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A new technique is presented to statically check a given procedure against a user-provided property. The method requires no annotations; it automatically infers a context-dependent specification for each procedure call, so that only as much information about a procedure is used as is needed to analyze its caller. Specifications are inferred iteratively. Empty specifications are initially used to over-approximate the effects of all procedure calls; these are later refined in response to spurious counterexamples. When the analysis terminates, any remaining counterexample is guaranteed to be valid. However, since the heap is finitized, the absence of a counterexample does not guarantee the validity of the given property in general.