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PROGRAMMING LANGUAGES

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## On Geometry of Interaction

Resource type

Authors/contributors

- Girard, Jean-Yves (Author)
- Schwichtenberg, Helmut (Editor)

Title

On Geometry of Interaction

Abstract

The paper expounds geometry of interaction, for the first time in the full case, i.e. for all connectives of linear logic, including additives and constants. The interpretation is done within a C*-algebra which is induced by the rule of resolution of logic programming, and therefore the execution formula can be presented as a simple logic programming loop. Part of the data is public (shared channels) but part of it can be viewed as private dialect (defined up to isomorphism) that cannot be shared during interaction, thus illustrating the theme of communication without understanding. One can prove a nilpotency (i.e. termination) theorem for this semantics, and also its soundness w.r.t. a slight modification of familiar sequent calculus in the case of exponential-free conclusions.

Date

1995

Proceedings Title

Proof and Computation

Place

Berlin, Heidelberg

Publisher

Springer

Pages

145-191

Series

NATO ASI Series

Language

en

DOI

10/fr557p

ISBN

978-3-642-79361-5

Library Catalog

Springer Link

Extra

ZSCC: NoCitationData[s0]

Citation

Girard, J.-Y. (1995). On Geometry of Interaction. In H. Schwichtenberg (Ed.),

*Proof and Computation*(pp. 145–191). Berlin, Heidelberg: Springer. https://doi.org/10/fr557p
CATEGORICAL LOGIC

PROGRAMMING LANGUAGES

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