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The purpose of these notes is to provide a gentle introduction to attribute systems using plumbing diagrams. When developing your own attribute systems, you are strongly encouraged to work them out (and present them) as plumbing diagrams. Typical plumbing diagram of an attribute system. An attribute system is made up of components, which may be connected together in any number and arrangement consistent with the types of the interfaces. Plumbing diagram exhibiting circular dependencies. This one represents a valid computation. Plumbing diagrams are a notation – a visual language – for attribute systems and their in stances. As seen in Figure 2 and Figure 1, respectively, they are an intuitive component-based way to visually sum up all the elements of an attribute system and to present an arbitrary instance. A component’s surface (the “pants”) represents the datatype constructor declaration. The terminal data circles in a plumbing diagram of an abstract component can be thought of as empty, typed slots. The same circles in the plumbing diagram of a concrete instance of the (strict) datatype would contain type-compatible values in these slots.
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