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Matching is a relation between object types originally designed to support type-safe subclassing with binary methods. In this paper we generalize it to deal with general covariance by allowing eld and method parameter types to change covariantly in matching types. The result is a signi cant increase in the exibility of subclassing. The generalization is in a di erent direction than the recent proposal for supporting type-safe virtual types via matching between mutually recursive types. The newdoi:10.1006/inco.2001.3048 fatcat:4qfgobza2bd2vpa24ad67gieeu