Abstract
We present an extension of the Interaction Abstract Machine (IAM) 10, 4 to full Linear Logic with Girard’s Geometry of Interaction (GoI) [6]. We propose a simplified way to interpret the additives and the interaction between additives and exponentials by means of weights [7]. We describe the interpretation by a token machine which allows us to recover the usual MELL case by forgetting all the additive information.
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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.
Andrea Asperti, Cecilia Giovannetti, and Andrea Naletto. The bologna optimal higher-order machine. Journal of Functional Programming, 6(6):763–810, November 1996.
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.
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.
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.
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.
Jean-Yves Girard. Proof-nets: the parallel syntax for proof-theory. In Ursini and Agliano, editors, Logic and Algebra, New York, 1996. Marcel Dekker.
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.
Olivier Laurent. Polarized proof-nets and λμ-calculus. To appear in Theoretical Computer Science, 2001.
Ian Mackie. The geometry of interaction machine. In Proceedings of Principles of Programming Languages, pages 198–208. ACM Press, January 1995.
Marco Pedicini and Francesco Quaglia. A parallel implementation for optimal lambda-calculus reduction. In Proceedings of Principles and Practice of Declarative Programming, 2000.
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© 2001 Springer-Verlag Berlin Heidelberg
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Laurent, O. (2001). A Token Machine for Full Geometry of Interaction (Extended Abstract). In: Abramsky, S. (eds) Typed Lambda Calculi and Applications. TLCA 2001. Lecture Notes in Computer Science, vol 2044. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45413-6_23
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DOI: https://doi.org/10.1007/3-540-45413-6_23
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