Abstract
A set P(DO, R) of all invariants that ensure termination and where the postcondition R is true after termination is defined for every loop DO and for every postcondition R. Complying with the corresponding properties required, these sets P(DO, R) induce a topology on wp(DO, R). The weakest precondition wp(DO, R) is the weakest invariant of DO with respect to R. The topology P(DO, R) has a non-trivial structure and contains arbitrary conjunctions of invariants.
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References
E.W.Dijkstra: Guarded commands, nondeterminacy and formal derivation of programs, Comm.ACM 18 (1975) 453–457.
E.W.Dijkstra: A Discipline of Programming, Prentice Hall, Englewood Cliffs, NJ, 1976.
E.W.Dijkstra, C.S.Scholten: Predicate Calculus and Program Semantics, Springer Verlag New York Inc., 1990.
D. Gries: The Science of Programming, Springer Verlag New York Inc., 1981.
C.A.R. Hoare: An axiomatic basis for computer programming, Comm. ACM 12 (1969) 576–580.
C.A.R. Hoare, I.J. Hayes et al.: Laws of Programming, Comm. ACM 30 (1987) 672–686.
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© 1993 Springer-Verlag Berlin Heidelberg
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Futschek, G. (1993). Algebraic properties of loop invariants. In: Bjørner, D., Broy, M., Pottosin, I.V. (eds) Formal Methods in Programming and Their Applications. Lecture Notes in Computer Science, vol 735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039700
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DOI: https://doi.org/10.1007/BFb0039700
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