Abstract
Equality is perhaps the most widely-used relation among data in programs. In this chapter, we consider equality among variables, constants, and function applications (Section 9.1); among recursive data structures (records, lists, trees, and stacks) and their elements (Section 9.4); and among elements of arrays (Section 9.5). For all three theories, we examine their quantifier-free fragments.
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Bibliographic Remarks
W. Ackermann. Solvable cases of the decision problem. The Journal of Symbolic Logic, 22(1):68–72, March 1957.
P. J. Downey, R. Sethi, and R. E. Tarjan. Variations on the common subex-pressions problem. Journal of the ACM, 27(4):758–771, 1980.
J. King. A Program Verifier. PhD thesis, Carnegie Mellon University, September 1969.
J. McCarthy. Towards a mathematical science of computation. In International Federation for Information Processing, pages 21–28, 1962.
G. Nelson and D. C. Oppen. Fast decision procedures based on congruence closure. Journal of the ACM, 27(2):356–364, April 1980.
D. C. Oppen. Reasoning about recursively defined data structures. In Principles of Programming Languages, pages 151–157. ACM Press, 1978.
D. C. Oppen. Reasoning about recursively defined data structures. Journal of the ACM, 27(3):403–411, July 1980.
R. E. Shostak. An algorithm for reasoning about equality. Communications of the ACM, 21(7):583–585, July 1978.
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). Quantifier-Free Equality and Data Structures. In: The Calculus of Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74113-8_9
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DOI: https://doi.org/10.1007/978-3-540-74113-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74112-1
Online ISBN: 978-3-540-74113-8
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