Editing Polymorphism (computer science) (section)

==Forms==
===Ad hoc polymorphism===
{{Further|Ad hoc polymorphism}}
[[Christopher Strachey]] chose the term ''ad hoc polymorphism'' to refer to polymorphic functions that can be applied to arguments of different types, but that behave differently depending on the type of the argument to which they are applied (also known as [[function overloading]] or [[operator overloading]]).<ref name=Strachey00/> The term "[[ad hoc]]" in this context is not pejorative: instead, it means that this form of polymorphism is not a fundamental feature of the type system. In the [[Java (programming language)|Java]] example below, the <code>add</code> functions seem to work generically over two types ([[Integer (computer science)|integer]] and [[String (computer science)|string]]) when looking at the invocations, but are considered to be two entirely distinct functions by the [[compiler]] for all intents and purposes:

<syntaxhighlight lang="java">
class AdHocPolymorphic {
    public String add(int x, int y) {
        return "Sum: " + (x + y);
    }

    public String add(String name) {
        return "Added " + name;
    }
}

public class Adhoc {
    public static void main(String[] args) {
        AdHocPolymorphic poly = new AdHocPolymorphic();

        System.out.println(poly.add(1,2));   // prints "Sum: 3"
        System.out.println(poly.add("Jay")); // prints "Added Jay"
    }
}
</syntaxhighlight>

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".<ref name="Luca"/><ref name="Tucker2004">{{cite book |last1=Tucker |first1=Allen B.|date=2004 |title=Computer Science Handbook |edition=2nd |url=https://books.google.com/books?id=9IFMCsQJyscC&pg=SA91-PA5 |publisher=Taylor & Francis |pages=91– |isbn=978-1-58488-360-9}}</ref>

===Parametric polymorphism===
{{Further|Parametric polymorphism}}
''Parametric polymorphism'' allows a function or a data type to be written generically, so that it can handle values ''uniformly'' without depending on their type.<ref name="bjpierce">{{cite book |last1=Pierce |first1=B.C. |date=2002 |chapter=23.2 Varieties of Polymorphism |chapter-url=https://books.google.com/books?id=ti6zoAC9Ph8C&pg=PA340 |title=Types and Programming Languages |publisher=MIT Press |isbn= 9780262162098 |pages=340–1 |url=}}</ref> 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 type]]s and [[Function (computer programming)|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 (abstract data type)|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 next example in [[Haskell]] shows a parameterized list data type and two parametrically polymorphic functions on them:

<syntaxhighlight lang="Haskell">
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)
</syntaxhighlight>

Parametric polymorphism is also available in several object-oriented languages. For instance, [[Template (C++)|templates]] in [[C++]] and [[D (programming language)|D]], or under the name [[Generics in Java|generics]] in [[C Sharp (programming language)|C#]], [[Delphi (software)|Delphi]], Java, and [[Go (programming language)|Go]]:

<syntaxhighlight lang="CSharp">
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) {
    ...
}
</syntaxhighlight>

[[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===
{{Further|Subtyping}}
Some languages employ the idea of ''subtyping'' (also called ''subtype polymorphism'' or ''inclusion polymorphism'') to restrict the range of types that can be used in a particular case of polymorphism. In these languages, subtyping 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 {{nowrap|''S'' <: ''T''}}. Conversely, ''T'' is said to be a ''supertype'' of ''S'', written {{nowrap|''T'' :> ''S''}}. Subtype polymorphism is usually resolved dynamically (see below).

In the following Java example cats and dogs are made subtypes of pets. The procedure <code>letsHear()</code> accepts a pet, but will also work correctly if a subtype is passed to it:

<syntaxhighlight lang="java">
abstract class Pet {
    abstract String speak();
}

class Cat extends Pet {
    String speak() {
        return "Meow!";
    }
}

class Dog extends Pet {
    String speak() {
        return "Woof!";
    }
}

static void letsHear(final Pet pet) {
    println(pet.speak());
}

static void main(String[] args) {
    letsHear(new Cat());
    letsHear(new Dog());
}
</syntaxhighlight>

[[File:UML class pet.svg]]

In another example, if ''Number'', ''Rational'', and ''Integer'' are types such that {{nowrap|''Number'' :> ''Rational''}} and {{nowrap|''Number'' :> ''Integer''}} (''Rational'' and ''Integer'' as subtypes of a type ''Number'' that is a supertype of them), 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 (object-oriented programming)|identity]]. 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)|Scheme language]], as a ''[[numerical tower]]'', and usually contains many more types.

[[Object-oriented programming language]]s offer subtype polymorphism using ''[[Subclass (computer science)|subclass]]ing'' (also known as ''[[inheritance in object-oriented programming|inheritance]]''). In typical implementations, each class contains what is called a ''[[virtual table]]'' (shortly called ''vtable'') — 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;
* ''[[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 <code>this</code> 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.

The interaction between parametric polymorphism and subtyping leads to the concepts of [[covariance and contravariance (computer science)|variance]] and [[bounded quantification]].

===Row polymorphism===
{{Further|Row polymorphism}}
{{see also|Duck typing}}

Row polymorphism<ref>
{{cite conference
 |first=Mitchell
 |last=Wand
 |title=Type inference for record concatenation and multiple inheritance
 |book-title=Proceedings. Fourth Annual Symposium on Logic in Computer Science
 |pages=92–97
 |date=June 1989
 |doi=10.1109/LICS.1989.39162
}}
</ref> is a similar, but distinct concept from subtyping. It deals with [[Structural type system|structural types]]. It allows the usage of all values whose types have certain properties, without losing the remaining type information.

===Polytypism===
{{Further|Generic programming#Functional languages}}
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".<ref>{{cite book |first1=Ralf |last1=Lämmel |first2=Joost |last2=Visser |chapter=Typed Combinators for Generic Traversal |title=Practical Aspects of Declarative Languages: 4th International Symposium |publisher=Springer |date=2002 |isbn=354043092X |pages=137–154, See p. 153 |citeseerx=10.1.1.18.5727 |url=}}</ref>

===Rank polymorphism===
Rank polymorphism is one of the defining features of the [[array programming]] languages, like [[APL (programming language)|APL]]. The essence of the rank-polymorphic programming model is implicitly treating all operations as aggregate operations, usable on arrays with arbitrarily many dimensions,<ref>{{cite arXiv |last1=Slepak |first1=Justin |last2=Shivers |first2=Olin |last3=Manolios |first3=Panagiotis |date=2019 |title=The semantics of rank polymorphism |class=cs.PL |eprint=1907.00509}}</ref> which is to say that rank polymorphism allows functions to be defined to operate on arrays of any shape and size.