We present a typed polymorphic calculus that supports a general mechanism for view definition and object sharing among classes. In this calculus, a class can contain inclusion specifications of objects from other classes. Each such specification consists of a em predicate determining the subset of objects to be included and a viewing function under which those included objects are manipulated. Both predicates and viewing functions can be any type consistent programs definable in the polymorphic calculus. Inclusion specifications among classes can be cyclic, allowing mutually recursive class definitions. These features achieve flexible view definitions and wide range of class organizations in a compact and elegant way. Moreover, the calculus provides a suitable set of operations for views and classes so that the programmer can manipulate views and classes just the same way as one deals with ordinary records and sets. The proposed calculus uniformly integrates views and classes in a polymorphic type system of a database programming language similar to Machiavelli. The calculus has a type inference algorithm that relieves the programmer from complicated type declarations of views and classes. The polymorphic type system of the calculus is also shown to be sound, which guarantees complete static check of type consistency of programs involving classes and views. Through these properties, the programmer can enjoy full advantages of polymorphism and type inference when writing object-oriented database programs.