S. Abramsky, M. Lenisa. A Fully-complete PER Model for ML Polymorphic Types, CSL'00 Conf. Proc., P. Clote, H.Schwichtenberg eds., LNCS 1862, 2000, 140-155.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to implement type passing and proves full abstraction for System F, though the result arguably relies on the somewhat syntactic nature of the model. Murawski and Ong [29] substantially simplify Hughes approach, but do not obtain full abstraction for impredicative polymorphism. Abramsky and Lenisa [5, 6] give a fully abstract model for predicative polymorphism using interaction combinators. Treatment of impredicative polymorphism is left as an open issue. In view of the relationship between calculi and game semantics [9, 16, 19] it would be interesting to use typed processes in the present ....

Abramsky, S., and Lenisa, M. A fully-complete PER model for ML polymorphic types. In Proc. of CSL'2000, LNCS. Springer, 2000.

....implement type passing and proves full abstraction for System F, though the result arguably relies on the somewhat syntactic nature of the model. Murawski and Ong [29] substan tially simplify Hughes approach, but do not obtain full abstraction for impred icative polymorphism. Abramsky and Lenisa [5, 6] give a fully abstract model for predicative polymorphism using interaction combinators. Treatment of impredicative polymorphism is left as an open issue. In view of the relationship between r calculi and game semantics [9, 16, 19] it would be interesting to use typed processes in the present ....

ABRAMSKY, S., AND LENISA, M. A fully-complete PER model for ML polymorphic types. In Proc. of CSL'2000, LNCS. Springer, 2000.

....type passing and proves full abstraction for System F. His model is somewhat complex due to its direct representation of type instantiation. Murawski and Ong [21] substantially simplify Hughes approach, but do not obtain full abstraction for impredicative polymorphism. Abramsky and Lenisa [3, 4] give a fully abstract model for predicative polymorphism using interaction combinators. Treatment of impredicative polymorphism is left as an open issue. In view of the relationship between calculi and game semantics [7, 11, 14] it would be interesting to use typed processes from the present ....

Abramsky, S., and Lenisa, M. A fully-complete PER model for ML polymorphic types. In Proc. of CSL'2000, LNCS. Springer, 2000.

....a correct essential net for the associated end sequent. Faithful completeness is proved with respect to a notion of equivalence of such nets. Evolving Games and Essential Nets for Ane Polymorphism 3 The only game model for IMAL2 in the literature is given in [1] Recently Abramsky and Lenisa [3] have constructed a linear combinatory algebra of partial involutions on the natural numbers, arising from Geometry of Interaction constructions; they show that a fully and faithfully complete model for ML polymorphic types of system F can be obtained in this way. To the best of our knowledge, our ....

Abramsky, S., Lenisa, M.: A Fully-complete PER Model for ML Polymorphic Types. In Proceedings of CSL

....a correct essential net for the associated end sequent. Faithful completeness is proved with respect to a notion of equivalence of such nets. Evolving Games and Essential Nets for Ane Polymorphism 3 The only game model for IMAL2 in the literature is given in [1] Recently Abramsky and Lenisa [3] have constructed a linear combinatory algebra of partial involutions on the natural numbers, arising from Geometry of Interaction constructions; they show that a fully and faithfully complete model for ML polymorphic types of system F can be obtained in this way. To the best of our knowledge, our ....

S. Abramsky and M. Lenisa. A fully-complete PER model for ML polymorphic types. In Proceedings of CSL2000, Annual Conference of the European Association of Computer Science Logic, August 2000, Fischbachau, Germany. Springer-Verlag, 2000. LNCS Vol. 1862.

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S. Abramsky, M. Lenisa. A Fully-complete PER Model for ML Polymorphic Types, CSL'00 Conf. Proc., P. Clote, H.Schwichtenberg eds., LNCS 1862, 2000, 140-155.

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S.Abramsky, M.Lenisa. A Fully-complete PER Model for ML Polymorphic Types, CSL'00, LNCS 1862, 2000, 140-155.

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S.Abramsky, M.Lenisa. A Fully-complete PER Model for ML Polymorphic Types, CSL'00, LNCS 1862, 2000, 140-155.

No context found.

S. Abramsky and M. Lenisa, A Fully Complete PER Model for ML Polymorphic Types, Proceedings of CSL 2000.

.... ) was suggested as the basic setting for particle GoI, while (Rel , as the basic setting for wave GoI. Particle style GoI categories subsume game categories in the [AJM00] style with various notions of strategies, Abr96] In the typed setting, the particlestyle GoI has been quite fruitful, [AL00,AL00a,AL01]. On the contrary, in the untyped setting, in [DFH99] it has been shown that game models capture only a very limited number of # theories, related to Bohm trees and Levy Longo trees. Wave GoI categories and algebras have been studied very little in the literature, apart from some special models, ....

S.Abramsky, M.Lenisa. A Fully-complete PER Model for ML Polymorphic Types, CSL'00, LNCS 1862, 2000, 140--155.

....used successfully by various people to de ne fully complete models for various fragments of Linear Logic, and to give fully abstract models for many programming languages, including PCF, and other functional and non functional languages. Recently, a new technique, called linear realizability (see [AL99,AL00]) has been proposed as a valid and less complex alternative to Game Semantics in providing fully complete and fully abstract models. In particular, this technique has been used in [AL99,AL00] to de ne a model fully complete w.r.t. the fragment of system F consisting of Work partially supported ....

....other functional and non functional languages. Recently, a new technique, called linear realizability (see [AL99,AL00] has been proposed as a valid and less complex alternative to Game Semantics in providing fully complete and fully abstract models. In particular, this technique has been used in [AL99,AL00] to de ne a model fully complete w.r.t. the fragment of system F consisting of Work partially supported by TMR Linear FMRX CT98 0170. ML polymorphic types, and in [AL99a] to provide a fully complete model for PCF. The linear (linear ane) realizability technique amounts to constructing a ....

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S.Abramsky, M.Lenisa. A Fully-complete PER Model for ML Polymorphic Types, CSL'00, LNCS 1862, 2000, 140-155.

....xed point free partial involutions on a set X are in bijective correspondence with pairwise disjoint families fx i ; y i g i2I of two element subsets of X (i.e. the set of pairs fx; yg such that f(x) y, and hence also f(y) x) Thus they can thought of as abstract systems of axiom links . See [AL00, AL01] where a combinatory algebra of partial involutions is introduced, and an extensive study is made of realizability over this combinatory algebra. For us, the important correspondence is with copy cat strategies, rst identi ed in [AJ94a] as central to the game semantical analysis of proofs (and ....

....: if : C; D ) then ( C ) A p 1 ) A q ) Then exactly one of the following cases applies. i) C; D (ii) D (C i ( 1 ; l i ) where 1 i q, and j : C; D ) B i;j ; 1 j l i The proof follows standard arguments [AJM00, AL00]. In particular, since is wellopened, the Bang Lemma (Proposition 3.3.4 of [AJM00] applies. The remainder of the proof follows Proposition 3.4.5 of [AJM00] The Decomposition Lemma provides for one step of decomposition of an arbitrary strategy into a form matching that of normal forms in ....

S. Abramsky, M. Lenisa. A Fully-complete PER Model for ML Polymorphic Types, CSL'00 Conf. Proc., P. Clote, H.Schwichtenberg eds., LNCS 1862, 2000, 140-155.

....model of computation. Our approach also has conceptual interest in that our constructions, while quite concrete, are based directly on ideas stemming from Linear Logic and Geometry of Interaction [18, 19, 20, 21] and developed in previous work by the present author and a number of colleagues [2, 3, 5, 6, 7, 9, 10]. Our work here can be seen as a (relatively) concrete manifestation of these more abstract and foundational developments. However, no knowledge of Linear Logic or Geometry of Interaction is required to read the present paper. The paper [16] contains some discussion of a reversible abstract ....

....exive, transitive closure) 8 4.2.3 Application f g = LApp(f; g) It can be veri ed that f g is a partial injective function. In fact, we have the following result. Theorem 4.1 (I; f AS ; f AK ) is a combinatory algebra. This theorem is a minor variation on the results established in [5, 6, 9, 7, 10]; see in particular [10] and the combinatory algebra of partial involutions studied in [7] The ideas on which this construction is based stem from Linear Logic [18, 21] and Geometry of Interaction [19, 20] in the form developed by the present author and a number of colleagues [2, 3, 5, 6, 9, 7, ....

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S. Abramsky and M. Lenisa, A Fully Complete PER Model for ML Polymorphic Types, Proceedings of CSL

....the previous work on the full completeness problem for system F has produced semantically satisfactory models only for algebraic types. In this paper, we present a set of axioms on models of system F, sufficient to guarantee full completeness for ML types. This axiomatization is put to use in [AL99,AL00], in order to provide a concrete denotational model fully complete for the whole class of ML types. The axioms presented in this paper are given on the models of system F originated from Lawvere ( Law70] which are called hyperdoctrines (see also [Pit88] As in [Abr97] our axiomatization works ....

....we introduce an axiom which rules out infinite trees from the model. The abstract work carried out in this paper has interesting concrete modeltheoretic consequences, in that it enables a clean conceptual structure to be given to the proof of full completeness of the concrete model studied in [AL99,AL00]. The model construction in [AL99,AL00] is based on the technique of linear realizability, which is used to define hyperdoctrine adjoint models. This technique, which is described in [AL99,AL00] is to construct a PER category over a Linear Combinatory Algebra. The proof of full completeness of ....

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S.Abramsky, M.Lenisa. A Fully Complete PER Model for ML Polymorphic Types, CSL'2000 Conf. Proc., to appear.

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Abramsky, S., and Lenisa, M. A fully-complete PER model for ML polymorphic types. In Proc. of CSL'2000, LNCS. Springer, 2000.

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