J. M. E. Hyland and C.-H. L. Ong. On Full Abstraction for PCF: I. Models, observables and the full abstraction problem, II. Dialogue games and innocent strategies, III. A fully abstract and universal game model. Information and Computation, 163:285-408, 2000.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....languages and logical systems. It has been used to construct the first syntax independent fully abstract models for a spectrum of programming languages ranging from purely functional languages to languages with non functional features such as control operators and locally scoped references [4, 21, 5, 19, 2, 22, 17, 11]. A substantial survey of the state of the art of Game Semantics circa 1997 was given in a previous Marktoberdorf volume [6] Our aim in this tutorial presentation is to give a first indication of how Game Semantics can be developed in a new, algorithmic direction, with a view to applications in ....

J. M. E. Hyland and C.-H. L. Ong. On Full Abstraction for PCF: I. Models, observables and the full abstraction problem, II. Dialogue games and innocent strategies, III. A fully abstract and universal game model. Information and Computation, 163:285--408, 2000.

....(respectively even length) play s has a pending O answer (respectively P answer) let a be the last such in s, and if s is followed by a question q, then q must be explicitly justi ed by a. We then consider conditionally copycat strategies, which are innocent strategies (in the sense of [7]) that behave in a copycat fashion as soon as an O answer is followed by a P answer. Together with a relevance condition, we prove that the recursive such strategies give a strongly universal model of Levy Longo trees i.e. every strategy is the denotation of a unique Levy Longo tree. To our ....

.... arena A is de ned as follows: MA = MA f q; a g A = A ; f (q; OQ) a; PA) g] A = f ( q) q; a) g [ f (a; m 0 ) A m 0 g [ f (m 1 ; m 2 ) m 1 ; m 2 2 MA m 1 A m 2 g The product arena construction A B and function space arena construction A ) B are standard (see e.g. [7]) A justi ed sequence over an arena A is a nite sequence of alternating moves such that, except the rst move which is initial, every move m has a justi cation pointer (or simply pointer) to some earlier move m whereby m A m; we say that m is explicitly justi ed by m . A question ....

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J. M. E. Hyland and C.-H. L. Ong. On Full Abstraction for PCF: I. Models, observables and the full abstraction problem, II. Dialogue games and innocent strategies, III. A fully abstract and universal game model. Information and Computation, 163:285-408, 2000.

....languages and logical systems. It has been used to construct the rst syntax independent fully abstract models for a spectrum of programming languages ranging from purely functional languages to languages with non functional features such as control operators and locallyscoped references [3,13,4,2,16]. In the game reading, types (speci cations) are interpreted as games, and programs (implementations) as strategies on games. Game Semantics captures the quantitative and algorithmic aspects of a computation typical of Operational Semantics, while admitting compositional methods in the style of ....

....P moves which are currently P visible. This has the important e ect of constraining the growth of states (attached to moves in a play) as the game unfolds. We show that [ M : A ] the strategy with state that denotes a third order IA term in context, is compactly innocent in the sense (of [13]) that the strategy is generated by a nite view function f M . Moreover [ M : A ] is closely related to the knowing strategy denotation, written [ M : A ] we prove in Theorem 25 that erase [ M : A ] M : A ] i.e. the knowing strategy denotation may be recovered by ....

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J. M. E. Hyland and C.-H. L. Ong. On Full Abstraction for PCF: I. Models, observables and the full abstraction problem, II. Dialogue games and innocent strategies, III. A fully abstract and universal game model. Information and Computation, 163:285-408, 2000. 55

....that have been introduced by earlier P moves which are currently P visible. This has the crucial effect of restraining the growth of states as the play unfolds. We show that [ M : A ] the strategy with state that denotes a 3rd order IA term in context, is compactly innocent in the sense (of [7]) that the strategy is generated by a finite view function fM . Moreover [ M : A ] is closely related to the knowing strategy denotation, written [ M : A ] we have (Theorem 4.3(i) erase [ M : A ] M : A ] i.e. the knowing strategy denotation may be recovered by erasing ....

....the knowingstrategy semantics of IA to give a characterization of IA without the bad variable constructor mkvar. Using the model he shows that adding mkvar is conservative for observational equivalence but not for observational preorder. 3 Game semantics We shall consider arenas as introduced in [7, 10], and use square and round parentheses in bold type as meta variables for moves as follows: O question P answer P question O answer [ We assume the reader is familiar with the following standard notions of Game Semantics: justified sequences, Pview psq and O view xsy of a justified ....

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J. M. E. Hyland and C.-H. L. Ong. On Full Abstraction for PCF: I. Models, observables and the full abstraction problem, II. Dialogue games and innocent strategies, III. A fully abstract and universal game model. Information and Computation, 163:285--408, 2000.

....universal, and hence fully abstract, model of the pure Lazy Lambda Calculus. 1 Introduction This paper presents a strongly universal innocent game model for Levy Longo trees [11, 12] i.e. every point in the model is the denotation of a unique LevyLongo tree) We consider arenas in the sense of [8, 14] in which questions may justify either questions or answers, but answers may only justify questions; and we say that an answer (respectively question) is pending in a justi ed sequence if no question (respectively answer) is explicitly justi ed by it. Plays are justi ed sequences that satisfy ....

....(respectively even length) play s has a pending O answer (respectively P answer) let a be the last such in s, and if s is followed by a question q, then q must be explicitly justi ed by a. We then consider conditionally copycat strategies, which are innocent strategies (in the sense of [8]) that behave in a copycat fashion as soon as an O answer is followed by a P answer. Together with a relevance condition, we prove that the recursive such strategies give a strongly universal model of Levy Longo trees i.e. every strategy is the denotation of a unique Levy Longo tree. To our ....

[Article contains additional citation context not shown here]

J. M. E. Hyland and C.-H. L. Ong. On Full Abstraction for PCF: I. Models, observables and the full abstraction problem, II. Dialogue games and innocent strategies, III. A fully abstract and universal game model. Information and Computation, 163:285-408, 2000.

.... u A v for a P location buc, v beginning with one of l; r; L and R, and F (buc) G 1 (w 1 ; w k ) G j (w 1 ; w k ) 2 (G(LO ) where each G i (w 1 ; w k ) is in G(LO ) such that the O locations that appear in it are among w 1 ; w k ) then in the P view [9] of smO there must be O moves which de ne dw i e for each i (i.e. the evolution argument which O has supplied at each w i ) Example 3. The strategy considered in Example 2 given by: f = f(RlR; LlR) LlL; RlL) RrR; LrR) LrL; RrL)g F = f(L; R) Lr; Rr)g is regular. Note that this is the ....

J. M. E. Hyland and C.-H. L. Ong. On Full Abstraction for PCF: I. Models, observables and the full abstraction problem, II. Dialogue games and innocent strategies, III. A fully abstract and universal game model. Information and Computation, 2000. 130 pages, in press. Ftp-able from Ong's home page.

....es all the terms which have the same L evy Longo tree. Key Words: Games Semantics, Lambda Calculus, B ohm trees Introduction In this paper we explore the methodology for giving denotational semantics based on games, recently introduced by Abramsky, Jagadeesan, Malacaria and Hyland, Ong (see [AJM96,HO00]) We use game semantics to build models of the untyped calculus, focusing on which theories can be modeled. theories are congruences over terms, which extend pure conversion. Their interest lies in the fact that they correspond to the possible operational (observational) semantics of ....

....since we feel that head reduction is intrinsic to games for which we can observe only interactions with the environment. This hypothesis seems to be con rmed also by the recent results presented in the related works [KNO00,KNO99] in the slight di erent game semantics paradigm of Hyland and Ong [HO00]. There, two particular games models are built and it is proved, using techniques quite di erent from ours, that the two models induce respectively the theories H and B. The present paper is organized as follows. In section 1, we introduce the categories of games that we shall utilize, ....

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J.M.E. Hyland and C.H.L. Ong. On full abstraction for PCF:I. Models, observables and the full abstraction problem, II. Dialogue games and innocent strategies, III. A fully abstract and universal game model. To appear in Information and Computation, 2000.

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