Circle–ellipse problem

The circle–ellipse problem in software development (sometimes called the square–rectangle problem) illustrates several pitfalls which can arise when using subtype polymorphism in object modelling. The issues are most commonly encountered when using object-oriented programming (OOP). By definition, this problem is a violation of the Liskov substitution principle, one of the SOLID principles.

The problem concerns which subtyping or inheritance relationship should exist between classes which represent circles and ellipses (or, similarly, squares and rectangles). More generally, the problem illustrates the difficulties which can occur when a base class contains methods which mutate an object in a manner which may invalidate a (stronger) invariant found in a derived class, causing the Liskov substitution principle to be violated.

The existence of the circle–ellipse problem is sometimes used to criticize object-oriented programming. It may also imply that hierarchical taxonomies are difficult to make universal, implying that situational classification systems may be more practical.

Description

It is a central tenet of object-oriented analysis and design that subtype polymorphism, which is implemented in most object-oriented languages via inheritance, should be used to model object types that are subsets of each other; this is commonly referred to as the is-a relationship. In the present example, the set of circles is a subset of the set of ellipses; circles can be defined as ellipses whose major and minor axes are the same length. Thus, code written in an object-oriented language that models shapes will frequently choose to make class Circle a subclass of class Ellipse, i.e.