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On proving inductive properties of abstract data types

Author:

David R. MusserAuthors Info & Claims

POPL '80: Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

Pages 154 - 162

https://doi.org/10.1145/567446.567461

Published: 28 January 1980 Publication History

Abstract

The equational axioms of an algebraic specification of a data type (such as finite sequences) often can be formed into a convergent set of rewrite rules; i.e. such that all sequences of rewrites are finite and uniquely terminating. If one adds a rewrite rule corresponding to a data type property whose proof requires induction (such as associativity of sequence concatenation), convergence may be destroyed, but often can be restored by using the Knuth-Bendix algorithm to generate additional rules. A convergent set of rules thus obtained can be used as a decision procedure for the equational theory for the axioms plus the property added. This fact, combined with a "full specification" property of axiomatizations, leads to a new method of proof of inductive properties--not requiring the explicit invocation of an inductive rule of inference.

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cover image ACM Conferences

POPL '80: Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

January 1980

261 pages

ISBN:0897910117

DOI:10.1145/567446

Conference Chairs:
Paul Abrahams
Courant Institute, New York, NY
,
Richard Lipton
University of California at Berkeley, Berkeley, CA
,
Program Chair:
Stephen Bourne
Bell Laboratories, Murray Hill, NJ

Copyright © 1980 ACM.

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Published: 28 January 1980

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https://dl.acm.org/doi/10.1145/3678232.3678236
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https://doi.org/10.1007/978-3-031-43345-0_1
Jones EOng CRamsay SJhala RDillig I(2022)CycleQ: an efficient basis for cyclic equational reasoningProceedings of the 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3519939.3523731(395-409)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519939.3523731
Stratulat S(2020)SPIKE, an automatic theorem prover — revisited2020 22nd International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)10.1109/SYNASC51798.2020.00025(93-96)Online publication date: Sep-2020
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