Liskov substitution principle

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In object-oriented programming, the Liskov substitution principle is a particular definition of subtype that was introduced by Barbara Liskov in a 1987 conference keynote address entitled Data abstraction and hierarchy ^[1].

Liskov formulated the principle succinctly in a subsequent paper^[2] as follows:

Let $q (x)$ be a property provable about objects $x$ of type $T$ . Then $q (y)$ should be true for objects $y$ of type $S$ where $S$ is a subtype of $T$ .

Thus, Liskov's notion of "subtype" is based on the notion of substitutability; that is, if S is a subtype of T, then objects of type T in a program may be replaced with objects of type S without altering any of the desirable properties of that program (e.g., correctness).

[edit] Design by contract

The Liskov substitution principle is closely related to the design by contract methodology, leading to some restrictions on how contracts can interact with inheritance:

Preconditions cannot be strengthened in a subclass.
Postconditions cannot be weakened in a subclass.

In addition, the principle implies that no new exceptions should be thrown by methods of the subclass, except where those exceptions are themselves subtypes of exceptions thrown by the methods of the superclass. See covariance and contravariance.

A function using a class hierarchy violating the principle uses a reference to a base class, yet must have knowledge of the subclasses. Such a function violates the open/closed principle because it must be modified whenever a new derivative of the base class is created.