Efficient Implementation of Evaluation Strategies via Token-Guided Graph Rewriting

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. We contributed to the study of this trade-off by the introduction of an abstract machine for call-by-need, inspired by Girard's Geometry of Interaction, a machine combining token passing and graph rewriting. This work presents an extension of the machine, to additionally accommodate left-to-right and right-to-left call-by-value strategies. We show soundness and completeness of the extended machine with respect to each of the call-by-need and two call-by-value strategies. Analysing time cost of its execution classifies the machine as "efficient" in Accattoli's taxonomy of abstract machines.