Formal Methods, Foundations and Applications: 14th Brazilian by Harald König, Michael Löwe (auth.), Adenilso Simao, Carroll

By Harald König, Michael Löwe (auth.), Adenilso Simao, Carroll Morgan (eds.)

This e-book constitutes the completely refereed post-conference court cases of the 14th Brazilian Symposium on Formal tools, SBMF 2011, held in Sao Paulo, Brazil, in September 2011; co-located with CBSoft 2011, the second one Brazilian convention on software program: conception and perform. The thirteen revised complete papers have been conscientiously reviewed and chosen from 37 submissions. The papers offered conceal a extensive diversity of foundational and methodological concerns in formal equipment for the layout and research of software program and platforms in addition to functions in quite a few domains.

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Additional resources for Formal Methods, Foundations and Applications: 14th Brazilian Symposium, SBMF 2011, São Paulo, Brazil, September 26-30, 2011, Revised Selected Papers

Example text

E. finite lists of labels) which are generated by steps of the operational semantics. To compare traces of different components and with different contexts, we abstract from package local types and types declared in the context. Package local types should not appear in the labels, because different components might use different local types. c) in Fig. c belong to the component (2) which of their methods are not overridden by the context. The reason for (1) is that these are the types of X that can be used in cast expressions in the context.

It is sufficient to prove that Traces(κX X ) ⊆ absX (Traces(κX Y )), which follows from the property that Traces(κX Y ) ⊆ Traces(κY Y ). The proof is done by induction on the length of the traces. The empty trace is trivially in both sets. As induction step, assume t · l such that (1) t ∈ Traces(κX X ), (2) t ∈ absX (Traces(κX Y )), and (3) t · l ∈ Traces(κX X ). The proof goal is then to show that t · l ∈ absX (Traces(κX Y )). : The claim follows directly by Lemma 2. : The initial configurations of κX X and κX Y are related by ctxt due to Lemma 6.

A renaming is a bijective relation on object identifiers. We write ρ for such a relation. We can then consider traces equivalent (or related) if they are equal modulo a renaming. Definition 2 (Related traces). t 1 ≡ρ t 2 iff the object identifiers appearing at the same positions in the traces are related under ρ and the types appearing at the same position are equal. If we are not interested in a particular ρ , we omit it for brevity. In the following, we use the straightforward generalization of this definition of equality modulo a renaming (≡ρ ) to arbitrary syntactic structures.

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