the geometry of optimal lambda reduction
Lamping discovered an optimal graph-reduction implementation of the &lgr;-calculus. Simultaneously, Girard invented the geometry of interaction, a mathematical foundation for operational semantics. In this paper, we connect and explain the geometry of interaction and Lamping's graphs. The geometry of interaction provides a suitable semantic basis for explaining and improving Lamping's system. On the other hand, graphs similar to Lamping's provide a concrete representation of the geometry of interaction. Together, they offer a new understanding of computation, as well as ideas for efficient and correct implementations.
geometry optimality reduction graph implementation interaction operational semantics semantic paper connection systems representation understandability computation efficiency