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Snippet from Wikipedia: 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.

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Snippet from Wikipedia: Barbara Liskov

Barbara Liskov (born November 7, 1939, as Barbara Jane Huberman) is an American computer scientist who has made pioneering contributions to programming languages and distributed computing. Her notable work includes the introduction of abstract data types and the accompanying principle of data abstraction, along with the Liskov substitution principle, which applies these ideas to object-oriented programming, subtyping, and inheritance. Her work was recognized with the 2008 Turing Award, the highest distinction in computer science.

Liskov is one of the earliest women to have been granted a doctorate in computer science in the United States, and the second woman to receive the Turing award. She is currently an Institute Professor and Ford Professor of Engineering at the Massachusetts Institute of Technology.

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