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6 Concepts of Behavioral Subtyping and a Sketch of their Extension to Component-Based Systems

Object-oriented systems are able to treat objects indirectly by message passing. This allows them to manipulate objects without knowing their exact runtime type. Behavioral subtyping helps one reason in a modular fashion about such programs. That is, one can reason based on the static types of expressions in a program, provided that static types are upper bounds of the runtime types in a subtyping preorder, and that subtypes satisfy the conditions of behavioral subtyping. We survey various notions of behavioral subtyping proposed in the literature for objectoriented programming. We also sketch a notion of behavioral subtyping for objects in component-based systems, where reasoning about the events that a component can raise is important.