Abstract
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is only evaluated if the first argument does not suffice to determine the value of the expression. In programming, short-circuit evaluation is widely used.
We review proposition algebra [2010], an algebraic approach to propositional logic with side effects that models short-circuit evaluation. Proposition algebra is based on Hoare’s conditional [1985], which is a ternary connective comparable to if-then-else. Starting from McCarthy’s notion of sequential evaluation [1963] we discuss a number of valuation congruences on propositional statements and we introduce Hoare-McCarthy algebras as the structures that model these congruences. We also briefly discuss the associated short-circuit logics, i.e., the logics that define these congruences if one restricts to sequential binary connectives.
Keywords
- Conditional composition
- reactive valuation
- sequential connective
- short-circuit evaluation
- side effect
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bergstra, J.A., Bethke, I., Rodenburg, P.H.: A propositional logic with 4 values: true, false, divergent and meaningless. Journal of Applied Non-Classical Logics 5(2), 199–218 (1995)
Bergstra, J.A., Heering, J., Klint, P.: Module algebra. Journal of the ACM 37(2), 335–372 (1990)
Bergstra, J.A., Middelburg, C.A.: Instruction sequence processing operators (2009), http://arxiv.org/:ArXiv:0910.5564v2 [cs.LO]
Bergstra, J.A., Ponse, A.: Proposition algebra. ACM Transactions on Computational Logic 12(3), Article 21 (36 pages) (2011)
Bergstra, J.A., Ponse, A.: Short-circuit logic (2010/2011), http://arxiv.org/abs/1012.3674v3 [cs.LO]
Bergstra, J.A., Ponse, A.: On Hoare-McCarthy algebras (2010), http://arxiv.org/abs/1012.5059v1 [cs.LO]
Bloom, S.L., Tindell, R.: Varieties of “if-then-else”. SIAM Journal of Computing 12(4), 677–707 (1983)
Mekler, A.H., Nelson, E.M.: Equational bases for if-then-else. SIAM Journal of Computing 16(3), 465–485 (1987)
Hoare, C.A.R.: A couple of novelties in the propositional calculus. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 31(2), 173–178 (1985)
Regenboog, B.C.: Reactive valuations. MSc. thesis Logic, University of Amsterdam. December 2010, http://arxiv.org/abs/1101.3132v1 [cs.LO] (2011)
Sioson, F.M.: Equational bases of Boolean algebras. Journal of Symbolic Logic 29(3), 115–124 (1964)
Terese. Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge University Press (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bergstra, J.A., Ponse, A. (2012). Proposition Algebra and Short-Circuit Logic. In: Arbab, F., Sirjani, M. (eds) Fundamentals of Software Engineering. FSEN 2011. Lecture Notes in Computer Science, vol 7141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29320-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-29320-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29319-1
Online ISBN: 978-3-642-29320-7
eBook Packages: Computer ScienceComputer Science (R0)