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Data flow analysis is model checking of abstract interpretations

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David A. SchmidtAuthors Info & Claims

POPL '98: Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

Pages 38 - 48

https://doi.org/10.1145/268946.268950

Published: 21 January 1998 Publication History

Abstract

This expository paper simplifies and clarifies Steffen's depiction of data flow analysis (d.f.a.) as model checking: By employing abstract interpretation (a.i.) to generate program traces and by utilizing Kozen's modal mu-calculus to express trace properties, we express in simplest possible terms that a d.f.a. is a model check of a program's a.i. trace. In particular, the classic flow equations for bit-vector-based d.f.a.s reformat trivially into modal mu-Calculus formulas. A surprising consequence is that two of the classical d.f.a.s are exposed as unsound; this problem is analyzed and simply repaired. In the process of making the above discoveries, we clarify the relationship between a.i. and d.f.a. in terms of the often-misunderstood notion of collecting semantics and we highlight how the research areas of flow analysis, abstract interpretation, and model checking have grown together.

References

[1]

S. Abramsky and (3. Hankin, editors. Abstract interpretation of declarative languages. Ellis Horwoodt Chichester, 1987.

Digital Library

[2]

P. A~zel.__ Non-Well-Founded Sets. Lecture No~es 14, Cent~er for Study of Language and Information, Stan. fordl CA,-- 1988.

[3]

A./~}ao, R. Sethi, and J. UUman. Compilers: Prinei. plest Techniques, and Tools. Addison Wesley~ 1986.

Digital Library

[4]

A. A_ho mad J. Ullman. Principles of Compiler Design. Addison Wesley, 1977.

[5]

A. Banerjee. A modular, polyvariant, type-based closure analysis. In Prac. ~d International Conference on Functional Programming: ICFP'97, 1997.

Digital Library

[6]

S. Bensalem, A. Bouajjani, C. Loiseaux, and J. Sifakis. Property preserving simulations. In G. vanBochman and D. Probst, editors, Computer Aided Verification: CA V'92, number 663 in Lecture Notes in Computer Science, pages 260-273. Springer-Verlag, 1992.

Digital Library

[7]

J. Bradfidd. Verifying Temporal Properties of Systems. Birkhauser, 1992.

Digital Library

[8]

G. Brtms. A practical eechnique for process abstraction. In 4th International Conference on Concurrency Theory (CONCUR'93), Lecture Notes in Computer Science 7'15, pages 37-49. Springer-Verlag, 1993.

Digital Library

[9]

E. Clarke, E. Emerson, and A. Sistla. Automatic verification of finite-state concurrent systems using temporal logic specifications. A CM Transactions on Programming Languages and Systems, 8:244-263, 1986.

Digital Library

[10]

E.M. Clarke, O. Grumberg, and D.E. Long. Verification tools for finite-state concurrent systems. In J.W. deBakker, W.-P. deRoever, and G. Rozenberg, editors, A Decade of Concurrency: Reflections and Perspecflues, number 803 in Lecture Notes in Computer Science, pages 124-175. Springer, 1993.

Digital Library

[11]

E.M. Clarke, O. Grumberg, and D.E. Long. Model checking and abstraction. A UM Transactions on Programming Languages and Systems, 16(5):1512-1542, 1994.

Digital Library

[12]

R. Cleaveland. Tableau-based model checking in the propositional mu-calculus. Acta Informatica, 27:725- 747, 1990.

Digital Library

[13]

R. Cleave.land, P. Iyer, and D. Yankelevich. Optimality in abstractions of mode{ checking. In SAS'95: Proc. ~d. Static Analysis Symposium, Lecture Notes in Computer Science 983, pages 51-63. Springer, 1995.

Digital Library

[14]

G. Cousineau and M. Nivat. On rational expressions representing infinite rational trees. In 8th Conf. Math. Foundations of Computer Science: MFC8"79, Lecture Notes in Computer Science 74, pages 567-580. Springer, 1979.

[15]

P. Cousot. Mdthodes itJratives de construction et d'approximation de points fixes d'opdrateurs monotones sur un treillis, analyse sdmantique de programmes. Phi) thesis, University of Grenoble, 1978.

[16]

P. Cousot and R. Cousot. Abstract interpretation: a unified lattice model for static analysis of programs. In Proc. ~th A CM Syrup. on Principles of Programming Languages, pages 238-252. ACM Press, 1977.

Digital Library

[17]

P. Cousot and R. Consot. Automatic synthesis of optimal invariant assertions: mathematical foundations. $IGPLAN Notices, 12(8):1-12, 1977.

Digital Library

[18]

P. Cousot and R. Cousot. Systematic design of program analysis frameworks. In Proc. 6th A CM Syrup. on Principles of Programming Languages, pages 269-282. ACM Press, 1979.

Digital Library

[19]

P. Cousot and R. Cousot. Abstract interpretation frameworks. Journal of Logic and Computation, 2(4):511-547', 1992.

[20]

P. Cousot and R. Cousot. Inductive definitions, semantics, and abstract interpretation. In Proc. 19th A CM Syrup. on Principles of Programming Languages, pages 83-94. ACM Press, 1992.

Digital Library

[21]

P. Cousot and R. Cousot. Higher-order abstract interpretation. In Proc. IEEE Int~. Conf. Programming Languages. IEEE Press, 1994.

[22]

D. Dams. Abstract interpretation and partition refinement for model checking. PhD thesis, Technische Oniversiteit Eindhoven, The Netherlands, 1996.

[23]

D. Dams, R. Gerth, and O. Grumberg. Abstract interpretation of reactive systems. A CM TOPLAS, 19:253- 291, 1997.

Digital Library

[24]

D. Dams, O. Grumberg, and R. Gerth. Abstract intepretation of reactive systems. In E.-R. Olderog, editor, Proc. IFIP Working Conference on Programming Concepts, Methods, and Calcul~ North-Holland, 1994.

[25]

V. Donzeau-Gouge. Denotational definition of properties of program's computations. In S. Muchnick and N.D. Jones, editors, Program Flow Analysis: Theory and Applications. Prentice-Hall, 1981.

[26]

E.A. Emerson and C.L. Lei. Efficient modal checking in fragments of the propositional ran-calculus. In First Annual Symposium on Logic in Computer Science, pages 267-278. IEEE, 1986.

[27]

V. Gouranton. Ddrivation d'analyseurs dynamiques et statiques h patir de spdcifications opdmtionnelles. Phi) thesis, University of Rennes, 1997.

[28]

V. Gouranton and D. LeM4tayer. Derivation of static analysers of functional programs from path properties of a natural semantics. Technical Report Research Report 2607, INRIA, 1995.

[29]

C. Hankln, A. Mycroft, F. Hie}son, and H. Riis- Nielson. Principles of Program Analysis. In Preparation, 1999.

[30]

M. Hecht. Flow Analysis of Computer Programs. Elsevier, 1977.

Digital Library

[31]

S. Jagannathan and S. Weeks. A nni~ed treatment of flow analysis in higher-order languages. In Proc. 2~d. A CM Syrup. Principles of Programming Languages, pages 393-407, 1995.

Digital Library

[32]

N. Jones and F. Nielson. Abstract interpretation: a semantics-based tool for program analysis. In S. Abramsky, D. Gabbay, and T. Maibaum, editors, Handbook of Logic in Computer Science, Vol. 4~, pages 527'-636. Oxford Univ. Press, 1995.

Digital Library

[33]

N.D. Jones and S. Mud~ck. Flow analysis and optimization of LISP-like structures. In Proc. 6th. ACM Syrup. Principles of Programming Languages, pages 244-256, 1979.

Digital Library

[34]

J. Kam and J. Ullman. Global data flow analysis and iterative algorithms. J. A CM, 23:158-171, 1976.

Digital Library

[35]

K. Kennedy. A survey of data flow analysis techniques. In S. Muchmck and N.D. Jones, editors, Program Flow Analysis: Theory and Applications, pages 5-54. Prentice-Hall, 1981.

[36]

M. Klein, D. Koschuetzki, J. Knoop, and B. Steffen. DFA&OPT-MetaFrame: a tool kit for program analysis and optimization. In Proc. TACAS'g5, pages 422--426. Lecture Notes in Computer Science 1055, Springer, Berlin, 1996.

Digital Library

[37]

D. Kozen. Results on the propositional ran-calculus. Theoretical Computer Science, 27:333-354, 1983.

[38]

Y.S. Kwong. On reduction of asynchronous systems. Theoretical Computer Science, 5:25-50, 1977.

[39]

K. Larsen. Proof systems for hermessy-milner logic with recursion. In M. Duache~ and M. NivaL, editors, CAAP88~ number 299 in Lecture Notes in" Computer Science. Springer-Verlag~ 1988.

Digital Library

[40]

K. Larsem Modal specificabions. In J. Sifakis, editor, CAV'89, number 407 in Lecture Notes in Computer Science, pages 232-246. Springer-Verlag, I989.

Digital Library

[41]

F. Levi. Abstract model checking of value-passing processes. In Annalisa'Bossi, editor, International Workshop on Verification, Model Checking and Abstra ct Interpretation, Port Jefferson, Long Island, N.Y., http://ww~.dsi, unive, it/-bossi/W4CAI, html, 1997.

[42]

K. McMillam Symbolic Model Checking. Kluwer Academic Publishers, 1993.

Digital Library

[43]

A. Me/ton, G. S~recker, and D. Schmidt. Galois connections and computer science applications. In Category Theory and Computer Programming, pages 299- 312. Lecture Notes in Computer Science 240, Springer- Verlag, 1985.

Digital Library

[44]

R. Milner.Communication and Concurrency. Prentice-Hall, 1989.

Digital Library

[45]

R. Milner and M. Torte. Co-induction in relational semantics. Theoretical Computer Science, 1I:209-220, I992.

Digital Library

[46]

S. Muchnick and N.D. Jones, editors. Program Flow Analysis: Theory and Applications. Prentice-Hall, 1981.

Digital Library

[47]

F. Nielson. Semantic foundations of data flow analysis. Technical Report Report DAIMI PB-131, Aarhus University, Denmark, 1981.

[48]

F. Nielson. A denotational framework for data flow analysis. Acta In/ormatica, 18:265-287, 1982.

[49]

F. Nielson. Program transformations in a denotational setting. ACM Trans. Prog. Languages and Systems, 7:359-379, 1985.

Digital Library

[50]

F. Nielson. Two-level semantics and abstract interpretation. Theoretical Computer Science, 69(2):117-242, 1989.

Digital Library

[51]

F. Nielson and H. R. Nielson. Infinitary control flow analysis: a collecting semantics for closure analysis. In Proc. A CM POPL'97, 1997.

Digital Library

[52]

H. R. Nielson and F. Nielson. Semantics with Appllca. tions, a formal introduction. Wiley Professional Computing. John Wiley and Sons, 1992.

Digital Library

[53]

D.A. Schraidt. Trace-based abstract interpre~a. lion of operational semantics. A Lisp and Symbolic Computation. In press. Available from ww~. cis.ksu, edu/-sclmidt/papers/aiosh, ps .Z

[54]

D.A. Schnddt. Natural-semantics-based abstract interpretation. In A. Mycroft, editor, Static Analysis Symposium, number 983 in Lecture Notes in Computer Science, pages 1-18. Springer-Verlhg, 1995.

Digital Library

[55]

D.A. Schmidt. Abstrac~ interpretation of small-step semantics. In M. Dam and F. Orava, editors, Proc. 5th LOMAPS Workshop on Analysis and Verification of Multiple-Agent Languages, Lecture Notes in Computer Science. Springer-Verlag, 1996.

Digital Library

[56]

P. Sestoft. Analysis and Efficient Implementation of Functional Programs. PhD thesis, Copenhagen University~ 1991.

[57]

O. Shivers. Control Flow Analysis of Higher-Order Languages. PhD thesis, Carnegie Mellon University, 1991.

Digital Library

[58]

J. Sifakis. Property preserving homomorphisms of transition systems. In Logics of Pro!from% Lecture Notes in Computer Sdence 164. Springer, 1983.

Digital Library

[59]

B. Steffen. Data flow analysis as model checking. In A. Meyer~ editor, Theoretical Aspects of Computer Software: TACS'91, volume 526 of Lecture Notes in Computer Science. Springer-Verlag, 1991.

Digital Library

[60]

B. Steffen. Generating data-flow analysis algorithms for modal specifications. Science of Computer Programming, 21:115-139, 1993.

Digital Library

[61]

B. Steffen. Property-oriented expansion, in R. Cousot and D. Schmidt, editors, Static Analysis Symposium: SAS'96, volume 1145 of Ledture Notes in Computer Science, pages 22-41. Springer-Verlag, 1996.

Digital Library

[62]

B. Steffen, A. Classen, M. Klein, 3. Knoop, and T. Margaria. The ftxpoint analysis machine. In I. Lee and S. Smolka, editors, Proc. CONGUR'g5, volume 962 of Lecture Notes in Computer Science, pages 72- 87. Springer-Verlag, 1995.

Digital Library

[63]

C. Stirling. Modal and temporal logics. In S. Abramsky, D. Gabbay, and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, volume 2, pages 477-563. Oxford University Press, 1992.

Digital Library

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Index Terms

Data flow analysis is model checking of abstract interpretations
1. Software and its engineering
2. Theory of computation
  1. Logic
    1. Verification by model checking

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cover image ACM Conferences

POPL '98: Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

January 1998

403 pages

ISBN:0897919793

DOI:10.1145/268946

Chairmen:
David B. MacQueen
Bell Labs
,
Luca Cardelli
Digital Equipment Corp.

Copyright © 1998 ACM.

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Published: 21 January 1998

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Brain MPolgreen E(2024)A Pyramid Of (Formal) Software VerificationFormal Methods10.1007/978-3-031-71177-0_24(393-419)Online publication date: 13-Sep-2024
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