The Dynamic Geometry of Interaction Machine: A Token-Guided Graph Rewriter

Abstract

In implementing evaluation strategies of the lambda-calculus, both correctness and efficiency of implementation are valid concerns. While the notion of correctness is determined by the evaluation strategy, regarding efficiency there is a larger design space that can be explored, in particular the trade-off between space versus time efficiency. Aiming at a unified framework that would enable the study of this trade-off, we introduce an abstract machine, inspired by Girard's Geometry of Interaction (GoI), a machine combining token passing and graph rewriting. We show soundness and completeness of our abstract machine, called the Dynamic GoI Machine (DGoIM), with respect to three evaluations: call-by-need, left-to-right call-by-value, and right-to-left call-by-value. Analysing time cost of its execution classifies the machine as "efficient" in Accattoli's taxonomy of abstract machines.

Making Concurrency Functional

“…Geometry of Interaction started as an investigation of the nature of proofs of linear logic, understood as networks [24]. It has subsequently been tied to optimal reduction in thecalculus [25], and inspired implementations via token machines on networks [30,33]; when the two components of a GoI game match events of exit and entry of a token at a link.…”