Modular reasoning in the presence of subclassing

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Abstract
Considerable progress has been made in understanding how to use subtyping in a way that facilitates modular reasoning. However, using subclassing in a way that facilitates modular reasoning is not well understood. Often methods must be overriden as a group because of dependencies on instance variables, and the programmers of subclasses cannot tell which methods are grouped without looking at the code of superclasses. Also, the programmers of subclasses must look at the code of superclasses to tell what assumptions inherited methods make about the behavior of overriden methods.We present a systematic way to use subclassing that facilitates formal and informal modular reasoning. Separate specifications are given to programmers writing code that manipulates instances of a class and to programmers writing subclasses of the class. The specifications given to programmers of subclasses are divided, by division of labor specifications , into multiple parts. Subclasses may inherit or override entire parts, but not sub-parts. Reasoning about the implementation of each part is done independently of other parts.