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The behavior of languages such as C++, Java, Smalltalk and Eiffel and the modeling features such classes, inheritance, polymorphism, message passing are discussed. The important theoretical approaches such as subtyping, F-bounds, matching and the object calculus are also discussed. A mathematical model was developed, that show the possibility of motivating the existence of something as relatively sophisticated as an object with a state and method. The two kind of type rules include: introduction rules that describes the formation of functions and records and elimination rules, describing the decomposition of constructions.

The Theory of Classification, Part 2: The Scratch-Built Typechecker.