English

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

Logic in Computer Science 2023-06-22 v3 Programming Languages

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.

Keywords

Cite

@article{arxiv.1803.00427,
  title  = {The Dynamic Geometry of Interaction Machine: A Token-Guided Graph Rewriter},
  author = {Koko Muroya and Dan R. Ghica},
  journal= {arXiv preprint arXiv:1803.00427},
  year   = {2023}
}

Comments

arXiv admin note: text overlap with arXiv:1802.06495

R2 v1 2026-06-23T00:38:15.759Z