Polymorphism (computer science)

In computer science, polymorphism is the idea of allowing the same code to be used with different types, resulting in more general and abstract implementations.

The concept of polymorphism applies to functions as well as types:

A function that can evaluate to and be applied to values of different types is known as a polymorphic function.
A datatype that contains elements of an unspecified type is known as a polymorphic datatype.

There are two fundamentally different kinds of polymorphism:

If the range of actual types that can be used is finite and the combinations must be specified individually prior to use, it is called ad-hoc polymorphism.
If all 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.

Programming using the latter kind is called generic programming.

Polymorphism gained most of its momentum when object-oriented programming became popular.

Table of contents

1 Parametric polymorphism

1.1 Subtyping polymorphism

2 Ad-hoc polymorphism

2.2 Overloading
2.3 Coercion

3 Example

3.4 Overloading
3.5 Coercion
3.6 Parametric polymorphism

Parametric polymorphism

Using parametric polymorphism, a function can be written generically so that it can deal equally well with objects of various types. For example, a function append that joins two lists can be constructed so that it does not depend on one particular type of list: it can append lists of integers, lists of real numbers, lists of strings, and so on. Let a denote the type of elements in the lists. Then append can be typed [a] × [a] → [a], where [a] denotes a list of elements of type a. We say that append is parameterized by a. (Note that since there is only one type parameter, the function cannot be applied to just any pair of lists: they must consist of the same type of elements.)

Parametric polymorphism was the first type of polymorphism developed, first identified by Christopher Strachey in 1967. It was also the first type of polymorphism to appear in an actual programming language, ML in 1976. It exists today in Standard ML, OCaml, Haskell, and others. Some argue that templates should be considered an example of parametric polymorphism, though instead of actually reusing generic code they rely on macros to generate specific code (which can result in code bloat).

Parametric polymorphism is a way to make a language more expressible, while still maintaining full static type-safety. It is thus irrelevant in dynamically typed languages, since they by definition lack static type-safety. However, any dynamically typed function f that takes n arguments can be given a static typed using parametric polymorphism: f : p₁ × ... × p_n → r, where p₁ ... p_n and r are type parameters. Of course, this type is completely insubstantial and thus essentially useless.

Subtyping polymorphism

Some languages employ the idea of a subtype to restrict the range types that can be used in a particular case of parametric polymorphism. Hence, subtyping polymorphism allows a function to be written so that it takes a certain type of object T, but will also work correctly if passed an object that belongs to a type S that is a subtype of T. This is sometimes written S <: T. Conversely, we say that T is a supertype of S—written T :> S.

For example, given the types Number, Integer, and Fractional, such that Number :> Integer and Number :> Fractional, a function could be written that takes any kind of Number, and works equally well whether an Integer or Fractional is passed. (This particular kind of type hierarchy is known—especially in the context of Scheme—as a numerical tower, and usually contains a lot more types.)

In object-oriented programming this is implemented with subclassing (inheritance), and is also known as late binding. See also:

Ad-hoc polymorphism

Ad-hoc polymorphism usually refers to simple overloading (see function overloading), but sometimes automatic type conversion, known as coercion, is also considered to be a kind of ad-hoc polymorphism (see the example section below). Common to these two types is the fact that the programmer has to specify exactly what types are to be usable with the polymorphic function.

The name refers to the manner in which this kind of polymorphism is typically introduced: “Oh, hey, let’s make the + operator work on strings, too!” Some argue that ad-hoc polymorphism is not polymorphism in a meaningful computer science sense at all—that it is just syntactic sugar for calling append_integer, append_string, etc., manually. One way to see it is that

to the user, there appears to be only one function, but one that takes different types of input and is thus type polymorphic; on the other hand,
to the author, there are several functions that need to be written—one for each type of input—so there’s essentially no polymorphism.

Overloading

Overloading allows multiple functions taking different types to be defined with the same name; the compiler or interpreter automatically calls the right one. This way, functions appending lists of integers, lists of strings, lists of real numbers, and so on could be written, and all be called append—and the right append function would be called based on the type of lists being appended. This differs from parametric polymorphism, in which the function would need to be written generically, to work with any kind of list. Using overloading, it is possible to have a function perform two completely different things based on the type of input passed to it; this is not possible with parametric polymorphism.

This type of polymorphism is common in object-oriented programming languages, many of which allow operators to be overloaded in a manner similar to functions (see operator overloading). It is also used extensively in the purely functional programming language Haskell. Many languages lacking ad-hoc polymorphism suffer from long-winded names such as print_int, print_string, etc. (see Objective Caml).

Coercion

Due to a concept known as coercion, a function can become polymorphic without being initially designed for it. Let f be a function that takes an argument of type T, and S be a type that can be automatically converted to T. Then f can be said to be polymorphic with respect to S and T.

Some languages (e.g., C, Java), provide a fixed set of conversion rules, while others (e.g., C Plus Plus) allow new conversion rules to be defined by the programmer. While calling C “polymorphic” is perhaps stretching it, the facility for automatic conversion (i.e., casting operators) found in C++ adds a whole new class of polymorphism to the language.

Example

This example aims to illustrates the three different kinds of polymorphism described in this article. Though overloading an originally arithmetic operator to do a wide variety of things in this way may not be the most clear-cut example, it allows some subtle points to be made. In practice, the different types of polymorphism are not generally mixed up as much as they are here.

Imagine, if you will, an operator + that may be used in the following ways:

1 + 2 ⇒ 3
3.14 + 0.0015 ⇒ 3.1415
1 + 3.7 ⇒ 4.7
[1, 2, 3] + [4, 5, 6] ⇒ [1, 2, 3, 4, 5, 6]
[true, false] + [false, true] ⇒ [true, false, false, true]
"foo" + "bar" ⇒ "foobar"

Overloading

To handle these six function calls, four different pieces of code are needed—or three, if strings are considered to be lists of characters:

In the first case, integer addition is invoked.
In the second and third cases, floating-point addition is invoked.
In the fourth and fifth cases, list concatenation is invoked.
In last case, string concatenation is invoked, unless this too is handled as list concatenation.

Thus, the name + actually refers to three or four completely different functions. This is an example of overloading.

Coercion

As we’ve seen, there’s one function for adding two integers and one for adding two floating-point numbers in this hypothetical programming environment, but note that there is no function for adding an integer to a floating-point number. The reason why we can still do this is that when the compiler/interpreter finds a function call f(a1, a2, ...) that no existing function named f can handle, it starts to look for ways to convert the arguments into different types in order to make the call conform to the signature of one of the functions named f. This is called coercion. Both coercion and overloading are kinds of ad-hoc polymorphism.

In our case, since any integer can be converted into a floating-point number without loss of precision, 1 is converted into 1.0 and floating-point addition is invoked. There was really only one reasonable outcome in this case, because a floating-point number cannot generally be converted into an integer, so integer addition could not have been used; but significantly more complex, subtle, and ambiguous situations can occur in, e.g., C++.

Parametric polymorphism

Finally, the reason why we can concatenate both lists of integers, lists of booleans, and lists of characters, is that the function for list concatenation was written without any regard to the type of elements stored in the lists. This is an example of parametric polymorphism. If you wanted to, you could make up a thousand different new types of lists, and the generic list concatenation function would happily and without requiring any augmentation accept instances of them all.

It can be argued, however, that this polymorphism is not really a property of the function per se; that if the function is polymorphic, it is due to the fact that the list datatype is polymorphic. This is true—to an extent, at least—but it is important to note that the function could just as well have been defined to take as a second argument an element to append to the list, instead of another list to concatenate to the first. If this were the case, the function would indisputably be parametrically polymorphic, because it could then not know anything about its second argument, except that the type of the element should match the type of the elements of the list.

Polymorphism, in computer underground terms, also refers to polymorphic code, computer code that mutates for each new time it is executed. This is sometimes used by computer viruses, computer worms and shellcodes to hide the presence of their decryption engines.