F. Lamarche. Sequentiality, games and linear logic. Manuscript, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....; however, he cannot, because it is Opponent s move in the sub game A . What saves the Player in Blass semantics is again the special case, which would force Opponent to move in both 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) ....

F. Lamarche. Sequential algorithms, games and linear logic. Unpublished Lecture, 1992.

.... work on sequentiality, obtaining intensional fully abstract models of the programming language PCF [1, 6] has been informed by the insight that Berry and Curien s category of concrete data structures and sequential algorithms [3] is got as a co Kleisli category from a games model of linear logic [3, 7]. Bistructures were introduced in [10] as a generalisation of event structures to represent a full subcategory of Berry s bidomains [2] Bidomains possess an intensional, stable ordering, based on the method of computation, and an extensional ordering, inherited from Scott s domain theory; their ....

Lamarche, F., Sequentiality, games and linear logic. Proceedings of the CLICS Workshop, Aarhus University, March

....of domains used in denotational semantics. For instance, Berry and Curien s Basic Research in Computer Science, Centre of the Danish National Research Foundation. category of concrete data structures and sequential algorithms [5] may be obtained as the co Kleisli category of a games model [6, 16]. The connection between games and sequentiality has in turn informed recent work on intensional models of PCF and their fully abstract extensional collapse [1, 12] After Berry isolated the mathematically natural notion of stability [3] it was soon realized that sequential functions are stable. ....

Lamarche, F., Sequentiality, games and linear logic, in Proc. CLICS Workshop, Aarhus University, Aarhus University DAIMI PB-397 (II), 1992.

....unique [25] But what domain like meant exactly was not really spelled out. In particular, the e ectivity criterion came only to light when it was made possible to contrast di erent sorts of game models. Indeed, the model of sequential algorithms was given a game theoretic presentation by Lamarche [23]: the main di erence with the AJM and HO models lies in the de nition of the connective, which is set based for sequential algorithms (whence its nitary character) and multiset based for the AJM and HO models. But this poorly stated long standing open problem did trigger an important amount ....

F. Lamarche, Sequentiality, games and linear logic, manuscript (1992).

....This set of plays constitutes a tree for the usual prefix ordering of sequences. We used this presentation in our informal discussion in section 2. But a game can also be presented directly as a tree of Opponent Player polarized positions, this choice has been done for example by Lamarche in [Lam92], and we prefer this presentation here. In this approach, a move is a transition from a position (starting position) to one of its immediate successors in the tree. A move is played by Player if the polarity of the starting position is Opponent, and by Opponent if the polarity of the starting ....

Francois Lamarche. Sequentiality, games and linear logic. Preprint, 1992.

....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 algorithms developed from more traditional denotational semantics; the connections between these several representations are explored in [23, 11]. So in addition to being a directly presented solution to our full abstraction problem, the sequential algorithms form a bridge between the highly intensional world which is being mapped by games semantics (with its close connections with syntax) and the various abstract notions of extensional ....

.... games [5, 6] The original de nition of the Berry Curien sequential algorithms [7] in terms of functions on concrete data structures is rather di erent in presentation, but the equivalence between sequential data structures and liform CDS is established in detail in [11] We follow Lamarche [23] in constructing a CCC of sequential algorithms on sequential data structures as the co Kleisli category of a (symmetric monoidal) co monad on a symmetric monoidal closed category (SMCC) the latter fragment being essentially equivalent to the one used in the AJM model. As in [10] error moves ....

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F. Lamarche. Sequentiality, games and linear logic. In Proceedings, CLICS workshop, Aarhus University. DAIMI-397{II, 1992.

.... by Vuillemin and Milner (cf. V] and [Mi] The problem of extending this notion to higher order programs, like those of Godel system T, has led to various definitions: ffl Sequential algorithms on concrete data structures (see [C1] and more recently various gametheoretic models (see [AJ, C2, HO, L]) inspired by the work of Blass [Bl1, Bl2] which are quite intentional models where programs of functional type are not simply interpreted by functions, but by more complicated objects ( algorithms or strategies ) which contain detailed informations about their behaviour. ffl Strong stability, ....

F. Lamarche. Sequentiality, games and linear logic. Manuscript (1992).

....of cell such that Z be the exponentiation of X and Y , but both these notions use in a very strong way the intensional components of sequential algorithms. This approach has been developed by Berry and Curien [C1] and has now interesting developments in the direction of models of linear logic [L, C2, AJ] which have strong analogies with the game theoretic model proposed by Blass [Bl] This 2 approach has been very successful since it has allowed for a new characterization of the fully abstract model of PCF [AJM, HO] With Bucciarelli, we also developed an abstract theory of sequential algorithms ....

F. Lamarche. Sequentiality, Games and Linear Logic (abstract). In G. Winskel, ed., Proceedings of the CLICS Workshop, 23-27 March

....composition) These model were intensional in nature: thus the usual completeness results, stating that provability of a formula is reflected in the model, were strengthened to full completeness results where each proof is itself represented. Another games model for linear logic was given in [Lam94], while the ones in [LafStr91] or [Mey94] the latter for predicate logic without contractions) are not intensional. Subsequently this lead in 1993 to the development of intensional game theoretical models in the semantics of programming languages independently by [AbrJagMal94, HylOng1, Ni96] ....

F. Lamarche, Sequentiality, games and linear logic (Announcement), in: Workshop on Categorical Logic in Computer Science, 1994

....strategies or another analogous restricted class could also be useful in tightening the link. There are also other investigations [11] along the same lines which were already lead in the intuitionistic case. Specifically, Ehrhard s extensional collapse of sequential algorithms, which Lamarche [10] and Curien showed could be thought of as games model, to strongly stable functions in [7, 8] To track down the relation between the present attempt and those former investigations should serve well the general purpose of bridging both kinds of models. Let us recall that the category we described ....

F. Lamarche. Sequentiality, games and linear logic (announcement). In Workshop on Categorical Logic in Computer Science. Publications of the Computer Science Department of Aarhus University, DAIMI PB-397-II, 1992.

....of domains used in denotational semantics. For instance, Berry and Curien s 1 Basic Research in Computer Science, Centre of the Danish National Research Foundation. 1 category of concrete data structures and sequential algorithms [5] may be obtained as the co Kleisli category of a games model [6, 16]. The connection between games and sequentiality has in turn informed recent work on intensional models of PCF and their fully abstract extensional collapse [1, 12] After Berry isolated the mathematically natural notion of stability [3] it was soon realized that sequential functions are stable. ....

Lamarche, F., Sequentiality, games and linear logic, in Proc. CLICS Workshop, Aarhus University, Aarhus University DAIMI PB-397 (II), 1992.

....provides a data element, are included in this scheme; they are types with trivial access protocols. This generalization of the notion of data type seems to be quite independent of the generalization by admitting partially defined data elements that is the intuitive basis for domain theory. See [11] for a combination of the two generalizations. We could even incorporate the transmission of data at the end of the client server interaction into the access protocol. Instead of having the server provide, after the access protocol is complete, an element of a set S of possible data, we can ....

....but nothing of this sort seems to be implicit in the formalism or the underlying intuitions of linear logic. But see the discussion of A below. As suggested by the title of this paper, the protocols considered here can be viewed as games (or debates or dialogs) between the client and the server [1, 2, 10, 11]. In this connection, the server is usually called the proponent or player, and the client is called the opponent. The protocol specifies who is to move (see Note 2) and what moves are legal at any point during a play of the game. Our protocols, unlike some versions of games [1, 2] but like the ....

[Article contains additional citation context not shown here]

F. Lamarche, Sequentiality, games and linear logic, preprint (1992).

....; however, he cannot, because it is Opponent s move in the sub game A B . What saves the Player in Blass semantics is again the special case, which would force Opponent to move in 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) ....

F. Lamarche. Sequential algorithms, games and linear logic. Unpublished Lecture, 1992.

.... here (see [17] Since the morphisms preserve behaviour, the existence of a morphism from one net to another may be interpreted as saying that one net (the implementation) satisfies another (the specification) Recently categories of games have been shown to be models of linear classical logic [1, 36, 45, 21]. The games have the structure of special Petri nets in which the distinction between moves of a player and opponent is made through one being conditions and the other events (linear negation is caught as reversal of the roles of the players corresponding to swapping the nature of conditions and ....

Lamarche, F., Sequentiality, games and linear logic, Proceedings of CLICS Workshop--Part I & II, Aarhus, March 1992 DAIMI PB 398, Aarhus University, 1992.

....; however, he cannot, because it is Opponent s move in the sub game A B . What saves the Player in Blass semantics is again the special case, which would force Opponent to move in 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) ....

F. Lamarche. Sequential algorithms, games and linear logic. Unpublished Lecture, 1992.

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F. Lamarche. Sequentiality, games and linear logic. Manuscript, 1992.

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F. Lamarche. Sequentiality, games and linear logic. Manuscript, 1992.

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F. Lamarche. Sequentiality, games and linear logic. Manuscript, 1992.

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F. Lamarche. Sequentiality, games and linear logic. Manuscript, 1992.

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F. Lamarche, Sequentiality, games and linear logic (Announcement), in: Workshop on Categorical Logic in Computer Science, 1994

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F. Lamarche, Sequentiality, games and linear logic, manuscript (1992).

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