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A technical correspondence item by Kenneth Baclawski and Bipin Indurkhya titled The Notion of Inheritance in Object-Oriented Programming (CACM 37, No. 9, September 1994). Here s a quote: [In other approaches,] it is taken for granted that CIRCLE is a subtype of ELLIPSE. A hierarchy in which ELLIPSE is a subtype of CIRCLE is, therefore, considered an aberration ( nonstandard ) ... [But we] would like to affirm a stronger point of view in which there are no standard conceptual hierarchies. According to Baclawski and Indurkhya, therefore, we can t simply claim as I did earlier that CIRCLE just is a subtype of ELLIPSE. Note: I ve set the type names CIRCLE and ELLIPSE in the quote in uppercase for clarity (they re in lowercase in the original). A paper by Nelson Mattos and Linda G. DeMichiel titled Recent Design Trade-Offs in SQL3 (ACM SIGMOD Record 23, No. 4, December 1994; as you probably know, SQL3 was the working title for what subsequently became SQL:1999, the version of the SQL standard that was current when this chapter was first written). Again, here s a quote: [The] most appropriate [approach] is to not permit specialization via constraints (see the next bullet item below). In essence, what this quote means is that we shouldn t and indeed in SQL we can t define type CIRCLE to be a specialization of type ELLIPSE such that an ellipse is in fact a circle if and only if it satisfies the constraint a = b. A tutorial by Stanley B. Zdonik and David Maier titled Fundamentals of Object-Oriented Databases (in Zdonik and Maier, eds., Readings in Object-Oriented Database Systems, Morgan Kaufmann, 1990). Actually, this tutorial isn t 100 percent clear on the matter at hand, but if it doesn t actually adopt the circles aren t ellipses position, it certainly comes very close to doing so. To be specific, it first defines something it calls specialization via constraints, thus: Specialization via constraints happens whenever the following is permitted: B subtype_of A and T subtype_of S and f(...b:T,...) returns r:R in Ops(B) and f(...b:S,...) returns r:R in Ops(A) That is, specialization via constraints occurs whenever the operation redefinition on a subtype constrains one of the arguments to be from a smaller value set than the corresponding operation on the supertype. Now, the implications of this definition of specialization via constraints for the circles and ellipses controversy in particular might not be very clear to you (they certainly aren t to me), but perhaps it doesn t matter, because it s also not clear as to whether Zdonik and Maier want to adopt the concept or not. They do, however, suggest that the concept implies that if we assign a circle value to an ellipse variable, we can t subsequently assign a value to that variable that s just an ellipse and not a circle ( ) and this state of affairs certainly has something to do with the question of whether a circle is an ellipse.
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To repeat, therefore, Stroustrup is not alone in arguing in favor of the position that circles aren t ellipses. For definiteness, however, I want to focus in the rest of this chapter on Stroustrup s argument specifically. Stroustrup is well known and widely respected as the inventor of the C++ language, and his views thus deserve the courtesy of careful attention. But I want to make it as clear as I possibly can that what follows is not meant as any kind of ad hominem attack. Nor is it meant as an attack on the C++ language specifically. Rather, I just want to use C++ or the quote from Stroustrup s book on C++, rather as a convenient hook off which to hang my argument. That argument, of course, is that any approach to inheritance in which a circle is not an ellipse is fundamentally flawed. This criticism apparently does apply to the C++ approach in particular, but it s very far from being limited to C++ alone.
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