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{{Short description|Subsumption relationship between abstractions}}{{multiple issues|{{essay-like|date=August 2018}}{{technical|date=August 2018}}}}In knowledge representation and ontology components, including for object-oriented programming and design, is-a (also written as is_a or is a) is a (wikt:subsume|subsumptive){{efn|See Liskov substitution principle.}} relationship between abstractions (e.g., types, classes), wherein one class A is a subclass of another class B (and so B is a superclass of A).In other words, type A is a subtype of type B when A's specification implies B's specification. That is, any object (or class) that satisfies A's specification also satisfies B's specification, because B's specification is weaker.WEB, Subtypes and Subclasses,weblink MIT OCW, 2 October 2012, For example, a cat 'is a' animal, but not vice versa. All cats are animals, but not all animals are cats.Behaviour that are is relevant to all animals is defined on an animal class, whereas behaviour that is relevant only for cats is defined in a cat class. By defining the cat class as 'extending' the animal class, all cats 'inherit' the behaviour defined for animals, without the need to explicitly code that behaviour for cats.

Related concepts

The is-a relationship is to be contrasted with the has-a (has_a or has a) relationship between types (classes); confusing the relations has-a and is-a is a common error when designing a model (e.g., a computer program) of the real-world relationship between an object and its subordinate. The is-a relationship may also be contrasted with the instance-of relationship between objects (instances) and types (classes): see Type–token distinction.To summarize the relations, there are:

• hyperonym–hyponym (supertype/superclass–subtype/subclass) relations between types (classes) defining a taxonomic hierarchy, where
  • for a subsumption relation: a hyponym (subtype, subclass) has a type-of (is-a) relationship with its hyperonym (supertype, superclass);
• holonym–meronym (whole/entity/container–part/constituent/member) relations between types (classes) defining a possessive hierarchy, where
  • for an aggregation (i.e. without ownership) relation:
    • a holonym (whole) has a has-a relationship with its meronym (part),
  • for a composition (i.e. with ownership) relation:
    • a meronym (constituent) has a part-of relationship with its holonym (entity),
  • for a containmentSee also Containment (computer programming). relation:
    • a meronym (member) has a member-of relationship with its holonym (container);
• concept–object (type–token) relations between types (classes) and objects (instances), where
  • a token (object) has an instance-of relationship with its type (class).

Examples of subtyping

Subtyping enables a given type to be substituted for another type or abstraction. Subtyping is said to establish an is-a relationship between the subtype and some existing abstraction, either implicitly or explicitly, depending on language support. The relationship can be expressed explicitly via inheritance in languages that support inheritance as a subtyping mechanism.

C++

The following C++ code establishes an explicit inheritance relationship between classes B and A, where B is both a subclass and a subtype of A, and can be used as an A wherever a B is specified (via a reference, a pointer or the object itself).class A{ public: };class B : public A{ public: };void UseAnA(A const& some_A){ }void SomeFunc(){ }BOOK

Python

The following python code establishes an explicit inheritance relationship between classes {{var|B}} and {{var|A}}, where {{var|B}} is both a subclass and a subtype of {{var|A}}, and can be used as an {{var|A}} wherever a {{var|B}} is required.class A: class B(A): def use_an_a(some_a): def some_func(): The following example, {{var|type(a)}} is a "regular" type, and {{var|type(type(a))}} is a metatype. While as distributed all types have the same metatype ({{var|PyType_Type}}, which is also its own metatype), this is not a requirement. The type of classic classes, known as {{var|types.ClassType}}, can also be considered a distinct metatype.WEB, Guido van Rossum, Subtyping Built-in Types,weblink 2 October 2012,

Java

In Java, is-a relation between the type parameters of one class or interface and the type parameters of another are determined by the extends and implements clauses.Using the {{code|Collections}} classes, {{code|ArrayList}} implements {{code|List}}, and {{code|List}} extends {{code|Collection}}. So {{code|ArrayList}} is a subtype of {{code|List}}, which is a subtype of {{code|Collection}}. The subtyping relationship is preserved between the types automatically. When defining an interface, {{code|PayloadList}}, that associates an optional value of generic type P with each element, its declaration might look like:interface PayloadList extends List { }The following parameterizations of PayloadList are subtypes of {{code|List}}:PayloadListPayloadListPayloadList

Liskov substitution principle

Liskov substitution principle explains a property, "If for each object o1 of type S there is an object o2 of type T such that for all programs P defined in terms of T, the behavior of P is unchanged when o1 is substituted for o2 then S is a subtype of T,".BOOK, Liskov, Barbara, Data Abstraction and Hierarchy, May 1988, SIGPLAN Notices,weblinkweblink Jun 21, 2020, unfit, Following example shows a violation of LSP.Here is perhaps an example of violation of LSP:class Rectangle{ };From a programing point of view, the Square class may be implemented by inheriting from the Rectangle class.public class Square : Rectangle{ };void Square::SetWidth(double w){ }void Square::SetHeight(double h){ }However, this violates LSP even though the is-a relationship holds between Rectangle and SquareConsider the following example, where function g does not work if a Square is passed in, and so the open-closed principle might be considered to have been violated.void g(Rectangle& r){ }Conversely, if one considers that the type of a shape should only be a constraint on the relationship of its dimensions, then it is the assumption in g() that SetHeight will change height, and area, but not width that is invalid, not just for true squares, but even potentially for other rectangles that might be coded so as to preserve area or aspect ratio when height changes.WEB, The Liskov Substitution Principle,weblink Robert C. Martin, 1996, 2 October 2012, dead,weblink" title="web.archive.org/web/20150905081111weblink">weblink 5 September 2015,

See also

• Inheritance (object-oriented programming)
• Liskov substitution principle (in object-oriented programming)
• Subsumption
• Is-a
  • Hypernymy (and supertype)
  • Hyponymy (and subtype)
• Has-a
  • Holonymy
  • Meronymy

Notes

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References

• Ronald J. Brachman; "What IS-A is and isn't. An Analysis of Taxonomic Links in Semantic Networks". IEEE Computer, 16 (10); October 1983
• Jean-Luc Hainaut, Jean-Marc Hick, Vincent Englebert, Jean Henrard, Didier Roland: weblink" title="web.archive.org/web/20070211062250weblink">Understanding Implementations of IS-A Relations. ER 1996: 42-57