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

02/28/2018
by   Koko Muroya, et al.
0

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 contribute to the study of this trade-off by the introduction of 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/19/2018

Efficient Implementation of Evaluation Strategies via Token-Guided Graph Rewriting

In implementing evaluation strategies of the lambda-calculus, both corre...
research
09/15/2020

An Abstract Machine for Strong Call by Value

We present an abstract machine that implements a full-reducing (a.k.a. s...
research
04/28/2021

The Space of Interaction (long version)

The space complexity of functional programs is not well understood. In p...
research
02/13/2020

The Abstract Machinery of Interaction (Long Version)

This paper revisits the Interaction Abstract Machine (IAM), a machine ba...
research
07/13/2019

Crumbling Abstract Machines

Extending the lambda-calculus with a construct for sharing, such as let ...
research
10/24/2020

The (In)Efficiency of Interaction

Evaluating higher-order functional programs through abstract machines in...
research
02/11/2021

Strong Call by Value is Reasonable for Time

The invariance thesis of Slot and van Emde Boas states that all reasonab...

Please sign up or login with your details

Forgot password? Click here to reset