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A framework for numeric analysis of array operations

Authors:

Denis Gopan,

Thomas Reps,

Mooly SagivAuthors Info & Claims

ACM SIGPLAN Notices, Volume 40, Issue 1

Pages 338 - 350

https://doi.org/10.1145/1047659.1040333

Published: 12 January 2005 Publication History

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Abstract

Automatic discovery of relationships among values of array elements is a challenging problem due to the unbounded nature of arrays. We present a framework for analyzing array operations that is capable of capturing numeric properties of array elements.In particular, the analysis is able to establish that all array elements are initialized by an array-initialization loop, as well as to discover numeric constraints on the values of initialized elements.The analysis is based on the combination of canonical abstraction and summarizing numeric domains. We describe a prototype implementation of the analysis and discuss our experience with applying the prototype to several examples, including the verification of correctness of an insertion-sort procedure.

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Cited By

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Ballabriga CForget JRuiz J(2022)Relational abstract interpretation of arrays in assembly codeFormal Methods in System Design10.1007/s10703-022-00399-359:1-3(103-135)Online publication date: 2-Oct-2022
https://dl.acm.org/doi/10.1007/s10703-022-00399-3
Chakraborty SGupta AUnadkat D(2022)Full-program induction: verifying array programs sans loop invariantsInternational Journal on Software Tools for Technology Transfer10.1007/s10009-022-00676-w24:5(843-888)Online publication date: 29-Sep-2022
https://doi.org/10.1007/s10009-022-00676-w
Chakraborty SGupta AUnadkat D(2021)Diffy: Inductive Reasoning of Array Programs Using Difference InvariantsComputer Aided Verification10.1007/978-3-030-81688-9_42(911-935)Online publication date: 15-Jul-2021
https://doi.org/10.1007/978-3-030-81688-9_42
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Index Terms

A framework for numeric analysis of array operations
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
      1. Semantics
2. Theory of computation
  1. Semantics and reasoning
    1. Program reasoning
      1. Program analysis
    2. Program semantics

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Reviews

Reviewer: Pierre Jouvelot

Abstract interpretation is a powerful framework for performing static analysis of computer programs. Some programming constructs, however, such as array data structures, have proven difficult to tackle using this approach. One of the key issues that needs to be addressed when trying to integrate arrays into an existing scalar abstract interpretation is the design of a proper abstract domain, able to statically encode relations among array elements, their indices, and values. In this paper, the authors suggest using a new partitioning scheme for arrays that mixes summary and nonsummary abstract elements; nonsummary elements are associated with array elements whose indices correspond exactly to the value of a scalar variable, while summary ones are used otherwise. This complex abstraction mechanism, whose detailed description is provided in the paper, is able to analyze a variety of simple programs, such as an array-initialization loop or an insertion-sort routine. Other issues related to the abstract interpretation of array programs are briefly addressed, such as performing widening operations on array-based abstract states, which are necessary to complete the analysis of loops in finite time, or specifying the abstract semantics in the presence of array constructs. I found the overall paper to be well organized and easy to read, although a thorough understanding of abstract interpretation is a prerequisite. The authors used motivational examples throughout the presentation, and made an effort to implement their technique and test it on some toy examples. This work should be required reading for researchers interested in the abstract interpretation of imperative languages. Online Computing Reviews Service

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Information & Contributors

Information

Published In

ACM SIGPLAN Notices Volume 40, Issue 1

Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages

January 2005

391 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/1047659

Issue’s Table of Contents

POPL '05: Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
January 2005
402 pages
ISBN:158113830X
DOI:10.1145/1040305
General Chair:
Jens Palsberg
University of California, Los Angeles, CA
,
Program Chair:
Martín Abadi
University of California, Santa Cruz, CA

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 January 2005

Published in SIGPLAN Volume 40, Issue 1

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https://dl.acm.org/doi/10.1007/s10703-022-00399-3
Chakraborty SGupta AUnadkat D(2022)Full-program induction: verifying array programs sans loop invariantsInternational Journal on Software Tools for Technology Transfer10.1007/s10009-022-00676-w24:5(843-888)Online publication date: 29-Sep-2022
https://doi.org/10.1007/s10009-022-00676-w
Chakraborty SGupta AUnadkat D(2021)Diffy: Inductive Reasoning of Array Programs Using Difference InvariantsComputer Aided Verification10.1007/978-3-030-81688-9_42(911-935)Online publication date: 15-Jul-2021
https://doi.org/10.1007/978-3-030-81688-9_42
Braine JGonnord LChen LGhorbal K(2020)Proving array properties using data abstractionProceedings of the 9th ACM SIGPLAN International Workshop on Numerical and Symbolic Abstract Domains10.1145/3427762.3430179(17-21)Online publication date: 17-Nov-2020
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Essertel GWei GRompf T(2019)Precise reasoning with structured time, structured heaps, and collective operationsProceedings of the ACM on Programming Languages10.1145/33605833:OOPSLA(1-30)Online publication date: 10-Oct-2019
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Sardar TFaizabadi A(2019)Parallelization and analysis of selected numerical algorithms using OpenMP and Pluto on symmetric multiprocessing machineData Technologies and Applications10.1108/DTA-05-2018-0040Online publication date: 7-Feb-2019
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