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This paper presents a way to describe design patterns rigorously based on role concepts. Rigorous pattern descriptions are a key aspect for patterns to be used as rules for model evolution in the MDA context, for example. We formalize the role concepts commonly used in defining design patterns as a role metamodel using Object-Z. Given this role metamodel, individual design patterns are specified generically as a formal pattern role model using Object-Z. We also formalize the properties that must be captured in a class model when a design pattern is deployed. These properties are defined generically in terms of role bindings from a pattern role model to a class model. Our work provides a precise but abstract approach for pattern definition and also provides a precise basis for checking the validity of pattern usage in designs.