semantics pages 35--84. Cambridge University Press, 1985.

....PCF using domain theoretic ideas. Recently, Winskel [Win94] refined Berry s bidomains to bistructures, and arrived at a better model incorporating stable and pointwise orders. The initial failures of stable functions led to the third approach of sequential algorithms. Previously, Berry and Curien [BC85, Cur86] described a model composed of algorithms (not functions) for PCF which had a game like structure. Computations proceed by dialogues of questions and answers composed of filling cells . Cartwright and Felleisen, subsequently built a fully abstract model for SPCF an extension of PCF that ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: The kernel of the applicative language CDS. In J. C. Reynolds and M. Nivat, editors, Algebraic Semantics, pages 35--84. Cambridge University Press, 1985.

....inputs. Up to now there is no satisfactory model of PCF for our purposes. Here we mention only two. The standard model based on partial continuous functionals contains functions which are not sequential, e.g. parallel or, hence it violates (2) cf. Plo77] The model of Berry and Curien [BC85, Cur86] based on sequential algorithms gives a concrete description of the interaction between the program and the input, but the possible use of intensional aspects of the inputs violates (3) For example the algorithms left strict or and right strict or are distinguishable by a sequential algorithm but ....

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In M. Nivat and J. C. Reynolds, editors, Algebraic methods in semantics, pp. 35--87, Cambridge university press, 1985.

....denotations. Berry eliminated many parallel functions from these domains by forcing functions to be stable. This construction eliminated some of the spurious distinctions between phrases in the conventional model, but it introduced some new ones. 2 To address this problem, Berry and Curien [4, 5] proposed interpreting procedures as sequential algorithms over concrete domains [14] Roughly speaking, a concrete domain is a domain that is isomorphic to a domain consisting of potentially infinite trees. A sequential algorithm is a function plus a strategy for evaluating its arguments. While ....

....Since their domains do not include error elements, they associate distinct trees with the same function. For example, l and r correspond to distinct concrete sequential algorithms but they denote the same function [4:316] In this framework, tree representations are intensional. In later work [5, 8], Berry and Curien noted that sequential algorithms can distinguish different algorithms for the same function, but they did not make a connection between intensional procedures and control operators like CATCH. Curien has recently shown that our model for SPCF is indeed closely related to the ....

[Article contains additional citation context not shown here]

Berry, G. and P-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language cds. In Algebraic Methods in Semantics, edited by J. Reynolds and M.Nivat. Cambridge University Press. London, 1985, 35--88.

....is limited to first order programs operating on atomic data. More recently Holst has generalised that work to programs operating on lazy data structures, but higher order functions still present a problem. This paper takes a new approach based on Berry and Curien s theory of sequential algorithms[5]. A sequential algorithm encapsulates more information than a mapping from inputs to outputs: it tells us also how each part of the output depends on the parts of the input. This extra information makes it possible to define an efficient fix point finder, which detects self dependent parts of the ....

G. Berry and P.-L. Curien,Theory and practice of sequential algorithms: the kernel of the applicative language CDS, in Algebraic Methods in semantics, 35-87, Cambridge University Press (1985).

....higher order functions 1. INTRODUCTION In [Loulergue and Hains 1997] we have introduced the elements of an explicitly parallel functional language CDS : denotational semantics, operational semantics and full abstraction result. It is inspired by Berry and Curien s sequential language CDS [Berry and Curien 1985] but uses Brookes and Geva s generalized concrete data structures (gcds) Brookes and Geva 1991] for compatibility with parallel execution. Here we present a detailed rewriting semantics and illustrate the language s advantages through examples. Theory guarantees the existence of ....

Berry, G. and Curien, P.-L. 1985. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In J. C. Reynolds and M. Nivat Eds., Algebraic Semantics, pp. 35--84. Cambridge University Press.

....eliminated many parallel functions from the domain of procedure denotations by forcing functions to be stable. This construction eliminated some of the spurious distinctions between phrases in the conventional model, but it introduced some new ones. 2 To address this problem, Berry and Curien [3, 4] imposed further restrictions on the space of procedure denotations by interpreting procedures as sequential algorithms over concrete domains [12] A sequential algorithm is a function plus a strategy for evaluating its arguments. While this approach eliminates all parallel functions, the ....

....algorithms. Since their domains do not include error elements, they associate distinct trees with the same function. For example, l and r denote distinct concrete sequential algorithms but denote the same function [3:316] In this framework, evaluation information is intensional. In later work [4, 8], Berry and Curien noted that sequential algorithms can distinguish different algorithms for the same function[8:210] But they did not make a connection between intensional procedures and control operators like catch. Recent discussions with Curien have revealed a surprising relationship between ....

[Article contains additional citation context not shown here]

Berry, G. and P-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language cds. In Algebraic Methods in Semantics, edited by J. Reynolds and M.Nivat. Cambridge University Press. London, 1985, 35--88.

No context found.

G. Berry and P.-L. Curien, Theory and practice of sequential algorithms: the kernel of the applicative language CDS, in Algebraic methods in semantics, Nivat and Reynolds eds., Cambridge University Press, 35-87 (1985).

.... 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 a programming language called CDS was developped [7]. The operational semantics of the language, which I presented in 1982 in a joint French US workshop held in Fontainebleau, was as far as I know the rst appearance of the notion of function composition as a dialogue, from an operational point of view. Function application is illustrated in ....

G. Berry and P.-L. Curien, Theory and practice of sequential algorithms: the kernel of the applicative language CDS, in Algebraic methods in semantics, Nivat and Reynolds eds, Cambridge University Press, 35-87 (1985).

....Pour y parvenir, on cherche a interpr eter un langage fonctionnel classique dans une famille de domaines qui soient a la fois des cas particuliers de domaines connus et qui puissent exprimer le parall elisme. Les domaines engendr es par les structures de donn ees concr etes de Berry et Curien [3, 9] permettent d interpr eter de fa con pr ecise un langage fonctionnel s equentiel, mais r esistent pour l instant a exprimer la s emantique de programmes parall eles. Cependant, les structures de donn ees concr etes g en eralis ees de Brookes et Geva [6, 5] qui sont une extension des ....

....d ecrire la r epartition physique des fonctions. Cette capacit e d expression est essentielle mais notre but est plus sp ecifique: nous voulons d eriver une implantation pour ce nouveau type de langage. Il est alors naturel de r eutiliser les concepts de base du langage CDS0 de Berry et Curien [3]. Le r esultat est un langage fonctionnel baptis e ADS0 [13] explicitement et statiquement typ e et dont la abstraction est absente. Le langage des types n est autre qu une notation de d efinition de structures de tableaux ou, ce qui revient au meme, de gCDS puisque toute ADS provient d une ....

G'erard Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS. In J. C. Reynolds and M. Nivat, editors, Algebraic Semantics, pages 35--84. Cambridge University Press, 1985.

No context found.

G. Berry and P-L Curien, "Theory and practice of sequential algorithms: the kernel of the programming language CDS," in Algebraic Methods in Semantics. Cambridge, U.K.: Cambridge Univ. Press, 1988, pp. 35--88.

No context found.

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS0. In M. Nivat and J. C. Reynolds, editors, Algebraic Methods in Semantics, chapter 2, pages 35--87. Cambridge University Press, 1985.

No context found.

G. Berry and P.-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language CDS, In G. Reynolds and M. Nivat, Eds., Algebraic Semantics pages 35--84. Cambridge University Press, 1985.

No context found.

Berry, G. and P-L. Curien. Theory and practice of sequential algorithms: the kernel of the applicative language cds. In Algebraic Methods in Semantics, edited by J. Reynolds and M.Nivat. Cambridge University Press. London, 1985, 35--88.

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