A Token Machine for Full Geometry of Interaction (Extended Abstract)
We present an extension of the Interaction Abstract Machine (IAM) 10, 4 to full Linear Logic with Girard’s Geometry of Interaction (GoI) . We propose a simplified way to interpret the additives and the interaction between additives and exponentials by means of weights . We describe the interpretation by a token machine which allows us to recover the usual MELL case by forgetting all the additive information.
KeywordsBasic Weight Parallel Machine Linear Logic Sequent Calculus Correct Weighting
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- Samson Abramsky, Radha Jagadeesan, and Pasquale Malacaria. Full abstraction for PCF (extended abstract). In M. Hagiya and J. C. Mitchell, editors, Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 1–15. Springer, April 1994.Google Scholar
- Vincent Danos, Hugo Herbelin, and Laurent Regnier. Games semantics and abstract machines. In Proceedings of Logic In Computer Science, New Brunswick, 1996. IEEE Computer Society Press.Google Scholar
- Vincent Danos and Laurent Regnier. Reversible, irreversible and optimal λ-machines. In J.-Y. Girard, M. Okada, and A. Scedrov, editors, Proceedings Linear Logic Tokyo Meeting, volume 3 of Electronic Notes in Theoretical Computer Science. Elsevier, 1996.Google Scholar
- Jean-Yves Girard. Geometry of interaction I: an interpretation of system F. In Ferro, Bonotto, Valentini, and Zanardo, editors, Logic Colloquium’ 88. North-Holland, 1988.Google Scholar
- Jean-Yves Girard. Geometry of interaction III: accommodating the additives. In J.-Y. Girard, Y. Lafont, and L. Regnier, editors, Advances in Linear Logic, volume 222 of London Mathematical Society Lecture Note Series, pages 329–389. Cambridge University Press, 1995.Google Scholar
- Jean-Yves Girard. Proof-nets: the parallel syntax for proof-theory. In Ursini and Agliano, editors, Logic and Algebra, New York, 1996. Marcel Dekker.Google Scholar
- Georges Gonthier, Martin Abadi, and Jean-Jacques Lévy. The geometry of optimal lambda reduction. In Proceedings of Principles of Programming Languages, pages 15–26. ACM Press, 1992.Google Scholar
- Olivier Laurent. Polarized proof-nets and λμ-calculus. To appear in Theoretical Computer Science, 2001.Google Scholar
- Ian Mackie. The geometry of interaction machine. In Proceedings of Principles of Programming Languages, pages 198–208. ACM Press, January 1995.Google Scholar
- Marco Pedicini and Francesco Quaglia. A parallel implementation for optimal lambda-calculus reduction. In Proceedings of Principles and Practice of Declarative Programming, 2000.Google Scholar