Editing Liskov substitution principle (section)

{{short description|Object-oriented programming principle}}
{{Redirect|Substitutability|the economic principle|Substitute good}}
{{More footnotes|date=October 2018}}
[[File:Barbara Liskov MIT computer scientist 2010.jpg|alt=Portrait of Barbara Liskov|thumb|Liskov substitution was introduced by [[Barbara Liskov]]]]
{{Solid principles}}

The '''Liskov substitution principle''' ('''LSP''') is a particular definition of a [[subtyping]] relation, called [[behavioral subtyping|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" {{endash}} a principle in [[object-oriented programming]] stating that an [[Object (computer science)|object]] (such as a [[Class (computer programming)|class]]) may be replaced by a sub-object (such as a class that extends the first class) without breaking the program. It is a [[Formal semantics of programming languages|semantic]] rather than merely syntactic relation, because it intends to guarantee semantic interoperability of [[data type|types]] in a hierarchy, object types in particular. Barbara Liskov and [[Jeannette Wing]] described the principle succinctly in a 1994 paper as follows:<ref name="liskov1994">{{Cite journal|last1=Liskov|first1=Barbara|last2=Wing|first2=Jeannette|date=1994-11-01|title=A behavioral notion of subtyping|journal=ACM Transactions on Programming Languages and Systems |language=EN|volume=16|issue=6|pages=1811–41|doi=10.1145/197320.197383|s2cid=999172|doi-access=free}}</ref>
<blockquote>''Subtype Requirement'': Let {{tmath|\phi(x)}} be a property provable about objects {{tmath|x}} of type {{math| T}}.  Then {{tmath| \phi(y) }} should be true for objects {{tmath|y}} of type {{math| S }} where {{math| S }} is a subtype of {{math| T}}. </blockquote>
Symbolically:
:<math>S \leq T \to (\forall x {:} T . \phi(x) \to \forall y {:} S . \phi(y))</math>
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 [[precondition]]s, [[postcondition]]s and [[Invariant (computer science)|invariants]].