Family Values: A Behavioral Notion of
Authors: Barbara Liskov and Jeannette M. Wing
Appears as CMU-CS-93-187 (supersedes CMU-CS-93-149 and CMU-CS-92-220).
The full text of this paper is here (in
The use of hierarchy is an important component of object-oriented
Hierarchy allows the use of type families, in which higher level
supertypes capture the behavior that all of their subtypes have
For this methodology to be effective, it is necessary to have
a clear understanding of how subtypes and supertypes are related.
This paper takes the position that the relationship should
ensure that any property proved about supertype objects also holds
for its subtype objects.
It presents two ways of defining
the subtype relation, each of which meets this criterion, and each
of which is easy for programmers to use.
The subtype relation is based on the specifications of the sub-
and supertypes; the paper presents a way of specifying types
that makes it convenient to define the subtype relation.
The paper also discusses the ramifications of
this notion of subtyping on the design of type families.