Polymorphism (computer science)

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In programming languages and type theory, polymorphism (from Greek πολύς, polys, "many, much" and μορφή, morphē, "form, shape") is the provision of a single interface to entities of different types.[1] A polymorphic type is a type whose operations can also be applied to values of some other type, or types.[2] There are several fundamentally different kinds of polymorphism:

  • If a function denotes different and potentially heterogeneous implementations depending on a limited range of individually specified types and combinations, it is called ad hoc polymorphism. Ad hoc polymorphism is supported in many languages using function overloading.
  • If the code is written without mention of any specific type and thus can be used transparently with any number of new types, it is called parametric polymorphism. In the object-oriented programming community, this is often known as generics or generic programming. In the functional programming community, this is often simply called polymorphism.
  • Subtyping (or inclusion polymorphism) is a concept wherein a name may denote instances of many different classes as long as they are related by some common superclass.[3] In object-oriented programming, this is often referred to simply as polymorphism.

The interaction between parametric polymorphism and subtyping leads to the concepts of variance and bounded quantification.

History[edit]

Ad hoc polymorphism and parametric polymorphism were originally described in Fundamental Concepts in Programming Languages, a set of lecture notes written in 1967 by British computer scientist Christopher Strachey.[4] In a 1985 paper, Peter Wegner and Luca Cardelli introduced the term inclusion polymorphism to model subtypes and inheritance.[2] However, implementations of subtyping and inheritance predate the term 'inclusion polymorphism', having appeared with Simula in 1967.

Types of polymorphism[edit]

Ad hoc polymorphism[edit]

Main article: Ad hoc polymorphism

Chris Strachey[4] chose the term ad hoc polymorphism to refer to polymorphic functions which can be applied to arguments of different types, but which behave differently depending on the type of the argument to which they are applied (also known as function overloading or operator overloading). The term "ad hoc" in this context is not intended to be pejorative; it refers simply to the fact that this type of polymorphism is not a fundamental feature of the type system. In the example below, the Add functions seem to work generically over various types when looking at the invocations, but are considered to be two entirely distinct functions by the compiler for all intents and purposes:

program Adhoc;
 
function Add( x, y : Integer ) : Integer;
begin
    Add := x + y
end;
 
function Add( s, t : String ) : String;
begin
    Add := Concat( s, t )
end;
 
begin
    Writeln(Add(1, 2));
    Writeln(Add('Hello, ', 'World!'));
end.

In dynamically typed languages the situation can be more complex as the correct function that needs to be invoked might only be determinable at run time.

Implicit type conversion has also been defined as a form of polymorphism, referred to as "coercion polymorphism".[5]

Parametric polymorphism[edit]

Parametric polymorphism allows a function or a data type to be written generically, so that it can handle values identically without depending on their type.[6] Parametric polymorphism is a way to make a language more expressive, while still maintaining full static type-safety.

The concept of parametric polymorphism applies to both data types and functions. A function that can evaluate to or be applied to values of different types is known as a polymorphic function. A data type that can appear to be of a generalized type (e.g., a list with elements of arbitrary type) is designated polymorphic data type like the generalized type from which such specializations are made.

Parametric polymorphism is ubiquitous in functional programming, where it is often simply referred to as "polymorphism". The following example shows a parametrized list data type and two parametrically polymorphic functions on them:

data List a = Nil | Cons a (List a)
 
length :: List a -> Integer
length Nil         = 0
length (Cons x xs) = 1 + length xs
 
map :: (a -> b) -> List a -> List b
map f Nil         = Nil
map f (Cons x xs) = Cons (f x) (map f xs)

Parametric polymorphism is also available in several object-oriented languages, where it often goes under the name "generics" (for example, Java) or "templates" (C++ and D):

class List<T> {
    class Node<T> {
        T elem;
        Node<T> next;
    }
    Node<T> head;
    int length() { ... }
}
 
List<B> map(Func<A,B> f, List<A> xs) {
    ...
}

John C. Reynolds (and later Jean-Yves Girard) formally developed this notion of polymorphism as an extension to lambda calculus (called the polymorphic lambda calculus, or System F). Any parametrically polymorphic function is necessarily restricted in what it can do, working on the shape of the data instead of its value, leading to the concept of parametricity.

Subtyping[edit]

Main article: Subtyping

Some languages employ the idea of subtyping to restrict the range of types that can be used in a particular case of polymorphism. In these languages, subtype polymorphism (sometimes referred to as inclusion polymorphism or dynamic polymorphism[citation needed]) allows a function to be written to take an object of a certain type T, but also work correctly if passed an object that belongs to a type S that is a subtype of T (according to the Liskov substitution principle). This type relation is sometimes written S <: T. Conversely, T is said to be a supertype of S—written T :> S.

In the following example we make cats and dogs subtypes of animals. The procedure letsHear() accepts an animal, but will also work correctly if a subtype is passed to it:

abstract class Animal {
    abstract String talk();
}
 
class Cat extends Animal {
    String talk() {
        return "Meow!";
    }
}
 
class Dog extends Animal {
    String talk() {
        return "Woof!";
    }
}
 
void letsHear(Animal a) {
    println(a.talk());
}
 
void main() {
    letsHear(new Cat());
    letsHear(new Dog());
}

In another example, if Number, Rational, and Integer are types such that Number :> Rational and Number :> Integer, a function written to take a Number will work equally well when passed an Integer or Rational as when passed a Number. The actual type of the object can be hidden from clients into a black box, and accessed via object identity. In fact, if the Number type is abstract, it may not even be possible to get your hands on an object whose most-derived type is Number (see abstract data type, abstract class). This particular kind of type hierarchy is known—especially in the context of the Scheme programming language—as a numerical tower, and usually contains many more types.

Object-oriented programming languages offer subtyping polymorphism using subclassing (also known as inheritance). In typical implementations, each class contains what is called a virtual table—a table of functions that implement the polymorphic part of the class interface—and each object contains a pointer to the "vtable" of its class, which is then consulted whenever a polymorphic method is called. This mechanism is an example of:

  • late binding, because virtual function calls are not bound until the time of invocation, and
  • single dispatch (i.e., single-argument polymorphism), because virtual function calls are bound simply by looking through the vtable provided by the first argument (the this object), so the runtime types of the other arguments are completely irrelevant.

The same goes for most other popular object systems. Some, however, such as Common Lisp Object System, provide multiple dispatch, under which method calls are polymorphic in all arguments.

Polytypism[edit]

A related concept is polytypism or data type genericity. A polytypic function is more general than polymorphic, and in such a function, "though one can provide fixed ad hoc cases for specific data types, an ad hoc combinator is absent".[7]

See also[edit]

References[edit]

  1. ^ Bjarne Stroustrup (February 19, 2007). "Bjarne Stroustrup's C++ Glossary". polymorphism - providing a single interface to entities of different types. 
  2. ^ a b Cardelli, Luca; Wegner, Peter (December 1985). "On understanding types, data abstraction, and polymorphism". ACM Computing Surveys (New York, NY, USA: ACM) 17 (4): 471–523. doi:10.1145/6041.6042. ISSN 0360-0300.  edit: "Polymorphic types are types whose operations are applicable to values of more than one type."
  3. ^ Booch, et all 2007 Object-Oriented Analysis and Design with Applications. Addison-Wesley.
  4. ^ a b C. Strachey - Fundamental Concepts in Programming Languages http://www.itu.dk/courses/BPRD/E2009/fundamental-1967.pdf
  5. ^ Allen B. Tucker (28 June 2004). Computer Science Handbook, Second Edition. Taylor & Francis. pp. 91–. ISBN 978-1-58488-360-9. 
  6. ^ Pierce, B. C. 2002 Types and Programming Languages. MIT Press.
  7. ^ Ralf Lammel and Joost Visser, "Typed Combinators for Generic Traversal", in Practical Aspects of Declarative Languages: 4th International Symposium (2002), p. 153.

External links[edit]