The notion directly extends to the product of an arbitrary finite number of types (a n-ary product type), and in this case, it characterizes the expressions which behave as tuples of expressions of the corresponding types. A degenerated form of product type is the unit type.
In call-by-value programming languages, a product type can be interpreted as a set of pairs whose first component is a value in the first type and whose second component is a value in the second type. In short, it is a cartesian product and it corresponds to a product in the category of types.
Most functional programming languages have a primitive notion of product type. For instance, the product of type1, ..., typen is written type1
* typen in ML and
) in Haskell. In both these languages, tuples are written
) and the components of a tuple are extracted by pattern-matching.
In many languages, product types take the form of a record type for which the components of a tuple can be accessed by label. In languages that have algebraic data types, as in most functional programming languages, algebraic data types with one constructor are isomorphic to a product type.
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