OBJECT INHERITANCE BEYOND SUBTYPING

A categorial semantic domain for objects is presented in order to clar ify both aggregation and specialization. Three kinds of specialization are discussed: (1) subtyping (specialization with no side effects and no non-monotonic overriding); (2) monotonic specialization (possibly with side effects but still only with monotonic overriding); and (3) n on-monotonic specialization (possibly with side effects and non-monoto nic overriding). A sequence of three categories of objects differing o nly in the morphisms is presented. The first one is used to explain ob ject aggregation (respecting locality through a frame constraint) and the strictest form of specialization (subtyping). The second category is shown to be adequate for explaining specialization with side effect s (by relaxing the frame constraint). Finally, the third category supp orts also non-monotonic overriding, by adopting as morphisms suitable partial morphisms of the second one. All these categories are complete and cocomplete. Colimits are used for explaining the semantics of agg regation and multiple inheritance.