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Abstract machines, optimal reduction, and streams

Published online by Cambridge University Press:  08 April 2019

Anna Chiara Lai ,
Marco Pedicini Open the ORCID record for Marco Pedicini [Opens in a new window]  and
Mario Piazza
Anna Chiara Lai
Affiliation:
Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, Via Antonio Scarpa 16, 00181 Rome, Italy
Marco Pedicini*
Affiliation:
Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, 00146 Rome, Italy
Mario Piazza
Affiliation:
Classe di Lettere e Filosofia, Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
*
*Corresponding author. Email: marco@iac.cnr.it
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Abstract

In this paper, we propose and explore a new approach to abstract machines and optimal reduction via streams, infinite sequences of elements. We first define a sequential abstract machine capable of performing directed virtual reduction (DVR) and then we extend it to its parallel version, whose equivalence is explained through the properties of DVR itself. The result is a formal definition of the λ-calculus interpreter called Parallel Environment for Lambda Calculus Reduction (PELCR), a software for λ-calculus reduction based on the Geometry of Interaction. In particular, we describe PELCR as a stream-processing abstract machine, which in principle can also be applied to infinite streams.

Keywords

Geometry of InteractionParallel ImplementationFunctional ProgrammingStreamsLinear LogicCurry-Howard Isomorphism
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 29 , Issue 9 , October 2019 , pp. 1379 - 1410
Copyright
© Cambridge University Press 2019 

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