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

TL;DR

This paper introduces the Dynamic GoI Machine, a token-guided graph rewriter that unifies evaluation strategies for lambda-calculus, balancing correctness and efficiency through a novel abstract machine framework.

Contribution

It presents the Dynamic GoI Machine, combining token passing and graph rewriting to analyze and optimize evaluation strategies for lambda-calculus.

Findings

Soundness and completeness for multiple evaluation strategies

Classified as efficient in Accattoli's taxonomy

Supports call-by-need and call-by-value evaluations

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.