Showing papers by "Jean-Yves Girard published in 1994"
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22 Aug 1994TL;DR: Geometry of Interaction is based on the idea that the ultimate explanation of logical rules is through the cut-elimination procedure, achieved by means of a pure geometric interpretation of normalization.
Abstract: Geometry of Interaction is based on the idea that the ultimate explanation of logical rules is through the cut-elimination procedure. This is achieved by means of a pure geometric interpretation of normalization:
proofs are operators on the Hilbert space describing I/O dependencies
cut-elimination is the solution of an I/O equation
(the cut σ expressing a feedback of some output of the proof U to some input of U)
termination is nilpotency of the operator σU
execution is expressed by
4 citations