The question of compatibility and equivalence becomes a complicated and controversial topic and relates to the problem of substitutability; in other words: given type A and type B, are they equal types or compatible? Can one use the value with type B in the place of the value with type A? If type A is compatible with type B, A is a subtype of B (but not always vice versa) - according to the Liskov substitution principle. Type conversion may ...

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Datatype, Datatype - Basis, Datatype - Type checking, Datatype - Static and dynamic typing, Datatype - Static and dynamic type checking in practice, Datatype - Strong and weak typing, Datatype - Polymorphism and types, Datatype - Explicit or implicit declaration and inference, Datatype - Collections of types, Datatype - Specialized types, Datatype - Compatibility equivalence and substitutability

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Datatype, Datatype - Basis, Datatype - Type checking, Datatype - Static and dynamic typing, Datatype - Static and dynamic type checking in practice, Datatype - Strong and weak typing, Datatype - Polymorphism and types, Datatype - Explicit or implicit declaration and inference, Datatype - Collections of types, Datatype - Specialized types, Datatype - Compatibility equivalence and substitutability, Datatype - Nominative vs structural typing

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Some languages employ the idea of subtypes to restrict the range of types that can be used in a particular case of parametric polymorphism. In these languages, subtyping polymorphism (sometimes referred to as dynamic polymorphism or dynamic typing) 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 < ...

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Polymorphism computer science, Polymorphism computer science - Parametric polymorphism, Polymorphism computer science - Predicative and impredicative polymorphism, Polymorphism computer science - Subtyping polymorphism, Polymorphism computer science - Ad-hoc polymorphism, Polymorphism computer science - Overloading, Polymorphism computer science - Coercion, Polymorphism computer science - Example, Polymorphism computer science - Overloading, Polymorphism computer science - Coercion, Polymorphism computer science - Parametric polymorphism

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This article is about type polymorphism. For another kind of polymorphism in computer science, related only in name to type polymorphism, see polymorphic code. In computer science, polymorphism means allowing a single definition to be used with different types of data (specifically, different classes of objects). For instance, a polymorphic function definition can replace several type-specific ones, and a single polymorphic operator can act in expressions of various ...

Including:

Polymorphism computer science - Parametric polymorphism
Polymorphism computer science - Predicative and impredicative polymorphism
Polymorphism computer science - Subtyping polymorphism Polymorphism computer science - Ad-hoc polymorphism
Polymorphism computer science - Overloading Polymorphism computer science - Coercion
Polymorphism computer science - Example
Polymorphism computer science - Overloading Polymorphism computer science - Coercion Polymorphism computer science - Parametric polymorphism

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In computer science, a datatype (often simply a type) is a name or label for a set of values and some operations which one can perform on that set of values. Programming languages implicitly or explicitly support one or more datatypes; these types may act as a statically or dynamically checked constraint, ensuring valid programs for a given language. Datatype - Basis. Assigning datatypes ("typing") has the basic purpose of giving some semantic meaning to otherwise meaningless collections of bits. Typ ...

Including:

Datatype - Basis Datatype - Type checking
Datatype - Static and dynamic typing Datatype - Static and dynamic type checking in practice
Datatype - Strong and weak typing Datatype - Polymorphism and types Datatype - Explicit or implicit declaration and inference Datatype - Collections of types Datatype - Specialized types Datatype - Compatibility equivalence and substitutability

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The process of verifying and enforcing the constraints of types - type checking - may occur either at compile-time (a static check) or run-time (a dynamic check). Static type-checking becomes a primary task of the semantic analysis carried out by a compiler. If a language enforces type rules strongly (that is, generally allowing only those automatic type conversions which do not lose information), one can refer to the process as strongly typed, if not, as weakly typed. Da ...

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Datatype, Datatype - Basis, Datatype - Type checking, Datatype - Static and dynamic typing, Datatype - Static and dynamic type checking in practice, Datatype - Strong and weak typing, Datatype - Polymorphism and types, Datatype - Explicit or implicit declaration and inference, Datatype - Collections of types, Datatype - Specialized types, Datatype - Compatibility equivalence and substitutability

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A piece of software is provided access to computer resources (such as memory, CPU, storage, etc.) by its underlying computer system; the availability of these resources to other software can have major ramifications -- sometimes disastrous ones -- for its functionality and stability. A key principle of component-based design is to prohibit access to all resources by default, allowing access only through ...

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Interface computer science, Interface computer science - Interfaces in practice, Interface computer science - Uses of interfaces

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The process of verifying and enforcing the constraints of types - type checking - may occur either at compile-time (a static check) or run-time (a dynamic check). Static type-checking becomes a primary task of the semantic analysis carried out by a compiler. If a language enforces type rules strongly (that is, generally allowing only those automatic type conversions which do not lose information), one can refer to the process as strongly typed, if not, as weakly typed. Da ...

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Datatype, Datatype - Basis, Datatype - Type checking, Datatype - Static and dynamic typing, Datatype - Static and dynamic type checking in practice, Datatype - Strong and weak typing, Datatype - Polymorphism and types, Datatype - Explicit or implicit declaration and inference, Datatype - Collections of types, Datatype - Specialized types, Datatype - Compatibility equivalence and substitutability, Datatype - Nominative vs structural typing

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Using parametric polymorphism, a function or datatype can be written generically so that it can deal equally well with any objects without depending on their type. For example, a function append that joins two lists can be constructed so that it does not care about the type of elements: it can append lists of integers, lists of real numbers, lists of strings, and so on. Let the type variable a denote the type of elements in the lists. Then append can be typed [a] × [a]&# ...

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Polymorphism computer science, Polymorphism computer science - Parametric polymorphism, Polymorphism computer science - Predicative and impredicative polymorphism, Polymorphism computer science - Subtyping polymorphism, Polymorphism computer science - Ad-hoc polymorphism, Polymorphism computer science - Overloading, Polymorphism computer science - Coercion, Polymorphism computer science - Example, Polymorphism computer science - Overloading, Polymorphism computer science - Coercion, Polymorphism computer science - Parametric polymorphism

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Type theorists make an important distinction between nominal subtyping, in which only types declared in a certain way may be subtypes of each other, and structural subtyping, in which the structure of two types determines whether or not one is a subtype of the other. The class-based object-oriented subtyping described above is nominal; a structural subtyping rule for an object-oriented language might say that if objects of type A can handle all of the messages that objects of type B can handle (that is, if they de ...

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Subtype, Subtype - Subtyping schemes

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Python makes extensive use of polymorphism in its basic types. For example, strings (immutable sequences of characters) and lists (mutable sequences of elements of any type) have the same indexing interface and the same lookup interface (which call the appropriate underlying methods). myString = 'Hello world' myList = [0, 'one', 1, 'two', 3, 'five', 8] print myString[:4] # prints Hell print myList[:4] # prints [0, 'one', 1, 'two'] print 'e' ...

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Polymorphism in object-oriented programming, Polymorphism in object-oriented programming - Advantages of polymorphism, Polymorphism in object-oriented programming - Examples, Polymorphism in object-oriented programming - Other concepts

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There are two primary schemes for determing whether two types are equivalent and/or subtypes; nominative (by name) and structural (by structure). As the names indicate, nominative type systems operate based on explicit annotations in the code; types are not "recognized" unless explicitly declared, and subtype relationships also must be explicitly declared. Structural type systems, on the other hand, perform type judgements based on the structure of the two types under consideration. Few languages are strictly nomi ...

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Datatype, Datatype - Basis, Datatype - Type checking, Datatype - Static and dynamic typing, Datatype - Static and dynamic type checking in practice, Datatype - Strong and weak typing, Datatype - Polymorphism and types, Datatype - Explicit or implicit declaration and inference, Datatype - Collections of types, Datatype - Specialized types, Datatype - Compatibility equivalence and substitutability, Datatype - Nominative vs structural typing

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Polymorphism allows client programs to be written based only on the abstract interfaces of the objects which will be manipulated (interface inheritance). This means that future extension in the form of new types of objects is easy, if the new objects conform to the original interface. In particular, with object-oriented polymorphism, the original client program does not even need to be recompiled (only relinked) in order to make use of new types exhibiting new (but interface-conformant) behavior. (In C++, for instance, this is possible becau ...

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Polymorphism in object-oriented programming, Polymorphism in object-oriented programming - Advantages of polymorphism, Polymorphism in object-oriented programming - Examples, Polymorphism in object-oriented programming - Other concepts

Read more here: » Polymorphism in object-oriented programming: Encyclopedia II - Polymorphism in object-oriented programming - Advantages of polymorphism

Many static type systems, such as C's and Java's, require type declarations: the programmer must explicitly associate each variable with a particular type. Others, such as Haskell's, perform type inference: the compiler draws conclusions about the types of variables based on how programmers use those variables. For example, given a function f(x,y) which adds x and y together, the compiler can infer that x and y must be numbers -- since addition is only defined for numbers. Therefore, any call to f elsewhere in the program that specifies a non-nu ...

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Datatype, Datatype - Basis, Datatype - Type checking, Datatype - Static and dynamic typing, Datatype - Static and dynamic type checking in practice, Datatype - Strong and weak typing, Datatype - Polymorphism and types, Datatype - Explicit or implicit declaration and inference, Datatype - Collections of types, Datatype - Specialized types, Datatype - Compatibility equivalence and substitutability, Datatype - Nominative vs structural typing

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The concept of interface is the cornerstone of modular programming, a forerunner and a standard ingredient of object-oriented programming. In object-oriented programming, an object's interface consists of a set of methods that the object must respond to. Note that the object does not make its instance variables a part of its interface - these are typically accessed by means of accessor methods. Some object-oriented programming languages mandate that the interface to the object be specified to the compiler separately from the implement ...

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Interface computer science, Interface computer science - Interfaces in practice, Interface computer science - Uses of interfaces

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Assigning datatypes ("typing") has the basic purpose of giving some semantic meaning to otherwise meaningless collections of bits. Types usually have associations either with values in memory or with objects such as variables. Because any value simply consists of a set of bits in a computer, hardware makes no distinction even between memory addresses, instruction code, characters, integers and floating-point numbers. Types inform programs and programmers how ...

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Datatype, Datatype - Basis, Datatype - Type checking, Datatype - Static and dynamic typing, Datatype - Static and dynamic type checking in practice, Datatype - Strong and weak typing, Datatype - Polymorphism and types, Datatype - Explicit or implicit declaration and inference, Datatype - Collections of types, Datatype - Specialized types, Datatype - Compatibility equivalence and substitutability, Datatype - Nominative vs structural typing

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Many static type systems, such as C's and Java's, require type declarations: the programmer must explicitly associate each variable with a particular type. Others, such as Haskell's, perform type inference: the compiler draws conclusions about the types of variables based on how programmers use those variables. For example, given a function f(x,y) which adds x and y together, the compiler can infer that x and y must be numbers -- since addition is only defined for numbers. Therefore, any call to f elsewhere in the program that specifies a non-nu ...

See also:

Datatype, Datatype - Basis, Datatype - Type checking, Datatype - Static and dynamic typing, Datatype - Static and dynamic type checking in practice, Datatype - Strong and weak typing, Datatype - Polymorphism and types, Datatype - Explicit or implicit declaration and inference, Datatype - Collections of types, Datatype - Specialized types, Datatype - Compatibility equivalence and substitutability

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Main article: strongly-typed programming language For a fuller discussion of the different meanings of the phrase strongly typed, see strongly-typed programming language. One definition of strongly typed involves not allowing an operation to succeed on arguments which have the wrong type. A C cast gone wrong exemplifies the absence of strong typing; if a programmer casts a value in C, not only must the compiler allow the code, but the runtime should allow it as well. This allows compact and fas ...

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Datatype, Datatype - Basis, Datatype - Type checking, Datatype - Static and dynamic typing, Datatype - Static and dynamic type checking in practice, Datatype - Strong and weak typing, Datatype - Polymorphism and types, Datatype - Explicit or implicit declaration and inference, Datatype - Collections of types, Datatype - Specialized types, Datatype - Compatibility equivalence and substitutability

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Ad-hoc polymorphism usually refers to simple 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 ...

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Polymorphism computer science, Polymorphism computer science - Parametric polymorphism, Polymorphism computer science - Predicative and impredicative polymorphism, Polymorphism computer science - Subtyping polymorphism, Polymorphism computer science - Ad-hoc polymorphism, Polymorphism computer science - Overloading, Polymorphism computer science - Coercion, Polymorphism computer science - Example, Polymorphism computer science - Overloading, Polymorphism computer science - Coercion, Polymorphism computer science - Parametric polymorphism

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This example aims to illustrate 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 → 3.141 ...

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Polymorphism computer science, Polymorphism computer science - Parametric polymorphism, Polymorphism computer science - Predicative and impredicative polymorphism, Polymorphism computer science - Subtyping polymorphism, Polymorphism computer science - Ad-hoc polymorphism, Polymorphism computer science - Overloading, Polymorphism computer science - Coercion, Polymorphism computer science - Example, Polymorphism computer science - Overloading, Polymorphism computer science - Coercion, Polymorphism computer science - Parametric polymorphism

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