research-article

Distilling abstract machines

Authors:

Beniamino Accattoli,

Pablo Barenbaum,

Damiano MazzaAuthors Info & Claims

ICFP '14: Proceedings of the 19th ACM SIGPLAN international conference on Functional programming

Pages 363 - 376

https://doi.org/10.1145/2628136.2628154

Published: 19 August 2014 Publication History

Abstract

It is well-known that many environment-based abstract machines can be seen as strategies in lambda calculi with explicit substitutions (ES). Recently, graphical syntaxes and linear logic led to the linear substitution calculus (LSC), a new approach to ES that is halfway between small-step calculi and traditional calculi with ES. This paper studies the relationship between the LSC and environment-based abstract machines. While traditional calculi with ES simulate abstract machines, the LSC rather distills them: some transitions are simulated while others vanish, as they map to a notion of structural congruence. The distillation process unveils that abstract machines in fact implement weak linear head reduction, a notion of evaluation having a central role in the theory of linear logic. We show that such a pattern applies uniformly in call-by-name, call-by-value, and call-by-need, catching many machines in the literature. We start by distilling the KAM, the CEK, and a sketch of the ZINC, and then provide simplified versions of the SECD, the lazy KAM, and Sestoft's machine. Along the way we also introduce some new machines with global environments. Moreover, we show that distillation preserves the time complexity of the executions, i.e. the LSC is a complexity-preserving abstraction of abstract machines.

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Cited By

Muroya KSanada TUrabe N(2024)Preorder-Constrained Simulations for Program Refinement with EffectsCoalgebraic Methods in Computer Science10.1007/978-3-031-66438-0_3(44-64)Online publication date: 6-Apr-2024
https://dl.acm.org/doi/10.1007/978-3-031-66438-0_3
Accattoli BStorm THirschfeld R(2023)Sharing a Perspective on the 𝜆-CalculusProceedings of the 2023 ACM SIGPLAN International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software10.1145/3622758.3622884(179-190)Online publication date: 18-Oct-2023
https://dl.acm.org/doi/10.1145/3622758.3622884
Accattoli BBarenbaum P(2023)A Diamond Machine for Strong EvaluationProgramming Languages and Systems10.1007/978-981-99-8311-7_4(69-90)Online publication date: 26-Nov-2023
https://dl.acm.org/doi/10.1007/978-981-99-8311-7_4
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Index Terms

Distilling abstract machines
1. Mathematics of computing
  1. Continuous mathematics
    1. Calculus
      1. Lambda calculus
  2. Mathematical analysis
    1. Calculus
      1. Lambda calculus
2. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language types
        Functional languages

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cover image ACM Conferences

ICFP '14: Proceedings of the 19th ACM SIGPLAN international conference on Functional programming

August 2014

390 pages

ISBN:9781450328739

DOI:10.1145/2628136

General Chair:
Johan Jeuring
Universiteit Utrecht, The Netherlands
,
Program Chair:
Manuel M.T. Chakravarty
University of New South Wales, Australia

ACM SIGPLAN Notices Volume 49, Issue 9
ICFP '14
September 2014
361 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2692915
Editors:
Mark W. Bailey
Hamilton College, Clinton, NY
,
Rajeev Balasubramonian
University of Utah
,
Al Davis
University of Utah
,
Sarita Adve
University of Illinois at Urbana-Champ
Issue’s Table of Contents

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Published: 19 August 2014

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French-Argentinian Laboratory in Computer Science

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ICFP'14: ACM SIGPLAN International Conference on Functional Programming

September 1 - 6, 2014

Gothenburg, Sweden

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ICFP '14 Paper Acceptance Rate 28 of 85 submissions, 33%;

Overall Acceptance Rate 333 of 1,064 submissions, 31%

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Cited By

Muroya KSanada TUrabe N(2024)Preorder-Constrained Simulations for Program Refinement with EffectsCoalgebraic Methods in Computer Science10.1007/978-3-031-66438-0_3(44-64)Online publication date: 6-Apr-2024
https://dl.acm.org/doi/10.1007/978-3-031-66438-0_3
Accattoli BStorm THirschfeld R(2023)Sharing a Perspective on the 𝜆-CalculusProceedings of the 2023 ACM SIGPLAN International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software10.1145/3622758.3622884(179-190)Online publication date: 18-Oct-2023
https://dl.acm.org/doi/10.1145/3622758.3622884
Accattoli BBarenbaum P(2023)A Diamond Machine for Strong EvaluationProgramming Languages and Systems10.1007/978-981-99-8311-7_4(69-90)Online publication date: 26-Nov-2023
https://dl.acm.org/doi/10.1007/978-981-99-8311-7_4
Accattoli BDal Lago UVanoni G(2022)Multi types and reasonable spaceProceedings of the ACM on Programming Languages10.1145/35476506:ICFP(799-825)Online publication date: 31-Aug-2022
https://dl.acm.org/doi/10.1145/3547650
Accattoli BDal Lago UVanoni G(2022)Reasonable Space for the λ-Calculus, LogarithmicallyProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533362(1-13)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3533362
Accattoli B(2022)Exponentials as Substitutions and the Cost of Cut Elimination in Linear LogicProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3532445(1-15)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3532445
Kesner D(2022)A fine-grained computational interpretation of Girard’s intuitionistic proof-netsProceedings of the ACM on Programming Languages10.1145/34986696:POPL(1-28)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3498669
Moy CNguyễn PTobin-Hochstadt SVan Horn D(2021)Corpse reviver: sound and efficient gradual typing via contract verificationProceedings of the ACM on Programming Languages10.1145/34343345:POPL(1-28)Online publication date: 4-Jan-2021
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Aguirre ABarthe GHsu JKaminski BKatoen JMatheja C(2021)A pre-expectation calculus for probabilistic sensitivityProceedings of the ACM on Programming Languages10.1145/34343335:POPL(1-28)Online publication date: 4-Jan-2021
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Accattoli BDal Lago UVanoni G(2021)The (In)Efficiency of interactionProceedings of the ACM on Programming Languages10.1145/34343325:POPL(1-33)Online publication date: 4-Jan-2021
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