article

Free access

Floyd-Hoare logic in iteration theories

Authors:

Stephen L. Bloom,

Zoltán ÉsikAuthors Info & Claims

Journal of the ACM (JACM), Volume 38, Issue 4

Pages 887 - 934

https://doi.org/10.1145/115234.115352

Published: 01 October 1991 Publication History

PDF eReader

References

[1]

APT, K.R. Ten years of Hoare's logic: A survey--Part I. A CM Trans. Prog. Lang. Syst. 3, 4 (Oct. 1981), 431-483.

Crossref

Google Scholar

[2]

ARTALEJO, M. R. Some questions about expressiveness and relatwe completeness in Hoare's logic. Theoret. Comput. Sci. 39 (1985), 189-206.

Google Scholar

[3]

BERGSTRA, J. A., AND TUCKER, J. Expressiveness and completeness of Hoare's logic. J. Comput. Syst. Sci. 25 (1982), 267-284.

Google Scholar

[4]

BLOOM, S. L. All solutions of a system of recursion equations in infinite trees and other contraction theories. J. Comput. Syst. Sci. 27, 2 (1983), 225-255.

Google Scholar

[5]

BLOOM, S.L. A note on guarded theories. Theoret. Comput. Sci. 70 (1990), 73-83.

Crossref

Google Scholar

[6]

BLOOM, S. L., ELGOT, C. C., AND WRIGHT, J. B. Solutions of the iteration equation and extensions of the scalar iteration operation. SIAM J. Comput. 9, 1 (1980), 26-45.

Google Scholar

[7]

BLOOM, S. L., ELGOT, C. C., AND WRIGHT, j.B. Vector iteration m pointed iterative theories. SIAM J. Comput. 9, 3 (1980), 525-540.

Google Scholar

[8]

BLOOM, S. L., AND I~SIK, Z. Axiomatizing schemes and their behaviors. J. Comput. Syst. Sci. 31, 3 (1985), 375-393.

Crossref

Google Scholar

[9]

BLOOM, S. L., AND t~S~K, Z. Varieties of iteration theories. SIAM J. Comput. 17. 5 (1988), 939-966.

Crossref

Google Scholar

[10]

BLOOM, S. L., AND }~SIK, Z. Equational logic of circular data type specification. Theoret. Comput. Sci. 63 3, (1989), 303-331.

Crossref

Google Scholar

[11]

BLOOM, S. L., AND ESIK, Z. Matrix and matricial iteration theories, Part I. J. Comput. Syst. Sci., to appear.

Google Scholar

[12]

BLOOM, S. L., AND I~SIK, Z. Matrix and matricial iteration theories, Part II. J. Comput. Syst. Sci., to appear.

Google Scholar

[13]

BLOOM, S. L., I~StK, Z., AND MANES, E. G. A Cayley theorem for Boolean algebras. Am. Math. Monthly 74 9 (1990), 831- 833.

Crossref

Google Scholar

[14]

BLOOM, S. L., ESIK, Z., AND TAUBNER, D. Iteration theories of synchronization trees. Inf. Comput., to appear.

Crossref

Google Scholar

[15]

BLOOM, S. L., GINALI, S., AND RUTLEDGE, J. Scalar and vector iteration. J. Comput. Syst. ~;Cl. 14 (1977), 231-230.

Google Scholar

[16]

BLOOM, S. L., THATCHER, J. W., WAGNER, E. G., AND WRIGHT, J.B. Recursion and Iteration in continuous theories: The M-construction. J. Comput. Syst. Sci. 27, 2 (1983), 148-164.

Google Scholar

[17]

BLOOM, S. L., AND TXNDELL, R. Compatible orderings on the metric theory of trees. SIAM J. Comput. 9, 4 (1980), 683-691.

Google Scholar

[18]

CAZANESCU, V. E., AND ~TEF,~NESCU, Gn. Feedback, iteration and repetition. Res. Rep. 42. Institute of Mathematics, Institute for Scientific and Technical Creation, Bucharest, Romania, 1988.

Google Scholar

[19]

CooK, S.A. Soundness and completeness of an axiom system for program verification. SIAM J. Comput. 7 (1978), 70-90.

Google Scholar

[20]

DE BAKKER, J. Mathematical Theory of Program Correctness. International Series in Computer Science. Prentice-Hall, New York, 1980.

Crossref

Google Scholar

[21]

ELCOT, C.C. Monadic computation and iterattve algebraic theories. In J. C. Shepherson, ed., L ogic Colloquium 1973, Studies in Logic, vol. 80. North Holland, Amsterdam, 1975, pp. 175-230.

Google Scholar

[22]

ELGOT, C.C. Structured programming with and without goto statements. IEEE Trans. Softw. Eng. SE-2, 1 (1976), 41-54.

Google Scholar

[23]

ELGOT, C. C., BLooM, S. L., AND TINDELL, R. On the algebraic structure of rooted trees. J. Comput. Syst. Sci. 16, 3 (1978), 362-399.

Google Scholar

[24]

ESlK, Z. Identities in iterative and rational theones. Computational Ling. Comput. Lang. 14 (t980), 183-207.

Google Scholar

[25]

I~SIK, Z. A note on the axiomatizatmn of iteration theories. Acta Cybern. 9 (1990), 375-384.

Google Scholar

[26]

FLOYD, R. W. Assigning meanings to programs. In Mathematical Aspects of Computer Science, Proceedings of Symposia in Applied Mathematics. American Mathematical Society, Providence, R.I., 1967, pp. 19-32.

Google Scholar

[27]

HOARE, C. A.R. An axiomatic basis for computer programming. Commun. ACM 12, 10 (Oct. 1969), 576-580 and 583.

Crossref

Google Scholar

[28]

HOARE, C. A. R., HAYES, I. J., JIFENG, HE, MORGAN, C. C., RoscoE, A. W., SANDERS, J. W., SORENSEN, I. H., SPIVEY, J. M., AND SUFRIN, B.A. Laws of programming. Commun. ACM 30, 8 (Aug. 1987), 672-686.

Crossref

Google Scholar

[29]

LAWVERE, F. W Functional semantics of algebraic theories. Proc. Nat. Acad. Sci. USA 50 (1963), 869-873.

Google Scholar

[30]

MANES, E. G. Assertional categories. In Lecture Notes in Computer Science, vol. 298. Springer-Verlag, New York, 1987, pp. 85-120.

Crossref

Google Scholar

[31]

MANES, E., AND ARBm, M.A. Algebraic approaches to program semantics. In Springer-Verlag Texts and Monographs in Computer Science. Springer-Verlag, New York, 1986.

Crossref

Google Scholar

[32]

MCKENSI~, R., MCNULTY, G., AND TAYLOR, W. Algebras, Lattices, Varieties, vol. I. Wadsworth & Brooks/Cole, Monterey, Calif., 1987.

Google Scholar

[33]

OLDEROG, E.-R. On the notion of expressiveness and the rule of adaptation. Theoret. Cornput. Sci. 24 (1983), 337-347.

Google Scholar

[34]

PLONKA, J Diagonal algebras. Fund. Math. LVIII (1966), 309-321.

Google Scholar

[35]

REYNOLDS, J. C. Programming with transition diagrams. In David Gnes, ed. Programming Methodology, A collection of articles by Members of IFIP WG2.3. Texts and Monographs in Computer Science. Springer-Verlag, New York, 1978, pp. 153-165.

Google Scholar

[36]

REYNOLDS, J. C. The craft of programming. In International Series m Computer Science. Prentice-Hall International, Inc., New York, 1981.

Crossref

Google Scholar

[37]

~TF.FXNF.SCU, G. On flowchart theories: Part I. The deterministic case. J. Comput. Syst. Sci. 35 (1987), 163-191.

Crossref

Google Scholar

[38]

,~TEFXNESCU, G. On flowchart theories: Part II. The nondetermimstlc case. Theoret. Comput. Sci. 52 (1987), 307-340.

Crossref

Google Scholar

[39]

WAGNER, E.G. Algebraic semantics. In D. M. Gabbay, T. S. E. Maibaum, and S. Abramsky, eds. The Handbook of Logic in Computer Science, vol. 2. Oxford University Press, Cambridge. England, to appear.

Google Scholar

[40]

WAND, M.A new incompleteness result for Hoare's system. J. ACM 25, 2 (Jan. 1978), 168-175.

Crossref

Google Scholar

[41]

WRIGHT, j. B., THATCHER, J. W., GOG~JEN, J., AND WAGNER, E.G. Rational algebraic theories and fixed-point solutions. In Proceedings 17th IEEE Symposium on Foundations of Computing (Houston, Tex.). IEEE, New York, 1976, pp. 147-158.

Google Scholar

Cited By

View all

Ésik Z(2019)Equational properties of fixed-point operations in cartesian categories: An overviewMathematical Structures in Computer Science10.1017/S096012951800036129:06(909-925)Online publication date: 24-May-2019
https://doi.org/10.1017/S0960129518000361
Ésik Z(2015)Equational Properties of Fixed Point Operations in Cartesian Categories: An OverviewMathematical Foundations of Computer Science 201510.1007/978-3-662-48057-1_2(18-37)Online publication date: 11-Aug-2015
https://doi.org/10.1007/978-3-662-48057-1_2
Ésik ZSutner K(2011)Stephen L. Bloom 1940-2010Fundamenta Informaticae10.5555/2361347.2361352109:4(369-381)Online publication date: 1-Dec-2011
https://dl.acm.org/doi/10.5555/2361347.2361352
Show More Cited By

Index Terms

Floyd-Hoare logic in iteration theories
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms
2. Theory of computation
  1. Logic
    1. Constraint and logic programming
  2. Semantics and reasoning
    1. Program reasoning
      1. Assertions

Recommendations

The Hoare Logic of Deterministic and Nondeterministic Monadic Recursion Schemes

The equational theory of deterministic monadic recursion schemes is known to be decidable by the result of Sénizergues on the decidability of the problem of DPDA equivalence. In order to capture some properties of the domain of computation, we augment ...
Floyd--hoare logic for quantum programs

Floyd--Hoare logic is a foundation of axiomatic semantics of classical programs, and it provides effective proof techniques for reasoning about correctness of classical programs. To offer similar techniques for quantum program verification and to build ...
On the Hoare theory of monadic recursion schemes
CSL-LICS '14: Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

The equational theory of monadic recursion schemes is known to be decidable by the result of Sénizergues on the decidability of the problem of DPDA equivalence. In order to capture some properties of the domain of computation, we augment equations with ...

Comments

Information & Contributors

Information

Published In

Journal of the ACM Volume 38, Issue 4

Oct. 1991

272 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/115234

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1991

Published in JACM Volume 38, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

17
Total Citations
View Citations
711
Total Downloads

Downloads (Last 12 months)30
Downloads (Last 6 weeks)3

Reflects downloads up to 10 Aug 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Ésik Z(2019)Equational properties of fixed-point operations in cartesian categories: An overviewMathematical Structures in Computer Science10.1017/S096012951800036129:06(909-925)Online publication date: 24-May-2019
https://doi.org/10.1017/S0960129518000361
Ésik Z(2015)Equational Properties of Fixed Point Operations in Cartesian Categories: An OverviewMathematical Foundations of Computer Science 201510.1007/978-3-662-48057-1_2(18-37)Online publication date: 11-Aug-2015
https://doi.org/10.1007/978-3-662-48057-1_2
Ésik ZSutner K(2011)Stephen L. Bloom 1940-2010Fundamenta Informaticae10.5555/2361347.2361352109:4(369-381)Online publication date: 1-Dec-2011
https://dl.acm.org/doi/10.5555/2361347.2361352
Bernátsky LÉsik Z(2011)Semantics of flowchart programs and the free Conway theoriesRAIRO - Theoretical Informatics and Applications10.1051/ita/1998321-30035132:1-3(35-78)Online publication date: 8-Jan-2011
https://doi.org/10.1051/ita/1998321-300351
Arthan RMartin UMathiesen EOliva P(2009)A general framework for sound and complete Floyd-Hoare logicsACM Transactions on Computational Logic10.1145/1614431.161443811:1(1-31)Online publication date: 6-Nov-2009
https://dl.acm.org/doi/10.1145/1614431.1614438
Bloom SÉsik Z(2009)Equational axioms for regular setsMathematical Structures in Computer Science10.1017/S09601295000001043:01(1)Online publication date: 4-Mar-2009
https://doi.org/10.1017/S0960129500000104
Kakutani Y(2009)A logic for formal verification of quantum programsProceedings of the 13th Asian conference on Advances in Computer Science: information Security and Privacy10.1007/978-3-642-10622-4_7(79-93)Online publication date: 14-Dec-2009
https://dl.acm.org/doi/10.1007/978-3-642-10622-4_7
Martin UMathiesen EOliva P(2006)Hoare logic in the abstractProceedings of the 20th international conference on Computer Science Logic10.1007/11874683_33(501-515)Online publication date: 25-Sep-2006
https://dl.acm.org/doi/10.1007/11874683_33
Bloom Sésik Z(2005)Program correctness and matricial iteration theoriesMathematical Foundations of Programming Semantics10.1007/3-540-55511-0_24(457-476)Online publication date: 30-May-2005
https://doi.org/10.1007/3-540-55511-0_24
Aceto LÉsik ZIngólfsdóttir A(2002)A Fully Equational Proof of Parikh's TheoremRAIRO - Theoretical Informatics and Applications10.1051/ita:200200736:2(129-153)Online publication date: 15-Dec-2002
https://doi.org/10.1051/ita:2002007
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

References

Cited By

Index Terms

Recommendations

The Hoare Logic of Deterministic and Nondeterministic Monadic Recursion Schemes

Floyd--hoare logic for quantum programs

On the Hoare theory of monadic recursion schemes

Comments

Information

Published In

Publisher

Publication History

Permissions

Check for updates

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations