Liskov substitution principle

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 based on the concept of "substitutability" – a principle in object-oriented programming stating that an object (such as a class) may be replaced by a sub-object (such as a class that extends the first class) without breaking the program. 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 described 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.

Symbolically:

${\displaystyle S\leq T\to \forall x{:}T.\phi (x)\to \forall y{:}S.\phi (y)}$

That is, if S subtypes T, what holds for T-objects holds for S-objects. In the same paper, Liskov and Wing detailed their notion of behavioral subtyping in an extension of Hoare logic, which bears a certain resemblance to Bertrand Meyer's design by contract in that it considers the interaction of subtyping with preconditions, postconditions and invariants.