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Abstract: : Sharing graphs are a way of representing linear logic proof-nets in such a way that their reduction never duplicates a redex. In their usual presentations, they present a problem of coherence: if the proof-net N reduces by standard cut-elimination to N 0 , then, by reducing the sharing graph of N we do not obtain the sharing graph of N 0 . We solve this problem by changing the way the information is coded into sharing graphs and introducing a new reduction rule (absorption). The... (Update)
Context of citations to this paper: More
.... boxes can be avoided indexing each formula by a level (see [MM95] which may be interpreted as the box nesting depth of the formula [Gue96,GMM96a]. A parsing grammar can then be given also for such leveled proof nets without boxes. Such a grammar, suitably extended to implement...
.... the motivation of the previous study is connected to the implementation of proof net rewriting by means of sharing graphs (see [GMM96]) On the other hand, the correctness criteria given in the previous sections extend to the case of classical MELL proof nets (i.e....
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BibTeX entry: (Update)
S. Guerrini, S. Martini, and A. Masini. Coherence for sharing proof nets. In Harald Ganzinger, editor, Proceedings of the 7th International Conference on Rewriting Techniques and Applications (RTA-96), volume 1103 of Lecture Notes in Computer Science, pages 215--229, New Brunswick, NJ, USA, 1996. Springer-Verlag. http://citeseer.ist.psu.edu/guerrini96coherence.html More
@inproceedings{ guerrini96coherence,
author = "Stefano Guerrini and Simone Martini and Andrea Masini",
title = "Coherence for Sharing Proof Nets",
booktitle = "{RTA}",
pages = "215-229",
year = "1996",
url = "citeseer.ist.psu.edu/guerrini96coherence.html" }
Citations (may not include all citations):215 Theoretical Computer Science (context) - Girard - 1987
75 The geometry of optimal lambda reduction - Gonthier, Abadi et al. - 1992
38 A computational interpretation of modal proofs - Martini, Masini - 1996
24 An algorithm for optimal lambda calculus reduction (context) - Lamping - 1990
14 Optimality and inefficiency: What isn't a cost model of the .. - Lawall, Mairson - 1996
13 Linear logic without boxes - Gonthier, Abadi et al. - 1992
10 Optimal reductions in the lambda-calculus (context) - L'evy - 1980
9 R'eductions Correctes et Optimales dans le lambdacalcul (context) - L'evy - 1978
7 comonads and optimal reductions (context) - Asperti - 1995
6 the complexity of beta-reduction (context) - Asperti - 1996
6 Optimizing optimal -calculus implementations (context) - Asperti - 1995
5 Paths in the lambda-calculus: three years of communications .. (context) - Asperti, Danos et al. - 1994
3 Theoretical and Practical Aspects of Optimal Implementations.. (context) - Guerrini - 1996
2 Interaction systems - Asperti, Laneve - 1993
1 sharing-morphisms (context) - Guerrini - 1995
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