research-article

A relational framework for higher-order shape analysis

Authors:

Suresh JagannathanAuthors Info & Claims

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

Pages 311 - 324

https://doi.org/10.1145/2628136.2628159

Published: 19 August 2014 Publication History

Abstract

We propose the integration of a relational specification framework within a dependent type system capable of verifying complex invariants over the shapes of algebraic datatypes. Our approach is based on the observation that structural properties of such datatypes can often be naturally expressed as inductively-defined relations over the recursive structure evident in their definitions. By interpreting constructor applications (abstractly) in a relational domain, we can define expressive relational abstractions for a variety of complex data structures, whose structural and shape invariants can be automatically verified. Our specification language also allows for definitions of parametricrelations for polymorphic data types that enable highly composable specifications and naturally generalizes to higher-order polymorphic functions.

We describe an algorithm that translates relational specifications into a decidable fragment of first-order logic that can be efficiently discharged by an SMT solver. We have implemented these ideas in a type checker called CATALYST that is incorporated within the MLton SML compiler. Experimental results and case studies indicate that our verification strategy is both practical and effective.

References

[1]

A. Ahmed. Step-Indexed Syntactic Logical Relations for Recursive and Quantified Types. In ESOP'06, pages 69--83, 2006.

Digital Library

[2]

N. Benton and B. Leperchey. Relational Reasoning in a Nominal Semantics for Storage. In TLCA, pages 86--101, 2005.

Digital Library

[3]

N. Benton, A. Kennedy, M. Hofmann, and L. Beringer. Reading, Writing and Relations: Towards Extensional Semantics for Effect Analyses. In APLAS, pages 114--130, 2006.

Digital Library

[4]

N. Benton, A. Kennedy, L. Beringer, and M. Hofmann. Relational Semantics for Effect-based Program Transformations: Higher-order Store. In PPDP, pages 301--312, 2009.

Digital Library

[5]

B.-Y. E. Chang and X. Rival. Relational Inductive Shape Analysis. In POPL, pages 247--260, 2008.

Digital Library

[6]

A. Charguraud. The Locally Nameless Representation. Journal of Automated Reasoning, 49(3):363--408, 2012. ISSN 0168-7433.

[7]

D. Dreyer, A. Ahmed, and L. Birkedal. Logical Step-Indexed Logical Relations. In LICS'09, pages 71--80, 2009.

Digital Library

[8]

F. Henglein. Generic Top-down Discrimination for Sorting and Partitioning in Linear Time*. J. Funct. Program., pages 300--374, 2012.

Digital Library

[9]

B. Jeannet, A. Loginov, T. Reps, and M. Sagiv. A relational approach to interprocedural shape analysis. ACM Trans. Program. Lang. Syst., 32(2), Feb. 2010.

Digital Library

[10]

G. Kaki and S. Jagannathan. A Relational Framework for Higher-Order Shape Analysis. Technical Report TR-14-002, Purdue University, 2014. URL http://docs.lib.purdue.edu/cstech/1772/.

Digital Library

[11]

M. Kawaguchi, P. Rondon, and R. Jhala. Type-based Data Structure Verification. In PLDI, pages 304--315, 2009.

Digital Library

[12]

S. Lindley and C. McBride. Hasochism: The Pleasure and Pain of Dependently Typed Haskell Programming. In Haskell Symposium, pages 81--92, 2013.

Digital Library

[13]

C. McBride. Faking it: Simulating dependent types in Haskell. J. Funct. Program., 12(5):375--392, July 2002.

Digital Library

[14]

M. Might. Shape Analysis in the Absence of Pointers and Structure. In VMCAI, pages 263--278, 2010.

Digital Library

[15]

MLton. http://mlton.org/.

[16]

Objective Caml. http://ocaml.org/.

[17]

C. Okasaki. Purely Functional Data Structures. Cambridge University Press, New York, NY, USA, 1998.

Digital Library

[18]

B. C. Pierce and D. N. Turner. Local Type Inference. ACM Trans. Program. Lang. Syst., 22(1), Jan. 2000.

Digital Library

[19]

R. Piskac, L. de Moura, and N. Bjørner. Deciding Effectively Propositional Logic with Equality. Technical Report MSR-TR-2008-181.

[20]

P. M. Rondon, M. Kawaguchi, and R. Jhala. Liquid Types. In PLDI, pages 159--169, 2008.

Digital Library

[21]

P.-Y. Strub, N. Swamy, C. Fournet, and J. Chen. Self-Certification: Bootstrapping Certified Typecheckers in F* with Coq. In POPL, pages 571--584, 2012.

Digital Library

[22]

P. Suter, M. Dotta, and V. Kuncak. Decision Procedures for Algebraic Data Types with Abstractions. In POPL, pages 199--210, 2010.

Digital Library

[23]

N. Swamy, J. Chen, C. Fournet, P.-Y. Strub, K. Bhargavan, and J. Yang. Secure distributed programming with value-dependent types. In ICFP, pages 266--278, 2011.

Digital Library

[24]

The Glasgow Haskell Compiler. https://www.haskell.org/ghc/.

[25]

N. Vazou, P. M. Rondon, and R. Jhala. Abstract Refinement Types. In ESOP, pages 209--228, 2013.

Digital Library

[26]

S. Weirich, B. A. Yorgey, and T. Sheard. Binders Unbound. In ICFP, pages 333--345, 2011.

Digital Library

[27]

H. Xi, C. Chen, and G. Chen. Guarded Recursive Datatype Constructors. In POPL, pages 224--235, 2003.

Digital Library

Cited By

Smith SZhang R(2024)A Pure Demand Operational Semantics with Applications to Program AnalysisProceedings of the ACM on Programming Languages10.1145/36498528:OOPSLA1(1154-1180)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649852
Illous HLemerre MRival X(2021)A relational shape abstract domainFormal Methods in System Design10.1007/s10703-021-00366-4Online publication date: 24-Apr-2021
https://doi.org/10.1007/s10703-021-00366-4
Montagu BJensen T(2020)Stable relations and abstract interpretation of higher-order programsProceedings of the ACM on Programming Languages10.1145/34090014:ICFP(1-30)Online publication date: 3-Aug-2020
https://dl.acm.org/doi/10.1145/3409001
Show More Cited By

Index Terms

A relational framework for higher-order shape analysis
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language types
        Functional languages
2. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program reasoning

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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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SIGPLAN: ACM Special Interest Group on Programming Languages

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Association for Computing Machinery

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Published: 19 August 2014

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Division of Computing and Communication Foundations

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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

Acceptance Rates

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

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

Upcoming Conference

ICFP '25

Sponsor:
sigplan

ACM SIGPLAN International Conference on Functional Programming

October 12 - 18, 2025

Singapore , Singapore

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Cited By

Smith SZhang R(2024)A Pure Demand Operational Semantics with Applications to Program AnalysisProceedings of the ACM on Programming Languages10.1145/36498528:OOPSLA1(1154-1180)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649852
Illous HLemerre MRival X(2021)A relational shape abstract domainFormal Methods in System Design10.1007/s10703-021-00366-4Online publication date: 24-Apr-2021
https://doi.org/10.1007/s10703-021-00366-4
Montagu BJensen T(2020)Stable relations and abstract interpretation of higher-order programsProceedings of the ACM on Programming Languages10.1145/34090014:ICFP(1-30)Online publication date: 3-Aug-2020
https://dl.acm.org/doi/10.1145/3409001
Kaki GPriya SSivaramakrishnan KJagannathan S(2019)Mergeable replicated data typesProceedings of the ACM on Programming Languages10.1145/33605803:OOPSLA(1-29)Online publication date: 10-Oct-2019
https://dl.acm.org/doi/10.1145/3360580
Andreescu OJensen TLescuyer SMontagu B(2019)Inferring frame conditions with static correlation analysisProceedings of the ACM on Programming Languages10.1145/32903603:POPL(1-29)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1145/3290360
Qiu XWang Y(2019)A Decidable Logic for Tree Data-Structures with MeasurementsVerification, Model Checking, and Abstract Interpretation10.1007/978-3-030-11245-5_15(318-341)Online publication date: 11-Jan-2019
https://doi.org/10.1007/978-3-030-11245-5_15
Lampropoulos LGallois-Wong DHriţcu CHughes JPierce BXia L(2017)Beginner's luck: a language for property-based generatorsACM SIGPLAN Notices10.1145/3093333.300986852:1(114-129)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3093333.3009868
Lampropoulos LGallois-Wong DHriţcu CHughes JPierce BXia LCastagna GGordon A(2017)Beginner's luck: a language for property-based generatorsProceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages10.1145/3009837.3009868(114-129)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3009837.3009868
Illous HLemerre MRival X(2017)A Relational Shape Abstract DomainNASA Formal Methods10.1007/978-3-319-57288-8_15(212-229)Online publication date: 9-Apr-2017
https://doi.org/10.1007/978-3-319-57288-8_15
Watanabe KSato RTsukada TKobayashi N(2016)Automatically disproving fair termination of higher-order functional programsACM SIGPLAN Notices10.1145/3022670.295191951:9(243-255)Online publication date: 4-Sep-2016
https://dl.acm.org/doi/10.1145/3022670.2951919
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