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The optimal approach to recursive programs

Authors:

Zohar Manna,

Adi ShamirAuthors Info & Claims

Communications of the ACM, Volume 20, Issue 11

Pages 824 - 831

https://doi.org/10.1145/359863.359885

Published: 01 November 1977 Publication History

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Abstract

The classical fixedpoint approach toward recursive programs suggests choosing the “least defined fixedpoint” as the most appropriate solution to a recursive program. A new approach is described which introduces an “optimal fixedpoint,” which, in contrast to the least defined fixedpoint, embodies the maximal amount of valuable information embedded in the program. The practical implications of this approach are discussed and techniques for proving properties of optimal fixedpoints are given. The presentation is informal, with emphasis on examples.

References

[1]

Burstall, R.M. Proving properties of programs by structural induction. Comptr. J. 12, 1 (Feb. 1969), 41-48.

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[2]

DeBakker, J.W., and Scott, D. A theory of programs. Unpublished memo. Aug. 1969.

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[3]

Manna, Z. Mathematical Theory of Computation. McGraw-Hill, New York, 1974.

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[4]

Manna, Z., and Shamir, A. The theoretical aspect of the optimal fixedpoint. SIAM J. Comptng. 5, 3 (Sept. 1976), 414-426.

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[5]

Shamir, A. The fixedpoints of recursive programs. Ph.D. Th., Appl. Math. Dept., Weizmann Inst. of Science, Rehovot, Israel, 1977.

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Fitting M(2024)Modal, Fuzzy, ..., Vanilla Fixpoint Theories of Truth: A Uniform ApproachSaul Kripke on Modal Logic10.1007/978-3-031-57635-5_7(151-192)Online publication date: 2-Oct-2024
https://doi.org/10.1007/978-3-031-57635-5_7
Dershowitz NGurevich Y(2014)A Natural Axiomatization of Computability and Proof of Church's ThesisBulletin of Symbolic Logic10.2178/bsl/123108137014:03(299-350)Online publication date: 15-Jan-2014
https://doi.org/10.2178/bsl/1231081370
Nielson FRiis Nielson H(2007)Heuristics for Safety and Security ConstraintsElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2007.02.018172(523-543)Online publication date: 1-Apr-2007
https://dl.acm.org/doi/10.1016/j.entcs.2007.02.018
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Published In

Communications of the ACM Volume 20, Issue 11

Nov. 1977

107 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/359863

Editor:
Robert L. Ashenhurst
Univ. of Chicago, Chicago, IL

Issue’s Table of Contents

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: 01 November 1977

Published in CACM Volume 20, Issue 11

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Fitting M(2024)Modal, Fuzzy, ..., Vanilla Fixpoint Theories of Truth: A Uniform ApproachSaul Kripke on Modal Logic10.1007/978-3-031-57635-5_7(151-192)Online publication date: 2-Oct-2024
https://doi.org/10.1007/978-3-031-57635-5_7
Dershowitz NGurevich Y(2014)A Natural Axiomatization of Computability and Proof of Church's ThesisBulletin of Symbolic Logic10.2178/bsl/123108137014:03(299-350)Online publication date: 15-Jan-2014
https://doi.org/10.2178/bsl/1231081370
Nielson FRiis Nielson H(2007)Heuristics for Safety and Security ConstraintsElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2007.02.018172(523-543)Online publication date: 1-Apr-2007
https://dl.acm.org/doi/10.1016/j.entcs.2007.02.018
Kupka I(2006)Unique fixpoints in complete lattices with applications to formal languages and semanticsFoundations of Computer Science10.1007/BFb0052079(107-115)Online publication date: 16-May-2006
https://doi.org/10.1007/BFb0052079
Delahaye JThibau V(2005)The optimal model of a program with negationLogics in AI10.1007/BFb0018441(180-195)Online publication date: 9-Jun-2005
https://doi.org/10.1007/BFb0018441
Jaffar JLassez JMaher M(2005)Some issues and trends in the semantics of logic programmingThird International Conference on Logic Programming10.1007/3-540-16492-8_78(223-241)Online publication date: 31-May-2005
https://doi.org/10.1007/3-540-16492-8_78
Krstić SMatthews J(2003)Inductive Invariants for Nested RecursionTheorem Proving in Higher Order Logics10.1007/10930755_17(253-269)Online publication date: 2003
https://doi.org/10.1007/10930755_17
Fitting M(1997)A Theory of Truth that Prefers FalsehoodJournal of Philosophical Logic10.1023/A:100421781235526:5(477-500)Online publication date: Oct-1997
https://doi.org/10.1023/A:1004217812355
You JCartwright RLi M(1996)Iterative belief revision in extended logic programmingTheoretical Computer Science10.1016/S0304-3975(96)80712-2170:1-2(383-406)Online publication date: Dec-1996
https://doi.org/10.1016/S0304-3975(96)80712-2
Delahaye JThibau V(1991)Programming in three-valued logicTheoretical Computer Science10.1016/0304-3975(51)90008-478:1(189-216)Online publication date: 21-Jan-1991
https://dl.acm.org/doi/10.1016/0304-3975%2851%2990008-4
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The Theoretical Aspects of the Optimal Fixedpoint

The optimal fixedpoint of recursive programs

A linearization of non-linear recursive programs in logic databases

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