Retired lemma card_Union_image; use the simpler card_UN_disjoint instead.
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\title{Hoare Logic for Parallel Programs}
\author{Leonor Prensa Nieto}
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\begin{abstract}\noindent
In the following theories a formalization of the Owicki-Gries and
the rely-guarantee methods is presented. These methods are widely
used for correctness proofs of parallel imperative programs with
shared variables. We define syntax, semantics and proof rules in
Isabelle/HOL. The proof rules also provide for programs
parameterized in the number of parallel components. Their
correctness w.r.t.\ the semantics is proven. Completeness proofs
for both methods are extended to the new case of parameterized
programs. (These proofs have not been formalized in Isabelle. They
can be found in~\cite{Prensa-PhD}.) Using this formalizations we
verify several non-trivial examples for parameterized and
non-parameterized programs. For the automatic generation of
verification conditions with the Owicki-Gries method we define a
tactic based on the proof rules. The most involved examples are the
verification of two garbage-collection algorithms, the second one
parameterized in the number of mutators.
For excellent descriptions of this work see
\cite{NipkowP-FASE99,PrenEsp00,Prensa-PhD,Prensa-ESOP03}.
\end{abstract}
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