Behavioral subtyping

Substitutability is a principle in object-oriented programming stating that, in a computer program, if S is a subtype of T, then objects of type T may be replaced with objects of type S (i.e. an object of type T may be substituted with any object of a subtype S) without altering any of the desirable properties of T (correctness, task performed, etc.). More formally, the Liskov substitution principle (LSP) is a particular definition of a subtyping relation, called (strong) behavioral subtyping, that was initially introduced by Barbara Liskov in a 1987 conference keynote address titled Data abstraction and hierarchy. It is a semantic rather than merely syntactic relation because it intends to guarantee semantic interoperability of types in a hierarchy, object types in particular. Barbara Liskov and Jeannette Wing formulated the principle succinctly in a 1994 paper as follows:

Subtype Requirement: Let ${\displaystyle \phi (x)}$ be a property provable about objects ${\displaystyle x}$ of type T. Then ${\displaystyle \phi (y)}$ should be true for objects ${\displaystyle y}$ of type S where S is a subtype of T.

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