Contract systems enable programmers to state specifications and enforce them at run time. First-order contracts are expressed using ordinary code, while higher-order contracts are expressed using the notation familiar from type systems. But most interface descriptions come with sophisticated properties, often informally stated, that involve not just assertions about single method calls, but entire call chains. Typical contracts cannot express these specifications concisely. Such specifications demand domain-specific notations. In response, this paper proposes abstracting contract systems over the notation used for stating specifications. It presents an architecture for such a system, some illustrative examples, and an evaluation in terms of notations from the literature.