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Inprogramming languages andtype theory, aproduct oftypes is another, compounded, type in a structure. The "operands" of the product aretypes, and the structure of a product type is determined by the fixed order of the operands in the product. An instance of a product type retains the fixed order, but otherwise may contain all possible instances of itsprimitive data types. The expression of an instance of a product type will be atuple, and is called a "tuple type" of expression. A product of types is adirect product of two or more types.
If there are only two component types, it can be called a "pair type". For example, if two component types and are the set of all possible values of that type, the product type written contains elements that are pairs, where and are instances of and respectively. The pair type is a special case of thedependent pair type, where the type may depend on the instance picked from.
In many languages, product types take the form of arecord type, for which the components of a tuple can be accessed bylabel. In languages that havealgebraic data types, as in mostfunctional programming languages, algebraic data types with one constructor areisomorphic to a product type.
In theCurry–Howard correspondence, product types are associated withlogical conjunction (AND) inlogic.
The notion directly extends to the product of an arbitrary finite number of types (an-ary product type), and in this case, it characterizes the expressions that behave as tuples of expressions of the corresponding types. A degenerate form of product type is theunit type: it is theproduct of no types.
Incall-by-value programming languages, a product type can be interpreted as a set of pairs whose first component is avalue in the first type and whose second component is a value in the second type. In short, it is acartesian product and it corresponds to aproduct in the category of types.
Mostfunctional programming languages have aprimitive notion of product type. For instance, the product is writtenT1 * T2 * ... * Tn inML and(T1, T2, ..., Tn) inHaskell. In both these languages, tuples are written(v1, v2, ..., vn) and the components of a tuple are extracted bypattern-matching. Additionally, many functional programming languages provide more generalalgebraic data types, which extend both product andsum types. Product types are thedual of sum types.
std::tuple (expressedtuple<Ts...> usingvariadic templates),[1] and for the specific case of two elements definesstd::pair (expressedpair<T, U>).[2]std::tuple can be empty (tuple<>).System.Tuple. There are specific instantiations for 1 to 8 elements. For the specific case of two elements (a pair), it usesTuple<T1, T2>.[3] In order to create a tuple with nine or more components, the final parameterTRest ofTuple<T1, T2, T3, T4, T5, T6, T7, TRest> is supplied as another tuple.[4] For iterating over collections like dictionary types, the classSystem.Collections.Generic.KeyValuePair (expressedKeyValuePair<TKey, TValue>) is provided.[5]Data.Tuple.[7]javafx.util.Pair (expressedPair<K, V>).[8] For iterating over associative containers such asjava.util.Map, a pair in the map is expressed asMap.Entry<K, V>.[9]kotlin.Pair (expressedPair<A, B>)[10] andkotlin.Triple (expressedTriple<A, B, C>).[11]tuple collection which can be annotated astyping.Tuple (expressedTuple[T1, T2, ..., TN]).[12](T1, T2, ..., TN), and a pair is just(T, U).[13]scala.Tuple,[14] which supports between 2 and 22 objects asscala.Tuple2 (expressed asTuple2[A, B])[15] toscala.Tuple22 (expressed asTuple22[A, B, ..., V]).[16](T1, T2, ..., TN).[17]