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Linear Logic Without Boxes (1992)  (Make Corrections)  (42 citations)
Georges Gonthier, Martín Abadi, Jean-Jacques Lévy
Proceedings 7th Annual IEEE Symp.\ on Logic in Computer Science, LICS'92, Santa Cruz, CA, USA, 22--25 June 1992



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Abstract: Girard's original definition of proof nets for linear logic involves boxes. The box is the unit for erasing and duplicating fragments of proof nets. It imposes synchronization, limits sharing, and impedes a completely local view of computation. Here we describe an implementation of proof nets without boxes. Proof nets are translated into graphs of the sort used in optimal -calculus implementations; computation is performed by simple graph rewriting. This graph implementation helps in... (Update)

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0.2:   A Brief Guide to Linear Logic - Scedrov (1993)   (Correct)
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33:   Theoretical Computer Science (context) - Girard - 1987
24:   The geometry of optimal lambda reduction - Gonthier, Abadi et al. - 1992
23:   An algorithm for optimal lambda calculus reductions (context) - Lamping - 1990

BibTeX entry:   (Update)

G. Gonthier, M. Abadi, and J.J. L'evy. Linear logic without boxes. In Proceedings 7 th Annual Symposium on Logic in Computer Science, 1992. http://citeseer.ist.psu.edu/gonthier92linear.html   More

@incollection{ gonthier92linear,
    author = "Georges Gonthier and Mart{\'i}n Abadi and Jean-Jacques L{\'e}vy",
    title = "Linear Logic Without Boxes",
    booktitle = "Proceedings 7th Annual {IEEE} Symp.\ on Logic in Computer Science, {LICS}'92, Santa Cruz, {CA}, {USA}, 22--25 June 1992",
    publisher = "IEEE Computer Society Press",
    address = "Los Alamitos, CA",
    pages = "223--34",
    year = "1992",
    url = "citeseer.ist.psu.edu/gonthier92linear.html" }
Citations (may not include all citations):
242   Linear logic (context) - Girard - 1987
233   Computational interpretations of linear logic - Abramsky - 1990
109   Interaction nets (context) - Lafont - 1990
75   The geometry of optimal lambda reduction - Gonthier, Abadi et al. - 1992
72   A new constructive logic: Classical logic (context) - Girard - 1991
70   An algorithm for optimal lambda calculus reduction (context) - Lamping - 1990
69   Geometry of interaction I: Interpretation of system F (context) - Girard - 1989
63   Optimal reductions in the lambdacalculus (context) - L'evy - 1980
51   Operational aspects of linear lambda calculus - Lincoln, Mitchell - 1992
24   Geometry of interaction II: Deadlock-free algorithms (context) - Girard
22   the unity of logic (context) - Girard - 1991
20   Optimal interpreters for lambdacalculus based functional lan.. (context) - Kathail - 1990
8   Linear ML (context) - Chirimar, Gunter et al. - 1991
6   Linear types can change the world - Wadler - 1990



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