research-article

Maximal sharing in the Lambda calculus with letrec

Authors:

Clemens Grabmayer,

Jan RochelAuthors Info & Claims

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

Pages 67 - 80

https://doi.org/10.1145/2628136.2628148

Published: 19 August 2014 Publication History

Abstract

Increasing sharing in programs is desirable to compactify the code, and to avoid duplication of reduction work at run-time, thereby speeding up execution. We show how a maximal degree of sharing can be obtained for programs expressed as terms in the lambda calculus with letrec. We introduce a notion of 'maximal compactness' for λ_letrec-terms among all terms with the same infinite unfolding. Instead of defined purely syntactically, this notion is based on a graph semantics. λ_letrec-terms are interpreted as first-order term graphs so that unfolding equivalence between terms is preserved and reflected through bisimilarity of the term graph interpretations. Compactness of the term graphs can then be compared via functional bisimulation.

We describe practical and efficient methods for the following two problems: transforming a λ_letrec-term into a maximally compact form; and deciding whether two λ_letrec-terms are unfolding-equivalent. The transformation of a λ_letrec-terms L into maximally compact form L₀ proceeds in three steps: (i) translate L into its term graph G = [[L]] ; (ii) compute the maximally shared form of G as its bisimulation collapse G₀ ; (iii) read back a λ_letrec-term L₀ from the term graph G₀ with the property [[L₀]] = G₀. Then L₀ represents a maximally shared term graph, and it has the same unfolding as L.

The procedure for deciding whether two given λ_letrec-terms L₁ and L₂ are unfolding-equivalent computes their term graph interpretations [[L₁]] and [[L₂]], and checks whether these are bisimilar.

For illustration, we also provide a readily usable implementation.

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Cited By

Grabmayer C(2024)From Compactifying Lambda-Letrec Terms to Recognizing Regular-Expression ProcessesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.408.2408(21-41)Online publication date: 1-Oct-2024
https://doi.org/10.4204/EPTCS.408.2
Blaauwbroek LOlšák MGeuvers H(2024)Hashing Modulo Context-Sensitive 𝛼-EquivalenceProceedings of the ACM on Programming Languages10.1145/36564598:PLDI(2027-2050)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656459
Grabmayer C(2019)Modeling Terms by Graphs with Structure Constraints (Two Illustrations)Electronic Proceedings in Theoretical Computer Science10.4204/EPTCS.288.1288(1-13)Online publication date: 6-Feb-2019
https://doi.org/10.4204/EPTCS.288.1
Show More Cited By

Index Terms

Maximal sharing in the Lambda calculus with letrec
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
        Recursion
2. Theory of computation
  1. Semantics and reasoning
    1. Program constructs
      1. Functional constructs

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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

Copyright © 2014 ACM.

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Published: 19 August 2014

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Nederlandse Organisatie voor Wetenschappelijk Onderzoek

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ICFP'14

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SIGPLAN

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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October 12 - 18, 2025

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Cited By

Grabmayer C(2024)From Compactifying Lambda-Letrec Terms to Recognizing Regular-Expression ProcessesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.408.2408(21-41)Online publication date: 1-Oct-2024
https://doi.org/10.4204/EPTCS.408.2
Blaauwbroek LOlšák MGeuvers H(2024)Hashing Modulo Context-Sensitive 𝛼-EquivalenceProceedings of the ACM on Programming Languages10.1145/36564598:PLDI(2027-2050)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656459
Grabmayer C(2019)Modeling Terms by Graphs with Structure Constraints (Two Illustrations)Electronic Proceedings in Theoretical Computer Science10.4204/EPTCS.288.1288(1-13)Online publication date: 6-Feb-2019
https://doi.org/10.4204/EPTCS.288.1
Condoluci AAccattoli BCoen CKomendantskaya E(2019)Sharing Equality is LinearProceedings of the 21st International Symposium on Principles and Practice of Declarative Programming10.1145/3354166.3354174(1-14)Online publication date: 7-Oct-2019
https://dl.acm.org/doi/10.1145/3354166.3354174
Grabmayer Cvan Oostrom V(2015)Nested Term Graphs (Work In Progress)Electronic Proceedings in Theoretical Computer Science10.4204/EPTCS.183.4183(48-65)Online publication date: 26-May-2015
https://doi.org/10.4204/EPTCS.183.4
Accattoli BCoen C(2015)On the Relative Usefulness of FireballsProceedings of the 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS.2015.23(141-155)Online publication date: 6-Jul-2015
https://dl.acm.org/doi/10.1109/LICS.2015.23
Grabmayer CRochel J(2014)Maximal sharing in the Lambda calculus with letrecACM SIGPLAN Notices10.1145/2692915.262814849:9(67-80)Online publication date: 19-Aug-2014
https://doi.org/10.1145/2692915.2628148
Grabmayer C(2021)Structure-Constrained Process Graphs for the Process Semantics of Regular ExpressionsElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.334.3334(29-45)Online publication date: 8-Feb-2021
https://doi.org/10.4204/EPTCS.334.3
Grabmayer CFokkink WHermanns HZhang LKobayashi NMiller D(2020)A Complete Proof System for 1-Free Regular Expressions Modulo BisimilarityProceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3373718.3394744(465-478)Online publication date: 8-Jul-2020
https://dl.acm.org/doi/10.1145/3373718.3394744
Accattoli BCoen C(2015)On the Relative Usefulness of FireballsProceedings of the 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS.2015.23(141-155)Online publication date: 6-Jul-2015
https://dl.acm.org/doi/10.1109/LICS.2015.23

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