Jean-Yves Girard. Geometry of interaction 2: Deadlock-free algorithms. In P. Martin-Lof and G. Mints, editors, International Conference on Computer Logic, COLOG 88, pages 76--93. Springer-Verlag, 1988. Lecture Notes in Computer Science 417.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....play. Thus such a strategy is induced by a partial function on the set of moves in the game. The interpretation of proofs in MLL MIX by strategies, when analysed in terms of these underlying functions on moves, turns out to be very closely related to the Geometry of Interaction interpretation [Gir89b, Gir89a, Gir88]. The contents of the reminder of this paper are as follows. Section 2 reviews MLL MIX. Section 3 describes our game semantics for MLL MIX. Section 4 is devoted to the proof of the Full Completeness Theorem. Section 5 outlines how our semantics can be extended to full Classical Linear Logic. ....

....the morphisms witnessing the autonomous structure in G hf , or equivalently the interpretations of proofs in MLL MIX [See89] can be defined directly in terms of these functions. When we do so, we find that the interpretation coincides exactly with the Geometry of Interaction interpretation [Gir89b, Gir89a, Gir88]. More precisely, it corresponds to a reformulation of the Geometry of Interaction, due to the present authors, in a typed version based on sets and partial functions, in the same spirit as the GI(C ) construction of [AJ92a] 3.4.1 Games and the Geometry of Interaction As a first illustration, ....

[Article contains additional citation context not shown here]

J.-Y. Girard. Geometry of interaction 2: Deadlock-free algorithms. In P. Martin-Lof and G. Mints, editors, International Conference on Computer Logic, COLOG 88, pages 76--93. Springer-Verlag, 1988. Lecture Notes in Computer Science 417.

....analogies between game semantics and concurrency semantics, and [Abr94] for other aspects. We now describe composition in terms of the functions inducing strategies. Say we have f : A B; g : B C. We want to nd h such that f ; g = h . We shall compute h by the execution formula [Gir89b, Gir89a, Gir88]. Before giving the formal de nition, let us explain the idea, which is rather simple. We want to hook the strategies up so that Player s moves in B under get turned into Opponent s moves in B for , and vice versa. Consider the following picture: 11 ....

Jean-Yves Girard. Geometry of interaction 2: Deadlock-free algorithms. In P. Martin-Lof and G. Mints, editors, International Conference on Computer Logic, COLOG 88, pages 76-93. Springer-Verlag, 1988. Lecture Notes in Computer Science 417.

....tokens around a network, rather than by graph rewriting. ffl There is a normal form analogous to the Kleene normal form in recursion theory: the entire process of cut elimination is described by the iterations of a single operator. Girard has implemented this programme in a sequence of papers [Gir89b, Gir89a, Gir88a], using the formalism of C algebras. While the ideas are highly original and striking, and the technical execution must be considered a tour de force, some desiderata remain. 1. Can one give a more systematic account, making clear what structure is really needed to carry out the ....

J.-Y. Girard. Geometry of interaction 2: Deadlock-free algorithms. In P. MartinL of and G. Mints, editors, International Conference on Computer Logic, COLOG 88, pages 76--93. Springer-Verlag, 1988. Lecture Notes in Computer Science 417. 63

.... These theories attempt to analyze and clarify the world of concurrently communicating processes (and associated programming languages) in much the same way as lambda calculus and other models of computation have done for the sequential world [26] In a different direction, Jean Yves Girard [13, 16, 17, 18] has instituted the rapidly growing area of linear logic, a radical modification of traditional logic which appears to have strong connections with theoretical computer science. In several publications [16, 15] Girard has suggested that linear logic should 2 have deeper connections with ....

.... (e.g. i) by introducing guarding of terms [25] or (ii) 3 by a version of Girard s theory of slicing of proof nets [13, 6] ffl Modify linear logic evaluation strategies to take into account the extant theory of calculus (e.g. restriction to Geometry of Interaction style evaluation strategies [17, 18]) One of the theses of this work is that the Abramsky style translations (of linear logic) into the process world actually have less to do with logic than one might think: they are essentially only about the abstract pluggings in proof structures [13, 16, 12] and we formulate many of our results ....

J-Y.Girard. Geometry of Interaction 2: Deadlock-free Algorithms. COLOG-88 (P. Martin-Lof, G. Mints, eds.) Springer LNCS, 417, 1990, pp. 76-93.

.... These theories attempt to analyze and clarify the world of concurrently communicating processes (and associated programming languages) in much the same way as lambda calculus and other models of computation have done for the sequential world [26] In a different direction, Jean Yves Girard [13, 16, 17, 18] has instituted the rapidly growing area of linear logic, a radical modification of traditional logic which appears to have strong connections with theoretical computer science. In several publications [16, 15] Girard has suggested that linear logic should 2 have deeper connections with ....

.... (e.g. i) by introducing guarding of terms [25] or (ii) 3 by a version of Girard s theory of slicing of proof nets [13, 6] ffl Modify linear logic evaluation strategies to take into account the extant theory of calculus (e.g. restriction to Geometry of Interaction style evaluation strategies [17, 18]) One of the theses of this work is that the Abramsky style translations (of linear logic) into the process world actually have less to do with logic than one might think: they are essentially only about the abstract pluggings in proof structures [13, 16, 12] and we formulate many of our results ....

J-Y.Girard. Geometry of Interaction 2: Deadlock-free Algorithms. COLOG-88 (P. Martin-Lof, G. Mints, eds.) Springer LNCS, 417, 1990, pp. 76-93.

....tokens around a network, rather than by graph rewriting. ffl There is a normal form analogous to the Kleene normal form in recursion theory: the entire process of cut elimination is described by the iterations of a single operator. Girard has implemented this programme in a sequence of papers [Gir89b, Gir89a, Gir88a], using the formalism of C algebras. While the ideas are highly original and striking, and the technical execution must be considered a tour de force, some desiderata remain. 1. Can one give a more systematic account, making clear what structure is really needed to carry out the ....

J.-Y. Girard. Geometry of interaction 2: Deadlock-free algorithms. In P. MartinL of and G. Mints, editors, International Conference on Computer Logic, COLOG 88, pages 76--93. Springer-Verlag, 1988. Lecture Notes in Computer Science 417.

....play. Thus such a strategy is induced by a partial function on the set of moves in the game. The interpretation of proofs in MLL MIX by strategies, when analysed in terms of these underlying functions on moves, turns out to be very closely related to the Geometry of Interaction interpretation [Gir89b, Gir89a, Gir88]. The contents of the reminder of this paper are as follows. Section 2 reviews MLL MIX. Section 3 describes our game semantics for MLL MIX. Section 4 is devoted to the proof of the Full Completeness Theorem. Section 5 outlines how our semantics can be extended to full Classical Linear Logic. ....

....the morphisms witnessing the autonomous structure in G hf , or equivalently the interpretations of proofs in MLL MIX [See89] can be defined directly in terms of these functions. When we do so, we find that the interpretation coincides exactly with the Geometry of Interaction interpretation [Gir89b, Gir89a, Gir88]. More precisely, it corresponds to a reformulation of the Geometry of Interaction, due to the present authors, in a typed version based on sets and partial functions, in the same spirit as the GI(C ) construction of [AJ92a] 3.4.1 Games and the Geometry of Interaction As a first illustration, we ....

[Article contains additional citation context not shown here]

J.-Y. Girard. Geometry of interaction 2: Deadlock-free algorithms. In P. Martin-Lof and G. Mints, editors, International Conference on Computer Logic, COLOG 88, pages 76--93. Springer-Verlag, 1988. Lecture Notes in Computer Science 417.

....play. Thus such a strategy is induced by a partial function on the set of moves in the game. The interpretation of proofs in MLL MIX by strategies, when analysed in terms of these underlying functions on moves, turns out to be very closely related to the Geometry of Interaction interpretation [Gir89b, Gir89a, Gir88]. The contents of the reminder of this paper are as follows. Section 2 reviews MLL MIX. Section 3 describes our game semantics for MLL MIX. Section 4 is devoted to the proof of the Full Completeness Theorem. Section 5 outlines how our semantics can be extended to full Classical Linear Logic. ....

....the morphisms witnessing the autonomous structure in G hf , or equivalently the interpretations of proofs in MLL MIX [See89] can be defined directly in terms of these functions. When we do so, we find that the interpretation coincides exactly with the Geometry of Interaction interpretation [Gir89b, Gir89a, Gir88]. More precisely, it corresponds to a reformulation of the Geometry of Interaction, due to the present authors, in a typed version based on sets and partial functions, in the same spirit as the GI(C ) construction of [AJ92b] 3.4.1 Games and the Geometry of Interaction As a first illustration, ....

[Article contains additional citation context not shown here]

J.-Y. Girard. Geometry of interaction 2: Deadlock-free algorithms. In P. Martin-Lof and G. Mints, editors, International Conference on Computer Logic, COLOG 88, pages 76--93. Springer-Verlag, 1988. Lecture Notes in Computer Science 417.

....the bracketing condition. 3. Composition is monotone and continuous with respect to v. We now describe composition in terms of the functions inducing strategies. Say we have oe f : A B; oe g : B C. We want to nd h such that oe f ; oe g = oe h . We shall compute h by the iexecution formulaj [15, 16, 17]. Before giving the formal de nition, let us explain the idea, which is rather simple. We want to hook the strategies up so that Player s moves in B under oe get turned into Opponent s moves in B for , and vice versa. Consider the following picture: oe Delta Delta Delta Delta Delta ....

J.-Y. Girard. Geometry of interaction 2: Deadlock-free algorithms. In P. MartinL #f and G. Mints, editors, International Conference on Computer Logic, COLOG 88, pages 7693. Springer-Verlag, 1988. Lecture Notes in Computer Science 417.

No context found.

Jean-Yves Girard. Geometry of interaction 2: Deadlock-free algorithms. In P. Martin-Lof and G. Mints, editors, International Conference on Computer Logic, COLOG 88, pages 76--93. Springer-Verlag, 1988. Lecture Notes in Computer Science 417.

No context found.

J.-Y. Girard. Geometry of interaction 2: Deadlock-free algorithms. In P. MartinL of and G. Mints, editors, International Conference on Computer Logic, COLOG 88, pages 76--93. Springer-Verlag, 1988. Lecture Notes in Computer Science 417. 63

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC