Article

Anti-unification algorithms and their applications in program analysis

Authors:

Peter E. Bulychev,

Egor V. Kostylev,

Vladimir A. ZakharovAuthors Info & Claims

PSI'09: Proceedings of the 7th international Andrei Ershov Memorial conference on Perspectives of Systems Informatics

Pages 413 - 423

https://doi.org/10.1007/978-3-642-11486-1_35

Published: 15 June 2009 Publication History

Abstract

A term t is called a template of terms t₁ and t₂ iff t₁=tη₁ and t₂=tη₂, for some substitutions η₁ and η₂. A template t of t₁ and t₂ is called the most specific iff for any template t′ of t₁ and t₂ there exists a substitution ξ such that t=t′ξ. The anti-unification problem is that of computing the most specific template of two given terms. This problem is dual to the well-known unification problem, which is the computing of the most general instance of terms. Unification is used extensively in automatic theorem proving and logic programming. We believe that anti-unification algorithms may have wide applications in program analysis. In this paper we present an efficient algorithm for computing the most specific templates of terms represented by labelled directed acyclic graphs and estimate the complexity of the anti-unification problem. We also describe techniques for invariant generation and software clone detection based on the concepts of the most specific templates and anti-unification.

References

[1]

Baader, F., Snyder, W.: Unification theory. In: Robinson, J. A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 1, pp. 447-533 (2001)

Digital Library

[2]

Baxter, I., Yahin, A., Moura, L. M., Sant'Anna, M., Bier, L.: Clone Detection Using Abstract Syntax Trees. In: Proc. of the 14th IEEE International Conference on Software Maintenance, pp. 368-377 (1998)

Digital Library

[3]

Bille, P.: A survey on tree distance and related problems. Theoretical Computer Science 337(1-3), 217-239 (2005)

Digital Library

[4]

Bulychev, P.: Duplicate code detection using Clone Digger. PythonMagazine 9, 18-24 (2008)

[5]

Bulychev, P., Minea, M.: An evaluation of duplicate code detection using antiunification. In: Proc. of the 3rd Int. Workshop on Software Clones, pp. 22-27 (2009)

[6]

Eder, E.: Properties of substitutions and unifications. Journal of Symbolic Computations 1, 31-46 (1985)

Digital Library

[7]

Evans, W., Fraser, C., Ma, F.: Clone detection via structural abstraction. In: Proc. of 14th Working Conference on Reverse Engineering, pp. 150-159 (2007)

Digital Library

[8]

Kovac, L. I., Jebelean, T.: An algorithm for automated generation of invariants for loops with conditionals. In: Proc. of the 7th Int. Symp. on Symbolic and Numeric Algorithms for Scientific Computing, pp. 245-250 (2005)

Digital Library

[9]

Nielson, F., Nielson, H. R., Hankin, C.: Principles of program analysis, 446 p. Springer, Heidelberg (1999)

Digital Library

[10]

Oancea, C. E., So, C., Watt, S. M.: Generalization in Maple. In: Maple Conference, pp. 277-382 (2005)

[11]

Palamidessi, C.: Algebraic properties of idempotent substitutions. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 386-399. Springer, Heidelberg (1990)

Digital Library

[12]

Plotkin, G. D.: A note on inductive generalization. Machine Intelligence 5(1), 153- 163 (1970)

[13]

Reynolds, J.C.: Transformational systems and the algebraic structure of atomic formulas. Machine Intelligence 5(1), 135-151 (1970)

[14]

Roy, C. K., Cordy, J. R.: A survey on software clone detection research. Technical Report N 2007-541, School of Computing Queen's University at Kingston Ontario, Canada

[15]

Sorensen, M. H.: Gluck. R. An algorithm of generalization in positive supercompilation. In: Proc. of the 1995 Int. Symposium on Logic Programming, pp. 465-479. MIT Press, Cambridge (1995)

[16]

Tiwari, A., Rueb, H., Saidi, H., Shankar, N.: A technique for invariant generation. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 113-127. Springer, Heidelberg (2001)

Digital Library

[17]

Watt, S. M.: Algebraic generalization. ACM SIGSAM Bulletin 39(3), 93-94 (2005)

Digital Library

[18]

Wettel, R., Marinescu, R.: Archeology of Code Duplication: Recovering Duplication Chains From Small Duplication Fragments. In: Proc. of the 7th Int. Symb. on Symbolic and Numeric Algorithms for Scientific Computing, pp. 63-70 (2005)

Digital Library

Cited By

Mahmoud MWalker RDenzinger J(2024)API usage templates via structural generalizationJournal of Systems and Software10.1016/j.jss.2024.111974210:COnline publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1016/j.jss.2024.111974
Vediramana Krishnan HChen YShoham SGurfinkel A(2024)Global guidance for local generalization in model checkingFormal Methods in System Design10.1007/s10703-023-00412-363:1-3(81-109)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s10703-023-00412-3
Barwell ABrown CHammond K(2018)Finding parallel functional pearlsFuture Generation Computer Systems10.1016/j.future.2017.07.02479:P2(669-686)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1016/j.future.2017.07.024
Show More Cited By

Recommendations

Anti-unification in constraint logics: foundations and applications to learnability in first-order logic, to speed-up learning, and to deduction
Completing Herbelin's programme
TLCA'07: Proceedings of the 8th international conference on Typed lambda calculi and applications

In 1994 Herbelin started and partially achieved the programme of showing that, for intuitionistic implicational logic, there is a Curry-Howard interpretation of sequent calculus into a variant of the λ-calculus, specifically a variant which manipulates ...
Unification of program expressions with recursive bindings
PPDP '16: Proceedings of the 18th International Symposium on Principles and Practice of Declarative Programming

This paper presents an algorithm for unification of meta-expressions of higher-order lambda calculi with recursive bindings. The meta-language uses higher-order abstract syntax. Besides usual unification variables for expressions and term variables, ...

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings

PSI'09: Proceedings of the 7th international Andrei Ershov Memorial conference on Perspectives of Systems Informatics

June 2009

423 pages

ISBN:3642114857

Editors:
Amir Pnueli
(1941-2009), The Weizmann Institute of Science, Rehovot, Israel New York University, NY
,
Irina Virbitskaite
Siberian Division of the Russian Academy of Sciences, A.P. Ershov Institute of Informatics Systems, 6, Acad. Lavrentiev pr., Novosibirsk, Russia
,
Andrei Voronkov
Department of Computer Science, University of Manchester, Oxford Road, Manchester, UK

Sponsors

INTEL: Intel Corporation
HP LABS (UK): HP LABS (UK)
Google Inc.
Microsoft Research: Microsoft Research
RFBR: Russian Foundation for Basic Research

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 15 June 2009

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

10
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 12 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Mahmoud MWalker RDenzinger J(2024)API usage templates via structural generalizationJournal of Systems and Software10.1016/j.jss.2024.111974210:COnline publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1016/j.jss.2024.111974
Vediramana Krishnan HChen YShoham SGurfinkel A(2024)Global guidance for local generalization in model checkingFormal Methods in System Design10.1007/s10703-023-00412-363:1-3(81-109)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s10703-023-00412-3
Barwell ABrown CHammond K(2018)Finding parallel functional pearlsFuture Generation Computer Systems10.1016/j.future.2017.07.02479:P2(669-686)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1016/j.future.2017.07.024
Baumgartner AKutsia T(2017)Unranked second-order anti-unificationInformation and Computation10.1016/j.ic.2017.01.005255:P2(262-286)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1016/j.ic.2017.01.005
Kamil SCheung AItzhaky SSolar-Lezama A(2016)Verified lifting of stencil computationsACM SIGPLAN Notices10.1145/2980983.290811751:6(711-726)Online publication date: 2-Jun-2016
https://dl.acm.org/doi/10.1145/2980983.2908117
Kamil SCheung AItzhaky SSolar-Lezama AKrintz CBerger E(2016)Verified lifting of stencil computationsProceedings of the 37th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/2908080.2908117(711-726)Online publication date: 2-Jun-2016
https://dl.acm.org/doi/10.1145/2908080.2908117
Zhozhikashvili A(2014)Monads for the formalization of a pattern matching procedureProgramming and Computing Software10.1134/S036176881403007440:3(117-127)Online publication date: 1-May-2014
https://dl.acm.org/doi/10.1134/S0361768814030074
Baumgartner AKutsia T(2014)Unranked Second-Order Anti-UnificationProceedings of the 21st International Workshop on Logic, Language, Information, and Computation - Volume 865210.1007/978-3-662-44145-9_5(66-80)Online publication date: 1-Sep-2014
https://dl.acm.org/doi/10.1007/978-3-662-44145-9_5
Baumgartner AKutsia T(2014)A Library of Anti-unification AlgorithmsProceedings of the 14th European Conference on Logics in Artificial Intelligence - Volume 876110.1007/978-3-319-11558-0_38(543-557)Online publication date: 24-Sep-2014
https://dl.acm.org/doi/10.1007/978-3-319-11558-0_38
Alcantara TDenzinger JFerreira JMaurer FHarrison R(2012)Learning gestures for interacting with low-fidelity prototypesProceedings of the First International Workshop on Realizing AI Synergies in Software Engineering10.5555/2666527.2666534(32-36)Online publication date: 5-Jun-2012
https://dl.acm.org/doi/10.5555/2666527.2666534

View Options

View options

Figures

Tables

Media

View Table of Conten