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Abstract: This note defines a new graphical local calculus, directed virtual reductions. It is designed to compute Girard's execution formula EX, an invariant of closed functional evaluation obtained from the "geometry of interaction" interpretation of -calculus [4]. The calculus is obtained by synchronizing another graphical local calculus presented in "local and asynchronous beta-reduction": virtual reductions [3]. This synchronization makes it easier to mechanize than general virtual reductions. In... (Update)
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...for which an extension of the algebraic structure is required. This makes the calculations rather complex. Directed Virtual Reduction [1], together with the so called combustion strategy, eliminates this complexity, but at a cost: the introduction of many bureaucratic...
...edges, for which an extension of the algebraic structure is required. This makes the calculations rather complex. Directed Virtual Reduction [1], applied with the combustion strategy, eliminates this complexity and achieves strong local con uence, but at a cost: the...
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3: Proof-nets and the Hilbert space - Danos, Regnier - 1995
2: Geometry of interaction 1: Interpretation of system F (context) - Girard - 1989
2: Theoretical Computer Science (context) - Girard - 1987
BibTeX entry: (Update)
V. Danos, M. Pedicini, and L. Regnier. Directed virtual reductions. In M. Bezem and D. van Dalen, editors, Computer Science Logic, 10th International Workshop, CSL '96, volume 1258 of Lecture Notes in Computer Science. Springer Verlag, 1997. http://citeseer.ist.psu.edu/danos96directed.html More
@inproceedings{ danos96directed,
author = "Vincent Danos and Marco Pedicini and Laurent Regnier",
title = "Directed Virtual Reductions",
booktitle = "{CSL}",
pages = "76-88",
year = "1996",
url = "citeseer.ist.psu.edu/danos96directed.html" }
Citations (may not include all citations):42 Linear logic without boxes - Abadi, Gonthier et al. - 1992
21 Geometry of interaction I: an interpretation of system F (context) - Girard - 1988
16 Local and asynchronous betareduction (context) - Danos, Regnier - 1993
7 Pure and Applied Mathematics (context) - Petrich - 1984
4 Geometry of interaction III: acommodating the additives (context) - Girard - 1995
2 ffi ffi (context) - Asperti - 1995
Documents on the same site (http://www.logique.jussieu.fr/www.danos/DRpapers.html):
Reversible, Irreversible and Optimal ...-machines - Danos, Regnier (Correct)
Timeless Games - Baillot, Danos, Ehrhard, Regnier (1998) (Correct)
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