Inheritance and explicit coercion

A method is presented for providing semantic interpretations for languages which feature inheritance in the framework of statically checked, rich type disciplines. The approach is illustrated by an extension of the language Fun of L. Cardelli and P. Wegner (1985), which is interpreted via a translation into an extended polymorphic lambda calculus. The approach interprets inheritances in Fun as coercion functions already definable in the target of the translation. Existing techniques in the theory of semantic domains can then be used to interpret the extended polymorphic lambda calculus, thus providing many models for the original language. The method allows the simultaneous modeling of parametric polymorphism, recursive types, and inheritance, which has been regarded as problematic because of the seemingly contradictory characteristics of inheritance and type recursion on higher types. The main difficulty in providing interpretations for explicit type disciplines featuring inheritance is identified. Since interpretations follow the type-checking derivations, coherence theorems are required, and the authors prove them for their semantic method