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
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Girard, JY. (1994). Geometry of Interaction (Abstract). In: Jonsson, B., Parrow, J. (eds) CONCUR ’94: Concurrency Theory. CONCUR 1994. Lecture Notes in Computer Science, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48654-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-48654-1_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58329-5
Online ISBN: 978-3-540-48654-1
eBook Packages: Springer Book Archive