Definition of A "type"
(Parnas, Shore & Weiss 1976) identified five definitions of a "type" that were used—sometimes implicitly—in the literature:
- Syntactic
- A type is a purely syntactic label associated with a variable when it is declared. Such definitions of "type" do not give any semantic meaning to types.
- Representation
- A type is defined in terms of its composition of more primitive types—often machine types.
- Representation and behaviour
- A type is defined as its representation and a set of operators manipulating these representations.
- Value space
- A type is a set of possible values which a variable can posses. Such definitions make it possible to speak about (disjoint) unions or Cartesian products of types.
- Value space and behaviour
- A type is a set of values which a variable can posses and a set of functions that one can apply to these values.
The definition in terms of a representation was often done in imperative languages such as ALGOL and Pascal, while the definition in terms of a value space and behaviour was used in higher-level languages such as Simula and CLU.
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