Preview
Unable to display preview. Download preview PDF.
References
G. Bergman, Actions of Boolean rings on sets, Algebra Universalis 28, 1991, 153–187.
S.L. Bloom and R. Tindell, Varieties of “if-then-else”, SIAM J. Comput. 12, 1983, 677–707.
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.
I. Guessarian and J. Meseguer, On the axiomatization of if-then-else, SIAM J. Comput. 16, 1987, 332–357.
F. Guzmán, Three-valued logics in the semantics of programming languages, preprint, 1990.
F. Guzmán and C. Squier, The algebra of conditional logic, Algebra Universalis 27, 1990, 88–110.
C.A.R. Hoare, Communicating Sequential Processes, Prentice-Hall, 1985.
E.V. Huntington, Sets of independent postulates for the algebra of logic, Trans. Amer. Math. Soc. 5, 1904, 288–309.
J.S. Johnson and E.G. Manes, On modules over a semiring, J. Algebra 15, 1970, 57–67.
S. Kleene, Introduction to Metamathematics, Van Nostrand, 1952.
E.G. Manes, Predicate Transformer Semantics, Cambridge University Press, 1992a, to appear.
E.G. Manes, Adas and the equational theory of if-then-else, Algebra Universalis, 1991b, to appear.
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.
J. McCarthy, Predicate calculus with “undefined” as a truth value, Stanford A.I. memo, Feb., 1979.
N.H. McCoy and D. Montgomery, A representation of generalized boolean rings, Duke Math. J. 3, 1937, 455–459.
A.H. Mekler and E.M. Nelson, Equational bases for if-then-else, SIAM J. Comput. 16, 1987, 465–485.
M.H. Stone, The theory or representations of Boolean algebras, Trans. Amer. Math. Soc. 40, 1936, 37–111.
Author information
Authors and Affiliations
Editor information
Rights 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