Practical Strengthening of Preconditions
نویسندگان
چکیده
This paper takes a closer look at behavioral subtyping in the context of concurrency, by considering an example of subtyping of a concurrent datastructure taken from sensor networks. Akin to the extension of a state-machine, this example illustrates conflicts caused by the interference of concurrency and inheritance. In short, the extension consists in declaring additional fields in a subclass, thus extending the state space of the super-class. Reminiscent of a famous illustration case for inheritance anomalies, the extension leads to violating behavioral subtyping by requiring the strengthening of preconditions in the subclass to account for the extended state space. We provide a solution to this bottleneck by characterizing cases in which such a strengthening can safely occur. To that end, we dissect preconditions according to various criteria, such as their semantics (wait or “traditional” correctness), or the objects they involve (method arguments or fields of the receiving object). Using denotational semantics, we formally prove that such strengthening of preconditions through wait conditions is safe nd does not break the contract. We implement our relaxation in Eiffel, and illustrate how it preserves modular reasoning – in particular about deadlocks.
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