Positive Sharing and Abstract Machines

Fuente: arXiv
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Main Authors: Accattoli, Beniamino, Coen, Claudio Sacerdoti, Wu, Jui-Hsuan
Format: Preprint
Published: 2025
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author Accattoli, Beniamino
Coen, Claudio Sacerdoti
Wu, Jui-Hsuan
author_facet Accattoli, Beniamino
Coen, Claudio Sacerdoti
Wu, Jui-Hsuan
contents Wu's positive $λ$-calculus is a recent call-by-value $λ$-calculus with sharing coming from Miller and Wu's study of the proof-theoretical concept of focalization. Accattoli and Wu showed that it simplifies a technical aspect of the study of sharing; namely it rules out the recurrent issue of renaming chains, that often causes a quadratic time slowdown. In this paper, we define the natural abstract machine for the positive $λ$-calculus and show that it suffers from an inefficiency: the quadratic slowdown somehow reappears when analyzing the cost of the machine. We then design an optimized machine for the positive $λ$-calculus, which we prove efficient. The optimization is based on a new slicing technique which is dual to the standard structure of machine environments.
format Preprint
id arxiv_https___arxiv_org_abs_2506_14131
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Positive Sharing and Abstract Machines
Accattoli, Beniamino
Coen, Claudio Sacerdoti
Wu, Jui-Hsuan
Logic in Computer Science
Programming Languages
Wu's positive $λ$-calculus is a recent call-by-value $λ$-calculus with sharing coming from Miller and Wu's study of the proof-theoretical concept of focalization. Accattoli and Wu showed that it simplifies a technical aspect of the study of sharing; namely it rules out the recurrent issue of renaming chains, that often causes a quadratic time slowdown. In this paper, we define the natural abstract machine for the positive $λ$-calculus and show that it suffers from an inefficiency: the quadratic slowdown somehow reappears when analyzing the cost of the machine. We then design an optimized machine for the positive $λ$-calculus, which we prove efficient. The optimization is based on a new slicing technique which is dual to the standard structure of machine environments.
title Positive Sharing and Abstract Machines
topic Logic in Computer Science
Programming Languages
url https://arxiv.org/abs/2506.14131