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arXiv · 1803.00427

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

Koko Muroya·Dan R. Ghica
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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 \emph{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.

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Koko Muroya, Dan R. Ghica. 2019-10-29. The Dynamic Geometry of Interaction Machine: A Token-Guided Graph Rewriter. https://doi.org/10.23638/lmcs-15(4%3A7)2019

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