Abstract
Proofs in Ludics are represented by designs. Designs (desseins) can be seen as an intermediate syntax between sequent calculus and proof nets, carrying advantages from both approaches, especially w.r.t. cut-elimination. To study interaction between designs and develop a geometrical intuition, we introduce an abstract machine which presents normalization as a token travelling along a net of designs. This allows a concrete approach, from which to carry on the study of issues such as: (i) which part of a design can be recognized interactively; (ii) how to reconstruct a design from the traces of its interactions in different tests.
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References
J.-M. Andreoli and R. Pareschi. Linear objects: logical processes with built-in inheritance. New Generation Computing, 9(3–4):445–473, 1991.
T. Coquand. A semantics of evidence for classical arithmetic. Journal of Symbolic Logic, (60), 1995.
P.-L. Curien and H. Herbelin. Computing with abstract bohm trees. In Third Fuji International Conference on Functional and Logic Programming, Kyoto, 1998. Word Scientific.
C. Faggian. On the Dynamics of Ludics. A Study of Interaction. PhD thesis, Université Aix-Marseille II, 2002.
C. Faggian and M. Hyland. Designs, disputes and strategies. In CSL 2002 (this volume), LNCS. Springer, 2002.
J.-Y. Girard. Locus solum. Mathematical Structures in Computer Science, 2001.
M. Hyland and L. Ong. On full abstraction for PCF. Information and Computation, 2000.
H. Nickau. Hereditarily sequential functionals. In Proceedings of the Symposium on Logical Foundations of Computer Science: Logic at St. Petersburg, LNCS. Springer, 1994.
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Faggian, C. (2002). Travelling on Designs. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_29
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DOI: https://doi.org/10.1007/3-540-45793-3_29
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