Nominative type system
Encyclopedia
In computer science
, a nominal or nominative type system (or name-based type system) is a major class of type system
, in which compatibility and equivalence of data type
s is determined by explicit declarations and/or the name of the types. Nominative systems are used to determine if types are equivalent, as well as if a type is a subtype of another. It contrasts with structural systems
, where comparisons are based on the structure of the types in question and do not require explicit declarations.
their declarations name the same type. For example, in C
, two
However, C also allows a
and do not differentiate the type from its alias for the purpose of type checking. This feature, present in many languages, can result in a loss of type safety when (for example) the same primitive integer type is used in two semantically distinct ways. Haskell
provides the C-style syntactic alias, as well as a declaration that does introduce a new, distinct type, isomorphic
to an existing type.
allows non-compatible subtypes to be declared). However, subtypes which are structurally compatible "by accident", but not declared as subtypes, are not considered to be subtypes.
C
, C++
, C# and Java
all primarily use both nominal typing and nominal subtyping.
Some nominally-subtyped languages, such as Java and C#, allow classes to be declared final (or sealed in C# terminology), indicating that no further subtyping is permitted.
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
, a nominal or nominative type system (or name-based type system) is a major class of type system
Type system
A type system associates a type with each computed value. By examining the flow of these values, a type system attempts to ensure or prove that no type errors can occur...
, in which compatibility and equivalence of data type
Data type
In computer programming, a data type is a classification identifying one of various types of data, such as floating-point, integer, or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of...
s is determined by explicit declarations and/or the name of the types. Nominative systems are used to determine if types are equivalent, as well as if a type is a subtype of another. It contrasts with structural systems
Structural type system
A structural type system is a major class of type system, in which type compatibility and equivalence are determined by the type's structure, and not by other characteristics such as its name or place of declaration. Structural systems are used to determine if types are equivalent and whether a...
, where comparisons are based on the structure of the types in question and do not require explicit declarations.
Nominal typing
Nominal typing means that two variables are type-compatible if and only ifIf and only if
In logic and related fields such as mathematics and philosophy, if and only if is a biconditional logical connective between statements....
their declarations name the same type. For example, in C
C (programming language)
C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....
, two
struct types with different names are never considered compatible, even if they have identical field declarations.However, C also allows a
typedefTypedeftypedef is a keyword in the C and C++ programming languages. The purpose of typedef is to assign alternative names to existing types, most often those whose standard declaration is cumbersome, potentially confusing, or likely to vary from one implementation to another.Under C convention , types...
declaration, which introduces an alias for an existing type. These are merely syntacticalSyntax
In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....
and do not differentiate the type from its alias for the purpose of type checking. This feature, present in many languages, can result in a loss of type safety when (for example) the same primitive integer type is used in two semantically distinct ways. Haskell
Haskell (programming language)
Haskell is a standardized, general-purpose purely functional programming language, with non-strict semantics and strong static typing. It is named after logician Haskell Curry. In Haskell, "a function is a first-class citizen" of the programming language. As a functional programming language, the...
provides the C-style syntactic alias, as well as a declaration that does introduce a new, distinct type, isomorphic
Isomorphism
In abstract algebra, an isomorphism is a mapping between objects that shows a relationship between two properties or operations. If there exists an isomorphism between two structures, the two structures are said to be isomorphic. In a certain sense, isomorphic structures are...
to an existing type.
Nominal subtyping
In a similar fashion, nominal subtyping means that one type is a subtype of another if and only if it is explicitly declared to be so in its definition. Nominally-typed languages typically enforce the requirement that declared subtypes be structurally compatible (though EiffelEiffel (programming language)
Eiffel is an ISO-standardized, object-oriented programming language designed by Bertrand Meyer and Eiffel Software. The design of the language is closely connected with the Eiffel programming method...
allows non-compatible subtypes to be declared). However, subtypes which are structurally compatible "by accident", but not declared as subtypes, are not considered to be subtypes.
C
C (programming language)
C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....
, C++
C++
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
, C# and Java
Java (programming language)
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
all primarily use both nominal typing and nominal subtyping.
Some nominally-subtyped languages, such as Java and C#, allow classes to be declared final (or sealed in C# terminology), indicating that no further subtyping is permitted.