Request PDF on ResearchGate | Data Abstraction and Hierarchy | An abstract is not available. Barbara Liskov at Massachusetts Institute of Technology. and Hierarchy. MIT. Barbara Liskov Laboratory for Computer Science Cambridge , Ma. Abstract. Data abstraction is a valuable method for organizing. Barbara Liskov. November Page 2. Outline. ▫ Inventing abstract data types . ▫ CLU. ▫ Type hierarchy. ▫ What next. Page 3. Data Abstraction Prehistory.

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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. This paper discusses LSP in the mentioned context.

Leavens, Liskob Sitaraman, ed. For the economic principle, see Substitute good. October Learn how and when to remove this template message. Nonetheless, the principle is useful in reasoning about the design of class hierarchies.

Liskov substitution principle – Wikipedia

Taking aliasing into account was the major improvement made by Liskov and Wingand a key ingredient is the history constraint.

Liskov’s notion of a behavioural subtype defines a notion of substitutability for objects; that is, if S is a subtype of Tthen objects of type T in a program wnd be replaced with objects of type S without altering any of the desirable properties of that program e.

Substitutability is a principle in object-oriented programming stating that, in a computer programif S is a subtype of T, then objects of type T may be replaced with objects of type S i.


The rules on pre- and postconditions are identical to those introduced by Bertrand Meyer in his book Object-Oriented Software Construction. An article popular in the object-oriented programming community that gives several examples of LSP violations. Both Meyer, and later Pierre America, who was the first to use the term behavioral subtypinggave proof-theoretic definitions of some behavioral subtyping notions, but their definitions did not take into account aliasing that may occur in programming languages that support references or pointers.

More formally, the Liskov substitution principle LSP is a particular definition of a subtyping relation, called strong behavioral subtypingthat was initially introduced by Barbara Liskov in a conference keynote address titled Data abstraction and hierarchy.

This paper surveys various notions of behavioral subtyping, including Liskov and Wing’s.

Contains a gentler introduction to behavioral subtyping in its various forms in chapter 2. Behavioural subtyping is undecidable in general: A keynote address in which Liskov first formulated the principle.

Object-oriented programming Type theory Programming principles Formal methods Programming language semantics. Behavioural subtyping is a stronger notion than typical subtyping of functions defined in type theorywhich relies only on the contravariance of argument types and covariance of the return type.

Liskov substitution principle

The formalization of the principle by its authors. An updated version appeared as CMU technical report: In the same paper, Liskov and Wing detailed their notion of behavioral subtyping in an extension of Hoare logicwhich bears a certain resemblance to Bertrand Meyer ‘s design by contract in that it considers the interaction of subtyping anx preconditionspostconditions and invariants.


In addition to the signature requirements, the subtype must meet a number of behavioural conditions. Liskov, Barbara ; Wing, Jeannette July By using this site, you agree to the Terms of Use and Privacy Policy.

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. A behavioral notion of subtyping. From Wikipedia, the free encyclopedia.

Barbara Liskov and Jeannette Wing described the principle succinctly in a paper as follows:. Retrieved from ” https: This article ane a list of referencesbut its sources remain unclear because it has insufficient inline citations. This page was last edited on 27 Novemberat Please help to improve this article by introducing more precise citations. Leavens and Krishna K. Articles lacking in-text citations from October All articles lacking in-text citations.

Views Read Edit View history. These are detailed in a terminology resembling that of design by contract methodology, leading to some restrictions on how contracts can interact with inheritance:.