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The geometry of optimal lambda reduction Georges Gonthier \Lambda Mart'in Abadi y JeanJacques L'evy \Lambda
 

Summary: The geometry of optimal lambda reduction
Georges Gonthier \Lambda Mart'in Abadi y Jean­Jacques L'evy \Lambda
Abstract
Lamping discovered an optimal graph­reduction im­
plementation of the –­calculus. Simultaneously, Gi­
rard invented the geometry of interaction, a mathe­
matical foundation for operational semantics. In this
paper, we connect and explain the geometry of in­
teraction and Lamping's graphs. The geometry of
interaction provides a suitable semantic basis for ex­
plaining and improving Lamping's system. On the
other hand, graphs similar to Lamping's provide a
concrete representation of the geometry of interac­
tion. Together, they offer a new understanding of
computation, as well as ideas for efficient and correct
implementations.
Acknowledgements
We have enjoyed discussions with Pierre­Louis Cu­
rien, Jean­Yves Girard, Yves Lafont, and John Lamp­
ing. Gordon Plotkin made useful suggestions on the

  

Source: Abadi, Martín - Department of Computer Science, University of California at Santa Cruz

 

Collections: Computer Technologies and Information Sciences