Object-oriented languages define the identity of an object to be an address-based object identifier. The programmer may customize the notion of object identity by overriding the equals() and hashCode() methods following a specified contract. This customization often introduces latent errors, since the contract is unenforced and at times impossible to satisfy, and its implementation requires tedious and error-prone boilerplate code. Relation types are a programming model in which object identity is defined declaratively, obviating the need for equals() and hashCode() methods. This entails a stricter contract: identity never changes during an execution. We formalize the model as an adaptation of Featherweight Java, and implement it by extending Java with relation types. Experiments on a set of Java programs show that the majority of classes that override equals() can be refactored into relation types, and that most of the remainder are buggy or fragile.