The authors give a formal semantics for the language Bounded Fun, which supports both parametric and subtype polymorphism. They show how to use partial equivalence relations to model inheritance in this language, which supports the notion of subtype and record types. A generalization of partial equivalence relations, known as omega -sets, is used in combination with modest sets to provide the first known model of Bounded Fun (with explicit polymorphism). Connections with previous work on the semantics of explicit parametric polymorphism is established by noting that the semantics of polymorphic types presented here (using dependent products) is isomorphic to that given by the intersection interpretation of polymorphism.