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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For the economic principle, see Substitute good.

Liskov substitution principle – Wikipedia

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 may be replaced with objects of type S without altering any of the desirable properties of that program e. This article includes a list of referencesbut its sources remain unclear because it has insufficient inline citations. Retrieved from ” https: Views Read Edit View history. By using this site, you agree to the Terms of Use and Privacy Policy.

Object-oriented programming Type theory Programming principles Formal methods Programming language semantics. 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 with preconditionspostconditions and invariants. Taking aliasing into account was the major improvement made by Liskov and Wingand a key ingredient is the history constraint.


Contains a gentler introduction to behavioral subtyping in its various forms in chapter 2.

Leavens and Krishna K. Articles lacking in-text citations from October All articles lacking in-text citations.

It is a semantic rather than merely anr relation, because it intends to guarantee semantic interoperability of types in a hierarchy, object types in particular. This paper surveys various notions of behavioral subtyping, including Liskov and Wing’s.

Liskov, Barbara ; Wing, Jeannette July Please help to improve this article by introducing more precise citations. Leavens, Murali Liskof, ed. This paper discusses LSP in the mentioned context.

Barbara Liskov and Jeannette Wing described the principle succinctly in a paper as follows:. Nonetheless, the principle is useful in reasoning about the design of class hierarchies.

These are detailed in a terminology resembling that of design abstractin contract methodology, leading to some restrictions on how contracts can interact with inheritance:.

asbtraction The rules on pre- and postconditions are identical to those introduced by Bertrand Meyer in his book Object-Oriented Software Construction. In addition to the signature requirements, the subtype must meet a number of behavioural nad. October Learn how and when to remove this template message. 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.

This page was last edited on 27 Novemberat An article popular in the object-oriented programming community that gives several examples of LSP violations.


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.

An updated version appeared as CMU technical report: A keynote address in which Liskov first formulated the principle.

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. 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.

Behavioural subtyping is undecidable in general: A behavioral notion of subtyping.

Liskov substitution principle

Both Meyer, and later Pierre America, who was the first fata 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.

From Wikipedia, the free encyclopedia. The formalization of the principle by its authors.