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Closure analysis in constraint form

Editor: Andrew W. Appel Author:

Jens PalsbergAuthors Info & Claims

ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 17, Issue 1

Pages 47 - 62

https://doi.org/10.1145/200994.201001

Published: 01 January 1995 Publication History

Abstract

Flow analyses of untyped higher-order functional programs have in the past decade been presented by Ayers, Bondorf, Consel, Jones, Heintze, Sestoft, Shivers, Steckler, Wand, and others. The analyses are usually defined as abstract interpretations and are used for rather different tasks such as type recovery, globalization, and binding-time analysis. The analyses all contain a global closure analysis that computes information about higher-order control-flow. Sestoft proved in 1989 and 1991 that closure analysis is correct with respect to call-by-name and call-by-value semantics, but it remained open if correctness holds for arbitrary beta-reduction.

This article answers the question; both closure analysis and others are correct with respect to arbitrary beta-reduction. We also prove a subject-reduction result: closure information is still valid after beta-reduction. The core of our proof technique is to define closure analysis using a constraint system. The constraint system is equivalent to the closure analysis of Bondorf, which in turn is based on Sestoft's.

References

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PALSBERG, J. 1993. Correctness of binding-time analysis. J. Functional Program. 3, 3,347-363.

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PALSBERG, J. AND SCHWARTZBACH, M. I. 1994a. Binding-time analysis: Abstract interpretation versus type inference. In Proceedzngs of ICCL '9~, 5th IEEE International Conference on Computer Languages. IEEE, New York, 289-298.

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PALSBERG, J. AND SCHWARTZBACH, M. I. 1994b. Object-Oriented Type Systems. John Wiley and Sons, New York.

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PALSBERG, J. AND SCHWARTZBACH, ~{. I. 1992a. Safety analysis versus type inference. Inf. Comput. To be published.

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PALSBERG, J. AND SCHWARTZBACH, M. I. 1992b. Safety analysis versus type inference for partial types. Inf. Process. Left. ~3, 175-180.

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PALSBERG, J. AND SCHWARTZBACH, M. I. 1991. Object-oriented type inference. In Proceedings of OOPSLA '91, A CM SIGPLAN 6th Annual Conference on Object-Oriented Programming Systems, Languages and Applications. ACM, New York, 146-161.

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SESTOFT, P. 1991. Analysis and efficient implementation of functional programs. Ph.D. thesis, DIKU, University of Copenhagen.

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SESTOFT, P. 1989. Replacing function parameters by global variables. M.S. thesis, DIKU, University of Copenhagen.

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SmvErtS, O. 1991a. Control-flow analysis of higher-order languages. Ph.D. thesis, CMU-CS- 91-145, Carnegie Mellon University, Pittsburgh, Pa.

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WAND, M. AND STECKLER, P. 1994. Selective and lightweight closure conversion. In Proceedings of POPL'94, 21st Annual Symposium on Principles of Programming Languages. ACM, New York, 434-445.

Cited By

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Germane KMcCarthy J(2021)Newly-single and loving it: improving higher-order must-alias analysis with heap fragmentsProceedings of the ACM on Programming Languages10.1145/34736015:ICFP(1-28)Online publication date: 19-Aug-2021
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Montagu BJensen TFreund SYahav E(2021)Trace-based control-flow analysisProceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3453483.3454057(482-496)Online publication date: 19-Jun-2021
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Index Terms

Closure analysis in constraint form
1. Software and its engineering
  1. Software creation and management
    1. Software verification and validation
      1. Operational analysis
  2. Software notations and tools
2. Theory of computation

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Reviews

Reviewer: Pierre Jouvelot

Closure analysis extends the classical algorithm that computes function call graphs to the realm of higher-order first-class functions. This analysis is important when optimization of such languages is called for, for instance when using partial evaluation or code inlining. Even when limited to untyped functional languages, the literature offers many different ways to tackle this problem. This paper shows that Sestoft's closure analysis, which has already been proven correct with respect to both call-by-name and call-by-value semantics, is valid for arbitrary reduction orders. This proof relies on a constraint-based formulation, related to Bondorf's, of such a closure analysis. Although this paper is easy to read, I would only recommend it to researchers already involved in closure analysis or, at least, the static semantics of functional languages. Indeed, although the result is new, it appears to be a mostly theoretical extension of existing research and, as such, seems of limited practical import to practitioners.

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Published In

cover image ACM Transactions on Programming Languages and Systems

ACM Transactions on Programming Languages and Systems Volume 17, Issue 1

Jan. 1995

179 pages

ISSN:0164-0925

EISSN:1558-4593

DOI:10.1145/200994

Editor:
Andrew W. Appel
Princeton Univ., Princeton, NJ

Issue’s Table of Contents

Copyright © 1995 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1995

Published in TOPLAS Volume 17, Issue 1

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Cited By

Germane K(2023)m-CFA Exhibits Perfect Stack PrecisionProgramming Languages and Systems10.1007/978-981-99-8311-7_14(290-309)Online publication date: 26-Nov-2023
https://dl.acm.org/doi/10.1007/978-981-99-8311-7_14
Germane KMcCarthy J(2021)Newly-single and loving it: improving higher-order must-alias analysis with heap fragmentsProceedings of the ACM on Programming Languages10.1145/34736015:ICFP(1-28)Online publication date: 19-Aug-2021
https://dl.acm.org/doi/10.1145/3473601
Montagu BJensen TFreund SYahav E(2021)Trace-based control-flow analysisProceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3453483.3454057(482-496)Online publication date: 19-Jun-2021
https://dl.acm.org/doi/10.1145/3453483.3454057
Bodin MGardner PJensen TSchmitt A(2019)Skeletal semantics and their interpretationsProceedings of the ACM on Programming Languages10.1145/32903573:POPL(1-31)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1145/3290357
Germane KMcCarthy JAdams MMight M(2019)Demand Control-Flow AnalysisVerification, Model Checking, and Abstract Interpretation10.1007/978-3-030-11245-5_11(226-246)Online publication date: 11-Jan-2019
https://doi.org/10.1007/978-3-030-11245-5_11
Lyde SByrd WMight M(2015)Control-flow analysis of dynamic languages via pointer analysisACM SIGPLAN Notices10.1145/2936313.281671251:2(54-62)Online publication date: 21-Oct-2015
https://dl.acm.org/doi/10.1145/2936313.2816712
Lyde SByrd WMight MSerrano M(2015)Control-flow analysis of dynamic languages via pointer analysisProceedings of the 11th Symposium on Dynamic Languages10.1145/2816707.2816712(54-62)Online publication date: 21-Oct-2015
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Midtgaard J(2012)Control-flow analysis of functional programsACM Computing Surveys10.1145/2187671.218767244:3(1-33)Online publication date: 14-Jun-2012
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Midtgaard JJensen T(2012)Control-flow analysis of function calls and returns by abstract interpretationInformation and Computation10.1016/j.ic.2011.11.005211(49-76)Online publication date: 1-Feb-2012
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Might MVan Horn D(2011)Family of abstract interpretations for static analysis of concurrent higher-order programsProceedings of the 18th international conference on Static analysis10.5555/2041552.2041568(180-197)Online publication date: 14-Sep-2011
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