Principle
Liskov's notion of a behavioral subtype defines a notion of substitutability for mutable objects; 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).
Behavioral subtyping is a stronger notion than typical subtyping of functions defined in type theory, which relies only on the contravariance of argument types and covariance of the return type. Behavioral subtyping is trivially undecidable in general: if q is the property "method for x always terminates", then it is impossible for a program (e.g. a compiler) to verify that it holds true for some subtype S of T even if q does hold for T. The principle is useful however in reasoning about the design of class hierarchies.
Liskov's principle imposes some standard requirements on signatures that have been adopted in newer object-oriented programming languages (usually at the level of classes rather than types; see nominal vs. structural subtyping for the distinction):
- Contravariance of method arguments in the subtype.
- Covariance of return types in the subtype.
- No new exceptions should be thrown by methods of the subtype, except where those exceptions are themselves subtypes of exceptions thrown by the methods of the supertype.
In addition to these, there are a number of behavioral conditions that the subtype must meet. These are detailed in a terminology resembling that of design by contract methodology, leading to some restrictions on how contracts can interact with inheritance:
- Preconditions cannot be strengthened in a subtype.
- Postconditions cannot be weakened in a subtype.
- Invariants of the supertype must be preserved in a subtype.
- History constraint (the "history rule"). Objects are regarded as being modifiable only through their methods (encapsulation). Since subtypes may introduce methods that are not present in the supertype, the introduction of these methods may allow state changes in the subtype that are not permissible in the supertype. The history constraint prohibits this. It was the novel element introduced by Liskov and Wing. A violation of this constraint can be exemplified by defining a MutablePoint as a subtype of an ImmutablePoint. This is a violation of the history constraint, because in the history of the Immutable point, the state is always the same after creation, so it cannot include the history of a MutablePoint in general. Fields added to the subtype may however be safely modified because they are not observable through the supertype methods. One may derive a CircleWithFixedCenterButMutableRadius from ImmutablePoint without violating LSP.
Read more about this topic: Liskov Substitution Principle
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