By Luca Cardelli

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In our framework only signatures are in some sense inherited, not object components. Inheritance of methods can be achieved manually by code sharing. Since such sharing is not enforced by the language, we acquire flexibility: a class signature can be implemented by many classes, hence different instances of the same class signature can have different methods. This confers a dynamic aspect to method binding, while not requiring any run-time search in the class hierarchy for method access. 1. Tuple subtypes The subtyping rule for tuples is as follows.

A lot of experience is required to understand where module boundaries should be located [Parnas 72]. In principle, any part of a program which could conceivably be reused should form a module. Any collection of routines which maintain an internal invariant that could be violated by careless use should also form a module. And almost every user-defined data type (or collection of closely related data types) should form a module, together with the relevant operations. Module boundaries should be located wherever there is some information that can or should be hidden; that is, information not needed by other modules, or information that can be misused by other modules.

To make an analogy with hardware, an open system is like a hardware box without a cover; anybody can plug wires into it. A closed system is a hardware box with a cover but with expansion slots: one can plug wires only into the outside connectors, but one can also add a new piece of hardware (with related external connectors) that has internal access to the box. Finally, a sealed system can be used only through the provided connectors. 1. Open systems Consider the following system organization, illustrated in the diagram.

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Typeful programming by Luca Cardelli


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