Skip to main content

Equations for if-then-else

  • Conference paper
  • First Online:
Mathematical Foundations of Programming Semantics (MFPS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 598))

  • 158 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • G. Bergman, Actions of Boolean rings on sets, Algebra Universalis 28, 1991, 153–187.

    Google Scholar 

  • S.L. Bloom and R. Tindell, Varieties of “if-then-else”, SIAM J. Comput. 12, 1983, 677–707.

    Google Scholar 

  • A.L. Foster, Generalized “Boolean” theory of universal algebras, Part II. Identities and subdirect sums of functionally complete algebras, Math. Zeit. 59, 1953, 191–199.

    Google Scholar 

  • I. Guessarian and J. Meseguer, On the axiomatization of if-then-else, SIAM J. Comput. 16, 1987, 332–357.

    Google Scholar 

  • F. Guzmán, Three-valued logics in the semantics of programming languages, preprint, 1990.

    Google Scholar 

  • F. Guzmán and C. Squier, The algebra of conditional logic, Algebra Universalis 27, 1990, 88–110.

    Google Scholar 

  • C.A.R. Hoare, Communicating Sequential Processes, Prentice-Hall, 1985.

    Google Scholar 

  • E.V. Huntington, Sets of independent postulates for the algebra of logic, Trans. Amer. Math. Soc. 5, 1904, 288–309.

    MathSciNet  Google Scholar 

  • J.S. Johnson and E.G. Manes, On modules over a semiring, J. Algebra 15, 1970, 57–67.

    Google Scholar 

  • S. Kleene, Introduction to Metamathematics, Van Nostrand, 1952.

    Google Scholar 

  • E.G. Manes, Predicate Transformer Semantics, Cambridge University Press, 1992a, to appear.

    Google Scholar 

  • E.G. Manes, Adas and the equational theory of if-then-else, Algebra Universalis, 1991b, to appear.

    Google Scholar 

  • J. McCarthy, A basis for a mathematical theory of computation, in P. Braffort and D. Hirschberg (eds.), Computer Programming and Formal Systems, North-Holland, 1963, 33–70.

    Google Scholar 

  • J. McCarthy, Predicate calculus with “undefined” as a truth value, Stanford A.I. memo, Feb., 1979.

    Google Scholar 

  • N.H. McCoy and D. Montgomery, A representation of generalized boolean rings, Duke Math. J. 3, 1937, 455–459.

    Google Scholar 

  • A.H. Mekler and E.M. Nelson, Equational bases for if-then-else, SIAM J. Comput. 16, 1987, 465–485.

    Google Scholar 

  • M.H. Stone, The theory or representations of Boolean algebras, Trans. Amer. Math. Soc. 40, 1936, 37–111.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Stephen Brookes Michael Main Austin Melton Michael Mislove David Schmidt

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Manes, E.G. (1992). Equations for if-then-else. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1991. Lecture Notes in Computer Science, vol 598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55511-0_23

Download citation

  • DOI: https://doi.org/10.1007/3-540-55511-0_23

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55511-7

  • Online ISBN: 978-3-540-47194-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics