Inheritance creates new classes from old ones by adding functions. Yet, can we be sure that the clients of new classes cannot foul up the clients of old ones? This paper answers this question, using process algebras and communicating sequential processes (CSP).

Failures refinement describes a class with the same functions, but reduced nondeterminism. The paper adds four new subtyping relations to this designation: weak, safe, optimal, and implementation. Weak subtyping allows the addition of functions that, when used, may change what older clients can do. Safe subtyping requires the added functions to behave like combinations of old ones. Optimal subtyping is safe, but the new functions are equivalent to old clients doing nothing. Implementation subtyping allows new private or invisible actions. The result is a hierarchy of subtyping relations. First, the author uses labeled transition systems to define them. The author then provides an equivalent testing scenario for each. These formalize the intuitive meanings above.

The paper is plausible and well written. It includes good examples before the abstractions and proofs. Some small errors got past the editors and reviewers, however, and the paper does not define one symbol. I still found the paper easy to read. It is rarefied. The author gives no connection to object-oriented modeling. Someone should link these forms of subtyping to state charts.